Towards Human-Centric, Traceable Negotiation Mechanisms for Sharing Autonomy in Multi-Agent Systems

Abstract

Digitalization and the use of autonomous systems challenge companies in new ways, particularly concerning the automatic distribution of tasks. Various approaches are being discussed in research, specifically in the field of multi-agent systems. However, there does not seem to be a universally applicable and generally accepted solution. Due to the multitude of different approaches and the associated challenges, traceability is of particular interest and requires further analysis. This paper reviews the traceability of different negotiation-based approaches for task allocation in multi-agent systems. We conducted a structured literature review and implemented a prototype using an existing workflow engine for the approach we identified as most suitable, applying a weighted scoring model. The evaluation of the implemented demonstrator, performed both with and without restarting negotiations, indicates that a traceable distribution of tasks with a negotiation mechanism is feasible.

1. Introduction

The timely adaptation to business trends and smooth transition to digitalization can be decisive survival factors for companies [1], as Amazon’s announcement revealed [2] with respect to the use of autonomous delivery drones in Europe starting in 2024. Despite the innovation of this solution, Amazon has not released specific details about the potential information infrastructure and process challenges it has faced.

Overall, an announcement like that from Amazon highlights the relevance of proactively adapting to business trends and integrating digital innovations. Such a novel solution can be one of these business trends Obikhod et al. [1] and ultimately become a survival factor. In view of this, companies should recognize that the adoption of trends and novel concepts—if not technologies—must be considered strategically. To this end, it is essential to analyze not only the potential but also the possible challenges concerning the associated information infrastructure and processes. Only through the interplay of these components can a system be created efficiently. Taking an information management perspective enables the conversion of performance potential into corporate success Heinrich et al. [3].

For instance, Amazon [4] relies on autonomous drones that act as loosely coupled process participants. They function independently of each other, reach their destinations autonomously, and automatically detect obstacles. These loosely coupled systems are coordinated by their own management system [4]. From a business process perspective, the automatic distribution of tasks, i.e., assignments between parcels and drones, is decisive for successful delivery. For a task to be completed, it must be assigned to an agent [5]. The assignment of tasks is a field of research in various areas [6]. One of these areas is the domain of multi-agent systems, which offers multiple solutions for the distribution of tasks [5,7].

Negotiation-based approaches, approaches based on game theory, optimization-based approaches (heuristic algorithms, metaheuristics, etc.), and machine learning have all been introduced to identify the optimal task distribution [7]. Depending on the technique used and the specific use case, an approximation can usually be found [7], although it may lack an all-encompassing approach. Consequently, Fiedler [8] and Zhu et al. [9]—potentially similarly to Amazon [2]—face the challenge of finding an optimal agent (e.g., a drone) for a specific task (e.g., delivery of a parcel). This challenge is then met using a negotiation-based approach.

It is unclear from the reported cases whether the negotiation outcomes are traceable and intelligible to humans. Nevertheless, even when the task distribution poses a methodological challenge due to the need for a proper approach, the traceability of the result is required. Otherwise, checking the result for issues such as correctness or efficiency remains a challenge. Among other things, it is essential to quickly identify the affected areas and their causes in the event of quality problems [10].

Therefore, this research deals with the following question: “How can networked participants in a multi-agent environment be assigned tasks at runtime in a traceable and intelligible form by humans when using a negotiation-based approach?”. To meet the objective of this work, we evaluate the traceability of existing negotiation-based protocols for task distribution in multi-agent systems and assess whether the most traceable approach can also be implemented in a workflow engine, given that multi-agent systems negotiate activity distribution at runtime. Therefore, we rely on message-based communication, as it is key for runtime support.

When analyzing negotiation-based approaches, key aspects of traceability, such as transparency, documentation, and comprehensibility, are considered. Particular attention is paid to practical embedding in a workflow engine. As proof of concept, the results of the proposed approach were implemented in a prototype to demonstrate its applicability. The results of this work ultimately answer the research question: “How can process participants be assigned tasks at runtime in a message-based and comprehensible manner using a negotiation-based approach?” We build on initial findings [11] on sharing autonomy in component-based architectures of cyber–physical systems.

This paper is structured as follows: Section 2 describes the applied methodology. In Section 3, we discuss relevant approaches regarding the distribution of tasks in multi-agent domains. Building on this, Section 4 examines negotiation-based approaches concerning the research question. Moreover, we present a prototypical implementation in Section 5. Finally, Section 6 concludes our contribution and provides an outlook on possible further research opportunities.

2. Methodology

This section details the applied methods and procedures we followed to meet the research objectives.

2.1. Analysis of Existing Findings

When starting with a structured literature search, we derived a basic vocabulary from the research question. Subsequently, we used Scopus and Google Scholar for the search. The search itself was iterative. We continuously adapted the search terms by reading various scientific articles. This process was also used to limit the search area and to search for relevant works.

The most important German and English keywords included the following: [DE]—multi-agent, term, tasks, negotiation, auction, allocation, traceable, comprehensible, and reproducibility; [EN]—agent, task, scheduling, negotiation, auction, allocation, traceable, documented, comprehensible, and reproducible. These keywords were combined into search strings using Boolean operations AND/OR. In addition, we conducted forward and backward searches.

To select relevant results, we first reviewed the abstracts and introductions of the articles identified during the search process. If these were promising, we analyzed the conclusions and main bodies of the identified works.

Overall, we identified a total of five scientific papers, which formed the conceptual basis for this work. Two of them are surveys, and three of them deal with specific negotiation processes. All negotiation processes were examined in relation to the research question.

2.2. Proof of Concept

The methodological approach incorporates theoretical findings with respect to networked agent architectures and is enriched with technological design and implementation. The prototypical implementation focuses on the practical application of the negotiation approach to demonstrate the applicability of the gained knowledge.

The prototype is based on the results of the key concepts and theories identified in the selected literature, as detailed in Section 5. The prototype implementation provides practical proof of the applied findings, utilizing an existing tool suite to substantiate the results concerning the research question.

3. Fundamentals and Related Work

In recent years, the field of automatic task allocation in the context of multi-agent systems has been investigated in the literature, and a variety of approaches have been discussed [7]. In this section, we introduce and explain fundamental terms; introduce the rationale for and concept of negotiation,; and, finally, review the negotiation-based approaches that have already been applied.

3.1. Fundamental Terms—Distribution/Allocation/Optimization

Section 3.1 documents the various terms in the relevant literature that deal with the distribution/allocation/optimization of tasks in the context of multi-agent systems.

The studied literature reveals that “task scheduling” [9], “task distribution” [5,8], and “task allocation” [7,12,13] are terms used in the context of task assignments. Singhal and Dahiya [5], Skaltsis et al. [7], and Quinton et al. [12] describe task distribution as a process in which a variety of tasks are specifically assigned to different agents. Therefore, “task distribution” and “task allocation” should be understood synonymously. In the work by Zhu et al. [9] and Fiedler [8], “task scheduling” and “task distribution” describe the optimization of a specific goal. Even if a goal is in the foreground, the core of the problem lies in how a series of tasks is distributed or assigned to agents to achieve an optimal result. For instance, in the work by Zhu et al. [9], the effectiveness of the negotiation-based approach is demonstrated using a rescue simulation with increasing damage; the optimization task, i.e., achieving minimal damage in the system, lies in the optimal allocation of rescue workers. In [8], optimal financing is viewed as an optimization task. The author examined the question of which investor is responsible for this task.

Despite the different terms and the variety of use cases, it should be noted that, concerning the research question, there is no significant differentiation to rule out any of the terms for further analysis to meet the research objectives.

3.2. Task Allocation in Multi-Agent Systems

The development of task allocation options has been addressed through negotiations [5], auctions, game theories, optimization, machine learning, and hybrid approaches [7]. In this subsection, we present the following identified approaches:

Negotiations: 

Singhal and Dahiya [5] describe a system in which agents communicate with each other and, thus, assign tasks via negotiations. Initiator agents who cannot fulfill tasks alone form coalitions with others. The best coalition that maximizes system benefits is selected. In this approach, negotiations are used as an instrument to achieve a goal [5].

Auctions: 

This type uses economic principles and allows agents to bid for tasks in auctions through a negotiation protocol [7]. At this point, it should be noted that the approach proposed by Skaltsis et al. [7] also implies negotiation in auction-based approaches. This approach is sometimes also referred to as a market-based approach [7,12]. The agents’ bids are based on their perception of the environment [7]. Agents bid based on a calculated benefit or costs and strive to achieve the highest benefit or the lowest cost for the given task(s) [7]. Auction-based approaches exhibit high solution efficiency, even if they do not always find the optimal solution [7].

Game theory: 

In game theory approaches, agents are viewed as players who select specific actions [7]. The distribution of tasks is their strategy [7]. The reward for their actions at the end of the game is called the “payoff” [7]. Once they have chosen the best strategy, players do not change it [7]. There are two types of games: cooperative games, in which agents cooperate, and non-cooperative games, in which agents act selfishly [7].

Optimization: 

Optimization is a mathematical field that finds solutions to problems by minimizing costs or maximizing profits [7]. For example, there is the deterministic “Hungarian” algorithm proposed by Kuhn [14], which makes use of graph theory. Metaheuristics include various methods, such as swarm intelligence, genetic algorithms, and simulated annealing [7].

Machine Learning: 

In the paper by Skaltsis et al. [7], the possibilities of machine learning are discussed. The authors cite reinforcement learning as a typical example, enabling agents to use their experience to act accordingly.

Hybrid approaches: 

In addition to the methods already mentioned for overcoming the identified challenges, there are other approaches to the challenge of task assignment [7]. These combine various of the techniques discussed above and are therefore classified as hybrid approaches [7].

Recent review studies on human-centered support of coordinated decision-making using Multi-Agent Systems (MASs), such as [15], reveal a significant focus on complex industrial environments, including fleet management, logistics, and manufacturing. Coordinated decision support aims to reduce mistrust and cognitive overload while optimizing interactions between humans and agents. Means to this end comprise transparency in decision making aligned with human values, iterative communication, behavioral alignment, context-aware assistance, multimodal interaction, and ethical design practices. Transparent agent behavior occurs when an agent makes its reasoning visible. In contrast, explainable behavior occurs when an agent offers reasons or narratives that humans can follow in decision making, thereby preserving user agency (autonomy). Both agent properties are effective for trust building.

A recent review across the domains of smart cities, urban management, logistics, and supply chains, as well as industrial automation [16], shows that collaborative decision making of agents negotiating task assignments and resource allocations includes the use of consensus algorithms, auction-based mechanisms, and contract networks. In industrial applications, contract net protocols are most widely implemented, followed by market-based approaches and distributed constraint optimization techniques. For conflict resolution, “systems implementing automated negotiation frameworks based on utility functions and preference revelation have shown success rates of 70–80 % in resolving inter-agent conflicts without human intervention, significantly enhancing system autonomy in domains ranging from industrial scheduling to resource management” [16], p. 52.

A particular research interest has been raised regarding the capabilities of large language model-based multi-agent systems. Aside from their particularities with respect to the application domain and architecture, various layers of communication have also been identified, including high-level communication referring to system architectures, goals, and protocols and system-internal communication with respect to strategies, paradigms, objects, and content. The effect on how agents interact also concerns negotiation and collective intelligence. A survey study [17] revealed that, for task allocation in terms of coordination of agents for collaborative decision making or distributed problem solving, among the benefits of a blackboard approach is the fact that it preserves a centralized information repository, which enables agents to collaboratively share, retrieve, and coordinate information through timely message passing. This approach to sharing information significantly enhances coordination effectiveness, facilitating a better understanding of current system states and decision-making processes. The survey also revealed the benefits of speech acts, as they enable agents to control interactions in dynamic contexts. The use of directive, commissive, or persuasive components as part of message exchanges adds intentional context to agent communication when negotiating task allocation.

The use of natural language constructs, such as speech acts, indicates a trend of influencing users’ attitudes or intentions in negotiations to reach a consensus. Strategy planning and expressive optimization become crucial aspects of effective negotiations. For instance, the Dual-Mind Negotiation Agent (DMNA) framework features the generation of rapid, experience-based responses and slow expression optimization [18]. Both training methods—using a Monte Carlo tree search and direct preference optimization—enable support for strategic planning and expression, as evidenced by empirical data on enhanced negotiation ability among agents. The negotiation datasets involve two roles with distinct goals and pre-defined negotiation strategies, aiming to reach consensus through conversation. Hence, the gap between planning-based and expression-based methods could be bridged through a language-centric approach to negotiation dialogue agents.

In agent-based, multi-issue bilateral automated negotiation, the influence of emotional deception and multi-attribute preferences on negotiation outcomes has also become a focus of interest [19]. An agent-based negotiation model can use reinforcement learning to endow agents with dynamically variable learning abilities. Emotions are quantified, and emotional deception is generated in automated negotiation. Agents learn continuously from opponents’ information during the negotiation process. The Q-learning algorithm applied by the authors iteratively updates the opponent’s attribute preferences and, thus, allows dynamic adjustments to achieve utility and efficiency maximization. The modeling of emotion and emotional deception assessment with the Weber–Fechner law enables the evaluation of the impact of fake messages by capturing the generation of emotion to balance an agent’s emotional deception. Empirical evidence in coal supply-chain procurement and sales negotiations shows that the proposed model can enhance joint utility. It then reduces the utility difference and negotiation rounds, thereby making it more effective at improving negotiation efficiency and fairness.

However, integrating decision making and communication effectively for human-centric multi-agent systems remains a challenge, particularly in creating agents that can seamlessly interact with humans in multi-agent settings, as highlighted by the limitations of current approaches [20]. Research has included self-play reinforcement learning and imitation learning, as well as experimentation with a regret minimization algorithm for the modeling of actions of human-like agents. Agents could communicate with humans using natural language when trained with a multitask scheme for latent language policies. On a strategic level, agents have been tested using a planning algorithm that regularizes self-play reinforcement learning and searches for a human imitation-learned policy. The overall target in human-centric interaction is the preservation of language semantics and the modeling of pragmatic communication.

A wide variety of terms are used for “negotiation” in the literature. Skaltsis et al. [7] state that auction-based approaches are occasionally also referred to as market-based approaches. Quinton et al. [12] use the term market-based synonymously with negotiation-based. Zhu et al. [9] and Fiedler [8] describe a negotiation-based approach in their works. Rinaldi et al. [13] deal with an auction-based approach. Lang and Fink [21] understand negotiation in two different ways—namely, in terms of negotiation-based and auction-based approaches. At a more abstract level, however, all approaches are concerned with deciding on the distribution of tasks through communication and the exchange of information.

In non-academic online databases, such as the dictionary of terms at https://www.oesterreich.gv.at/ (accessed on 12 February 2024), negotiation is defined as a decision-making process [22]. According to Wikipedia [23], negotiation is a dialogue on a topic in which the involved parties have different interests but the goal is to reach an agreement. These non-academic sources also understand negotiation as a process in which a decision is reached through communication and the exchange of information.

Although researchers use different terms or expressions for “negotiation”, they use them with the same meaning. However, they do not recommend an all-encompassing approach to the distribution of tasks, even when performing a comparative analysis Skaltsis et al. [7]. Machine learning approaches seem to be the most promising candidates for future work. Others, such as Rinaldi et al. [13], consider an auction-based approach, while Fiedler [8] and Zhu et al. [9] propose a proper negotiation-based approach. The survey by Quinton et al. [12] confirmed that market-based and negotiation-based approaches still have potential in the area of task allocation. For this reason, the following section examines the rationale for a negotiation- or auction-based approach to answer the addressed research question.

3.3. Selected Approaches

Although the diversity of allocation approaches was acknowledged in Section 3.2, there is no conclusion to recommend a specific approach, even though some authors have opted for a negotiation- or auction-based approach Zhu et al. [9], Fiedler [8], and Rinaldi et al. [13]. The following items provide the respective arguments to opt for one or the other approach:

Zhu et al. 

[9] consider game theory an effective tool, although this theory assumes that agents cannot communicate with each other. This can negatively impact the underlying use case (overall damage in the system). They also take a distributed system approach in which each agent has to make its own decision, making the system more flexible and robust. They also believe that the efficiency of the system can be maximized if the agents cooperate. They therefore opt for an automated negotiation system from the multi-agent area [9]. The description by Singhal and Dahiya [5] regarding the negotiation-based approach underlines this decision. It should be noted that in this context, the one task for which a coalition is to be formed represents the overall result of a system [5].

Fiedler 

[8] opted for a negotiation-based approach, which is more akin to a “reverse” auction. They derived their decision from the fact that the negotiation-based approach can achieve a Pareto-efficient state in which no one is better off. This seems, to the author, to be a suitable solution concerning the use case for optimal financing.

Rinaldi et al. 

[13] chose an auction-based approach based on the research result reported by Otte et al. [24], which indicates that multi-round auctions are very well-suited for constellations with communication losses. This is supported by the work of Skaltsis et al. [7], which demonstrates that auction-based approaches offer high solution efficiency.

In summary, both negotiation- and auction-based approaches have their specific advantages in different research contexts. While negotiation-based approaches, as preferred by Fiedler [8] and Zhu et al. [9], aim at Pareto efficiency and cooperation, respectively, the auction-based approach, as chosen by Rinaldi et al. [13], focuses on maximizing the outcome in complex and communication-intensive scenarios. The decision to opt for one of these approaches over the other depends heavily on the specific use case and the objectives of the respective research. The survey by Quinton et al. [12] confirms that negotiation for task allocation is still relevant. This work concludes that there is still a high level of research interest in market-based and auction-based approaches [12].

Therefore, the following section examines the negotiation mechanisms of Fiedler [8], Zhu et al. [9], and Rinaldi et al. [13] concerning the research question.

4. Analysis of Negotiation Mechanisms

The role of the multi-agent systems in the context of this work is detailed in Section 3. In this section, existing negotiation-based and auction-based approaches are analyzed with respect to their comprehensibility and ease of implementation (addressing the second part of the research question). We examine each approach from a use-case perspective, following the utility analysis approach for evaluation Zangemeister [25]. The analysis starts with the work of Rinaldi et al. [13], and continues with works by Fiedler [8] and Zhu et al. [9]. Finally, a summary is provided.

4.1. Assessment of Traceability

Before examining the respective mechanisms, the criteria for assessing traceability are defined. The method for systematic evaluation follows the utility analysis proposed by Zangemeister [25] and is based on the definition of comprehensibility in the context of multi-agent negotiations. The criteria for the assessment are specified in top-down manner and lead to three items for each criterion: In case of fulfillment, i.e., “yes”, a value of 1 is assigned; otherwise, in the case of non-fulfillment, i.e., “no”, a value of 0 is provided. In addition, each criterion is weighted. At the end, the sum is calculated based on a specific criterion, and a comparison is made according to the weighting for each criterion. The approach with the highest value is considered the “most comprehensible negotiation mechanism”.

4.1.1. Evaluation Criteria

Traceability plays a decisive role—not only in the rapid identification and root-cause analysis of quality problems [10] but also as a fundamental principle in scientific practice [26]. According to Balzert et al. [26], comprehensibility is defined as the fact that the content and the procedure for handling that content must be comprehensible. Based on this understanding, the following evaluation criteria are derived and formulated concerning comprehensibility:

Transparency at the model level (TM): 

This criterion assesses the transparency of the negotiation process within a workflow engine. It includes awareness of the rules and regulations before execution, the presentation of results, and the possibility of visual representation for third parties, e.g., a monitoring unit.

Transparency at the instance level (TI): 

This criterion represents the extent to which it is possible to analyze decisions in the system by backtracking to their origins. In this way, tracing the path of a decision from the initial negotiation to the final allocation of tasks can be enabled.

Comprehensibility (V): 

This criterion enables the determination of the protocol’s understandability, facilitating its implementation in a workflow engine. This property encompasses both the clarity of the process and the information necessary to negotiate.

Documentation and logging (DP): 

This criterion refers to the intelligibility of documentation and details of the system’s activities and decisions. All relevant steps and changes occurring in the system must be traceable and accessible to third parties, e.g., accessible to an auditor. It should be noted that the capabilities of the execution unit can influence compliance with this criterion.

4.1.2. Analysis Items per Criterion

Specific items are formulated for each of the mentioned criteria to facilitate the evaluation of their fulfillment.

• Transparency at model the level (TM)
• TM1: Are the rules and procedures of the negotiation process known before the start of the negotiation?
• TM2: Can the negotiation steps be visualized and presented to third parties, such as a monitoring unit?
• TM3: Does the protocol provide a mechanism for all parties to the negotiations to be informed of the outcome?

• Transparency at the instance level (TI)
• TI1: Is it possible to trace decisions back to their origin?
• TI2: Are negotiation results assigned to the respective decision-making and discussion phase?
• TI3: Is there a procedure for recognizing and correcting information gaps that could impair the traceability of decisions?

• Comprehensibility (V)
• V1: Is the protocol clear and understandable for implementation in a workflow engine?
• V2: Is the information required to trigger and run negotiations easily accessible and clearly presented?
• V3: Are potential misunderstandings or stalemates addressed and clarified in the negotiation process?

• Documentation and logging (DP)
• DP1: Can the activities and decisions be documented in detail and comprehensively?
• DP2: Can all relevant steps be defined for third parties, for example, an external auditor?
• DP3: Is up-to-date and complete documentation always guaranteed in the event of controlled demolition?

4.1.3. Weighting per Criterion

The weighting of each criterion depends on its importance relative to the others for the success of operating the overall system. The following weighting is suggested:

Transparency at the model level (35%): 

This criterion is crucial, as it forms the basis for visual monitoring, as well as trust and acceptance of the system.

Transparency at the instance level (20%): 

The ability to trace decisions back to their origins is essential for troubleshooting and quality control. This criterion is necessary for analyzing and improving processes.

Comprehensibility (20%): 

A clear and understandable protocol is essential for user-friendliness and effective integration into the system. However, it should be noted that comprehensibility may depend on the users’ qualifications.

Documentation and logging (25%): 

Comprehensive documentation is necessary to ensure traceability and compliance. This criterion is essential in ensuring the integrity of the system and supporting audits.

In summary, the presented method offers a systematic procedure for evaluating negotiation mechanisms to test approaches concerning their comprehensibility in accordance with the research question. We applied this method and documented the results in Section 4.2, Section 4.3, and Section 4.4.

4.2. Investigation of the Process Proposed by Rinaldi et al. [13]

Rinaldi et al. [13] proposed an auction process that enables the assignment of heterogeneous tasks to heterogeneous agents through an auction-inspired strategy in combination with deterministic scalar optimization. They offer two strategies: single-item and multi-item strategies.

In the single-item strategy, one task is put out to tender each round, and the bidder with the best offer is awarded the contract. Each agent’s bid for a task is the result of an optimization problem that considers costs and constraints according to task type, agent parameters, and the length of the least risky path. The process is repeated until all tasks are distributed.

In the multi-item strategy, the tasks that have not yet been awarded are announced to all participating agents at the beginning of a new auction round. This means that all agents are informed about which tasks are still available for bidding. Each agent considers all tasks and evaluates them according to the optimization function. The auctioneer receives all evaluations and compares them. The task is then assigned to the agent who has submitted the best bid. The process is repeated until all tasks have been assigned [13].

In an experiment, Rinaldi et al. [13] found that a multi-item auction requires higher computational effort compared to a single-item auction due to the necessity of multiple executions of the optimization function within a bidding round. For this reason, the single-item auction approach is considered further in this paper. Taking into account the use case of this work, the following negotiation process for task allocation could be derived based on the single-item auction approach:

• Initialization
  • Create a list of all packages to be delivered and a list of all available agents.
  • Define the parameters of the optimization function.
• Auction rounds
  • Conduct an auction round for each outstanding task in which all drones place their bids for the package to be delivered.
• Bidding
  • Each drone submits a bid for the current task based on the optimization function.
• Select the best bid
  • The best bid among all submitted bids is selected.
• Assignment of the task
  • The task is assigned to the drone with the best bid. This assignment is saved, and the task is removed from the list of open tasks.
• Repetition
  • Repeat the auction process until all tasks have been distributed.

Now that the adapted negotiation process is known, it can be evaluated in terms of comprehensibility using the evaluation items. The results are summarized in 

Table 1. Evaluation of the process proposed by Rinaldi et al. [13].

TM	Value	TI	Value	V	Value	DP	Value
TM1	1	TI1	1	V1	1	DP1	1
TM2	1	TI2	1	V2	0	DP2	1
TM3	0	TI3	0	V3	0	DP3	0
Total	2		2		1		2
Weighting	35%		20%		20%		25%
Result	0.7		0.4		0.2		0.5

.

• Transparency at the model level (TM)
• TM1: Yes, the steps are defined in advance.
• TM2: Yes, the steps are known, so in principle, it is also possible to visualize them.
• TM3: No, there is no explicit mention of such a mechanism.

• Transparency at the instance level (TI)
• TI1: Yes, if the auction rounds and bids are documented, traceability is possible.
• TI2: Yes, a clear allocation is possible with documented auction rounds.
• TI3: No, there is no information on such a procedure.

• Comprehensibility (V)
• V1: Yes, the process seems straightforward enough for implementation. It should be noted that borderline cases are not covered.
• V2: No, the paper leaves room for interpretation. Details on decisions can be found in the pseudo-code. Consequently, understanding depends on the reader’s ability to apply that code.
• V3: No, there are no explicit specifications for addressing misunderstandings or stalemates.

• Documentation and logging (DP)
• DP1: Yes, since the steps are known, detailed and comprehensive documentation is possible.
• DP2: Yes, if documentation is possible, these steps can also be recorded for use by third parties.
• DP3: No, there is no explicit indication that controlled termination can occur.

Table 1 shows the evaluation of the negotiation process proposed by Rinaldi et al. [13] using the previously defined evaluation items. Each answer to the items was converted into a numerical value, with “yes” coded as 1 and “no” as 0. The table summarizes the results, showing both the sum and the weighted sum of values for each category.

4.3. Investigation of the Fiedler [8] Process

Fiedler [8] describes an iterative process for determining a Pareto-efficient contract (or bid) in a negotiation scenario with an intermediary and several agents. The process is described as follows:

Preparation phase: 

In preparation, a debt capital rate is determined that would be due from an external bank. This is also the starting bid for the negotiation.

Negotiation and winner determination phase: 

A reverse auction characterizes the negotiation and winner determination phase:

• The mediator opens the auction with the previously determined interest rate.
• Interested internal investors submit a lower bid in each case.
• Uninterested investors drop out.
• A winner is not determined immediately. The lowest and therefore provisionally best bid is sought, which is also announced as the starting bid for the next round.
• Steps 2 and 3 are repeated either until no lower bids are submitted or all internal investors have exited.
• If no better bid can be found, the best provisional bid wins the auction and is therefore awarded the financing.
• If a provisionally best bid is found, the contract is awarded internally. Otherwise, the external bank wins. In either case, the winner is informed of the award.

Taking into account the use case of this work, the following negotiation process for task allocation could be derived based on the proposal by Fiedler [8]:

Preparation phase: 

It is assumed that no other service provider can currently offer delivery at the same speed. Consequently, the media provider determines a cost estimate in the form of delivery points during preparation. Delivery points represent the unit for evaluating the delivery. The lower the value, the more attractive it is for the mediator to award the contract. This value is also the starting bid for the negotiation.

Negotiation and winner determination phase: 

A reverse auction characterizes the negotiation and winner determination phase:

• The mediator opens the auction with the previously determined delivery points.
• All agents submit one bid each—either a lower value or the information that they are dropping out.
• A winner is not determined immediately. The lowest and therefore provisionally best bid is sought, which is also announced as the starting bid for the next round.
• Steps 2 and 3 are repeated until either no new bids are submitted or all agents have dropped out.
• If no new, better bid is found, the best bid for the time being wins the auction and is therefore awarded the contract for delivery.
• If no best bid is found that comes from an agent, the auction is canceled and restarted. This step is currently necessary, as it is assumed in this scenario that an external award is not possible. The re-evaluation follows the same procedure as the preparation phase.
• The identified best bid must be accepted for it to be valid.

Now that the adapted negotiation process is known, it is evaluated in terms of comprehensibility using the evaluation items. The result is summarized in

Table 2. Evaluation of the process proposed by Fiedler [8].

TM	Value	TI	Value	V	Value	DP	Value
TM1	1	TI1	1	V1	1	DP1	1
TM2	1	TI2	1	V2	1	DP2	1
TM3	0	TI3	0	V3	1	DP3	1
Total	2		2		3		3
Weighting	35%		20%		20%		25%
Result	0.7		0.4		0.6		0.75

.

• Transparency at the model level (TM)
• TM1: Yes, the auction rules and process are clearly defined and documented.
• TM2: Yes, since the steps are known, it is possible to visualize them.
• TM3: No, there is no explicit mention of a stakeholder information mechanism about the result.

• Transparency at the instance level (TI)
• TI1: Yes, decisions can be traced based on the documented bids and the auction history.
• TI2: Yes, every decision can be assigned based on the auction history.
• TI3: No, there is no information on such a procedure.

• Comprehensibility (V)
• V1: Yes, the auction mechanism and the steps are clearly defined.
• V2: Yes, the information required to conduct the auction is accessible and understandable.
• V3: Yes, the procedure includes mechanisms for handling situations when no best offer can be identified, and the auction is canceled.

• Documentation and logging (DP)
• DP1: Yes, the auction process and the decisions can be documented.
• DP2: Yes, the documented data is suitable for an external review.
• DP3: Yes, in addition to the individual steps, it is also defined when a controlled termination can occur. As a result, up-to-date and complete documentation can always be guaranteed.

Table 2 shows the evaluation of the Fiedler [8] negotiation process based on the previously defined evaluation items. Each answer is converted to a numerical value, with “yes” coded as 1 and “no” coded as 0. The table summarizes the results, showing both the sum and the weighted sum of values for each category.

4.4. Investigation of the Process Proposed by Zhu et al. [9]

Zhu et al. [9] propose a decentralized algorithm for task distribution to create a system optimum. They use a central agent to coordinate the negotiations. The algorithm is described as follows:

Step 1: Suggestions from the agents

• Each agent (j) in the agent group $Ag$ suggests two values: $u_j\left(1\right)$ and $u_j(-1)$.
• $u_j\left(1\right)$ represents the benefit when an additional agent is added to task j.
• $u_j(-1)$ represents the additional damage when an agent is removed from task j.
• A central agent collects these suggestions in two sequences: $U\left(1\right)$ for additional agents and $U(-1)$ for remote agents.
• If the minimum of $U(-1)$ is greater than the maximum of $U\left(1\right)$, the algorithm terminates, as no further effective redistribution is possible.

Step 2: Decision and redistribution

• The algorithm identifies the agent (i) with the lowest value in $U(-1)$ and the agent (j) with the highest value in $U\left(1\right)$.
• If $u_i(-1)$ is smaller than $u_j\left(1\right)$, agent i transfers one of its agents to agent j, which increases the overall efficiency. Subsequently, both agents are removed from sequences $U\left(1\right)$ and $U(-1)$. If this condition is not met, the algorithm returns to step 1.
• The process is repeated until effective redistribution is no longer possible.

The algorithm indicates that several agents are intended to collaborate on a single task. This makes it difficult to interpret the use case. Another component is that they see each task as an agent, which they call a “task agent”, and only ever list agents in the pseudo-code. It is therefore unclear how to address the issue of a package only being able to be processed by a single drone. This makes the transformation even more difficult. This difficulty must be noted accordingly in the evaluation concerning traceability. It should also be noted that the success already proven in their work cannot be guaranteed due to the occurrence of various changes. This represents a corresponding limitation of this work. Taking into account the difficulties mentioned above, the algorithm could look as follows:

• Evaluation by each drone:
  • Each drone (j) evaluates package i based on two criteria:

    –

    $u_j(1,i)$: How well does package i match drone j?

    –

    $u_j(-1,i)$: What would be the disadvantage if drone j did not deliver package i?

• Central coordinator collects evaluations:
  • The central coordinator collects the $u_j(1,i)$ and $u_j(-1,i)$ valuations.
• Decision making:
  • The central coordinator compares the assessments:

    –

    For each package (i), drone j is identified as that which offers the highest benefit ($u_j(1,i)$) and the one that has the lowest disadvantage ($u_j(-1,i)$).

  • If the benefit ($u_j(1,i)$) of assigning a drone (j) to a package (i) is greater than the disadvantage ($u_j(-1,i)$), this drone is assigned to the package.

Now that the adapted negotiation process is known, it is evaluated in terms of comprehensibility using the following evaluation items:

• Transparency at the model level (TM)
• TM1: No, the evaluation criteria are not entirely clear. The terms agent and task are sometimes used synonymously in the original form, making it difficult to interpret the application for the use case. It is also unclear whether success proven in the original paper is still valid under the given transformation.
• TM2: Yes, the evaluation and decision-making processes could be visualized.
• TM3: No, there is no explicit mention of a mechanism for informing the participants.

• Transparency at the instance level (TI)
• TI1: Yes, decisions can be traced back to individual assessments.
• TI2: Yes, each assignment can be traced back to specific assessments.
• TI3: No, there is no information on such a procedure.

• Comprehensibility (V)
• V1: No, the protocol is not entirely clear. The terms agent and task are sometimes used synonymously in the original form, making it difficult to interpret the transformation to the use case. It is also unclear whether the success proven in the original paper valid under the given transformation.
• V2: No, the terms agent and task are sometimes used synonymously in the original form, making it difficult to interpret the transformation to the use case. It is also unclear whether the success proven in the original paper is still valid under the given transformation.
• V3: No, there is no information on measures to avoid misunderstandings or stalemate situations.

• Documentation and logging (DP)
• DP1: Yes, the assessments and decision-making process can be documented.
• DP2: Yes, the documented data could be used for an external review.
• DP3: No, there is no indication of what happens, e.g., if an agent leaves the negotiation.

The result is summarized as follows in

Table 3. Evaluation of the process proposed by Zhu et al. [9].

TM	Value	TI	Value	V	Value	DP	Value
TM1	0	TI1	1	V1	0	DP1	1
TM2	1	TI2	1	V2	0	DP2	1
TM3	0	TI3	0	V3	0	DP3	0
Total	1		2		0		2
Weighting	35%		20%		20%		25%
Result	0.35		0.4		0		0.5

:

Table 3 shows the evaluation of the negotiation process proposed by Zhu et al. [9] using the previously defined evaluation items. Each answer was converted into a numerical value, with “yes” coded as 1 and “no” as 0. The table summarizes the results, showing both the sum and the weighted sum of values for each category.

4.5. Consolidated Analysis

In total, three negotiation approaches were reviewed concerning the research question. The approaches of Fiedler [8], Rinaldi et al. [13], and Zhu et al. [9] have the following common features:

• Several agents take part in the hearing.
• A central office is responsible for conducting the negotiations.
• The agents must provide information so that a task can be distributed.
• An iterative process is followed in all three approaches.
• The overarching objective in each case is to maximize overall success.

Despite these similarities, they differ in terms of comprehensibility.

Table 4. Summary of the study—weighted values (own presentation).

Criterion	Rinaldi et al. [13]	Fiedler [8]	Zhu et al. [9]
TM	0.7	0.7	0.35
TI	0.4	0.4	0.4
V	0.2	0.6	0
DP	0.5	0.75	0.5
Result	1.8	2.45	1.25

summarizes the results of the assessments carried out:

The overall result shows that the negotiation process of Fiedler [8] achieved the highest score of 2.45. With a maximum of three possible points, this corresponds to a comprehensibility rate of 81.67%. Therefore, this process can be described as a “comprehensible negotiation mechanism” compared to the others. This interim result provides an initial answer to the research question, which is practically proven in the next step of the work through the development and evaluation of a prototype.

5. Prototypical Implementation

In this section, the technological, methodological, and design aspects, as well as the results of the prototype implementation, are mutually adjusted for implementation. The starting point for the prototypical implementation is the analysis result reported in Section 4, i.e., the negotiation process of Fiedler [8], which was adapted to the use case of this work. Process modeling is carried out using the Compunity ToolSuite (http://www.compunity.eu (accessed on 15 December 2023)). In the first step, the main functions and elements of the tool suite and the procedure for implementation are described. Furthermore, the derivation and presentation of the model take into account the modeling possibilities. Finally, the implementation results and the summary of the prototype implementation are reported.

5.1. Compunity ToolSuite

The Compunity ToolSuite 1.0.0 is a solution for graphical process modeling [27]. The modeled elements are converted into program code by the system’s own engine [27]. As a result, the program, including the source code (C# [28]), is available [27].

The tool suite offers various levels or elements for the modeling of a solution. The first level is the Component Interaction Diagram (CID), in which the interaction between subjects (components) is mapped. The processes (skills) modeled in the system can be assigned to subjects, and their interaction with others can be defined. It is also possible to map external communication (input/output types). For example, an interface for HTTP responses and HTTP requests can be integrated. There are other elements at this level, but these are not described in detail, as they were not used for modeling in this work. It should be noted that the model and instance views are combined at this level. Therefore, both the subjects and their instances must be defined here. Figure 1 below shows the selection options at the CID level.

The next level comprises skills (processes). Various elements are, again, available for modeling (see Figure 2). Shapes are used to represent actions, such as sending or receiving messages. The system defines shapes and can only be filled with content. The most essential shapes for this work are Start, End, Decision Gateway, Receive Message, Send Message, and Execute Service. Services are used to model business functions. These must be created manually for use. Data models are self-created object shells for the use of a property bundle. This element is used, for example, to map a package.

One limitation is that there is currently no way to determine the number of messages sent by an instance. Furthermore, the decision as to which agents receive which messages cannot be made dynamically and selectively during runtime. For these reasons, it is essential to consider that all agents receive all messages; therefore, either the number of agents or the number of messages sent and received must be hard-coded.

The practical use of the tool suite shows that the desired program code (C# [28]) could already be stored in the tool side but that there is no code support available, as in a modern IDE such as Visual Studio [29]. For this reason, a best-practice approach was established in the course of this work to map the respective envelopes and communication flows in the tool suite, then directly export the code to formulate the functionalities with IDE support. This option for manually extending the code is also specified by the manufacturer [27].

Building on the understanding of the functions, levels, and elements of the Compunity ToolSuite, which serves as the basis for the prototypical implementation to answer the research question, the following sub-section continues with the elaboration of the procedure and the derivation of the process model.

5.2. Procedure and Derivation of the Process Model

This subsection documents the procedure for prototype implementation and the derivation of the process model.

5.2.1. Procedure for Prototype Implementation

Prototype implementation is carried out in an incremental process, with regular evaluations and adjustments being made. The following increments are defined: textual derivation of the negotiation process, taking into account modeling options; transfer of the model to the tool suite; implementation of the business logic; expansion to include external inputs and outputs; refinement of the code; application tests; and completion of code documentation. All steps, excluding the first, are described in Section 5.3, documented in the form of the results. The incremental approach enables step-by-step development and continuous improvement of the prototype, which remains closely linked to the research question. Regular evaluations and adjustments ensure that the results contribute directly to the answering of the research question.

5.2.2. Textual Derivation—Consideration of Modeling Options

The basis for modeling in the workflow engine is the result of Section 4, i.e., the negotiation process adapted to drone deliveries by Fiedler [8]. In the first step, the selected negotiation process is analyzed in terms of the modeling options. Any compromises or restrictions are documented. Regarding the research question, the textual derivation considers traceability as well, ensuring that both the final process result and the intermediate steps are available. Reference should be made here to the evaluation items (see Section 4.1.2), which deal with an inspection by a third party (e.g., auditor or monitoring unit). Therefore, the elements for traceability are supplemented in a second step. This division into two parts initially appears to involve additional work. Nevertheless, it avoids a possible mixing of the negotiation process with traceability.

Analysis of the Negotiation Process

The defined negotiation process shows that one mediator and several agents participate. Therefore, in the process model, there will be one mediator and (at least) two agents. The mediator’s primary responsibility is to identify the lowest bid for a package. Before that, however, they must also determine a starting bid. To fulfill these tasks, several skills are required. Therefore, the following skills are defined concerning the modeling options:

Effort estimation: 

Based on the message about the package to be delivered, a detailed analysis and evaluation are necessary. The logistics domain includes various metrics to this end; however, these are not part of this work. Instead, a value is calculated for the simulation based on a random number and the package properties to transform the delivery requirements into quantifiable delivery points. At the same time, this value represents the starting bid for the auction and is sent to the next skill. Two input points (the Receive steps) are necessary—one for package distribution and one in case an auction needs to be restarted.

Auction management: 

After the starting bid has been determined, the auction must be managed. The auction object including the starting bid must be sent to all agents. There is also the task of receiving bids or exit information and processing them accordingly. Corresponding status states are necessary to track the auction. In the reverse auction, bids are evaluated to determine the lowest acceptable bid at the time. This bid also serves as the new starting point for the next round. As the Compunity ToolSuite [27] does not provide for the dynamic, selective sending of messages, the process must be adapted so that all agents are always notified, even if they have already dropped out. The auction only ends when no lower bid is received. The winning agent must then be informed of the winning bid. Again, all agents are notified. If all agents drop out immediately in the first round, effort estimation is immediately carried out again. This step is necessary due to the process assumption that no alternative is available.

Several agents are available as counterparts. For demonstration purposes, the number of instances is set to two. Based on the starting bid, they must decide whether they can place a lower bid or withdraw from the auction. They must also accept the message that they have been awarded the task. Therefore, the following skill is defined concerning the modeling options:

Auction participation: 

Based on the received starting bid, either a lower bid or an exit is determined. Dropping out means that no lower bid can be submitted. If a bid has already been submitted and it was the best, the agent can still win the bid despite the withdrawal. In any case, the mediator is informed by a message. The exact calculation of the value is, again, the responsibility of the corresponding domain. For simulation purposes, a value is calculated using a random number and the packet properties. If an agent has already decided to exit in a previous round, it receives another bid request for the corresponding object. This is necessary due to the tool’s restrictions, which prevent messages from being sent or received dynamically and selectively. The process at the agent level is only terminated when a winner has been determined. This is necessary so that the bid instance remains active at the program level and any interim results can be accessed.

Quality of Traceability

To ensure traceability quality, both individual steps and the overall process result should be documented. In terms of the evaluation items, this should simulate a monitoring unit and a possible audit-capable format. Therefore, to fulfill this quality, a monitoring message should be sent after each send, receive, and service step. Thus, taking into account the modeling options, a step to send to a third party is necessary after each of the aforementioned process steps. Furthermore, each auction round, including the starting bid, temporary best bid (result of the round), and submitted bids, must be temporarily stored, then transferred to the package distribution for further use, along with the auction winner at the end.

In summary, this textual derivation lays the foundation for the further increments in the next section. Concerning the research question, the implementation-oriented foundation for the practical demonstration and the creation of evidence is laid here.

5.3. Implementation Results

This section documents the implementation results. For reasons of clarity, the individual increments are not discussed here, but the overall result is described. The starting point for the implementation is the textual derivation of Section 5.2.2. This section is structured so that the graphically modeled model is first presented in its individual parts. Model code mapping and code documentation are then explained. The subsection concludes with the results of the test cases.

5.3.1. Modeling Result

Figure 3 below shows the individual subjects and their communication at the model level. The specific communication at the instance level is discussed later. The “Mediator” and “Agent” subjects are shown, including their skills and the HTTP input and HTTP output. The “Mediator” subject is the central component that acts as a mediator. It receives package information from an external location, coordinates the negotiation in all its facets, and returns the interim results in the form of monitoring messages and the auction result at the end. For this purpose, it has “DeliveryPointEstimation” and “AuctionManagement” as “skills”.

The “Agent” subject has the “AuctionParticipation” skill to participate in the auction process. The HTTP input module represents the packet distribution and serves as the external input for transmitting packet information and receiving auction results. The HTTP output module is the output for a monitoring unit. The intermediate steps of the auction are transmitted to this external output for monitoring. The arrows and dotted lines represent the communication paths.

Figure 4 illustrates the instances created for the subjects, along with their exact communication flow, represented by numbers. In this setup, there is one mediator (“Mediator1”) and two agents (“Agent1” and “Agent2”). It should be noted that the cross-skill communication within “Mediator1” is somewhat difficult to recognize. This is why it is highlighted in color. The negotiation process begins with step 1 and ends with step 12. Steps 5 to 8 can be repeated, depending on the number of auction rounds. It is also possible that a new auction is initiated by step 13. In such a case, step 11 is applied later, and the process continues with step 3. The monitoring messages are not numbered. They are sent after each send, receive, or service step is triggered. The repetitive listing of monitoring messages is necessary due to tool restrictions.

Now that the communication channels have been defined, the process continues with the respective skills. Figure 5 below shows the modeled process for estimating the effort (Skill Delivery Point Estimation). Based on the message about the parcel information (Receive Parcel), a starting bid (Run EstimateDeliveryPoints) is determined, then transferred to the next skill (Send Bid) as a new starting bid (Bid). It can also be seen here that a monitoring message (Send Monitoring MSG n) is sent after each send, receive, and service step. A special feature is that the first receive step can receive either parcel information (Parcel) or a bid (Bid). The bid is the previously created starting bid, which is not followed by a lower bid.

The next skill is Auction Participation (see Figure 6), where a starting bid (Receive Message) is used to determine whether a lower bid can be placed or whether the auction is exited (Run Service). The process is only finally completed when the mediator sends the winning message (Receive Message). A special feature allows the userto receive either a bid or the winning message in one step.

Figure 7 below shows the final process, i.e., auction management. The starting point is the received starting bid (Receive Bid) from the effort estimate. The agents’ bids are also accepted via this receive step. Therefore, a decision must be made as to whether to send a starting bid to all agents (Send Bid) or wait for the bids. It is also checked here whether all bids have been received and whether the provisional winner can be determined (Run Service).

Special case: 

If two or more agents submit the same bid, the first in the list is the best. During the winner determination process, the provisional winner is identified, and a decision is made regarding the possibility of a lower bid. This decision is recorded in the form of an auction status. If yes, then this provisional best bid is sent out as the new starting bid (send bid). If not, it must be checked whether the auction needs to be restarted or whether there is a real winner. If a new auction has to be started, the original starting bid is sent back to effort estimation (Send new init Bid). In any case, a message is sent to all agents (Send Winner). If a real winner has been determined, the auction result is sent back (Send Auction Result), and the process ends. Furthermore, the monitoring messages (Send Monitoring MSG n) are also visible after each send, receive, and service step.

5.3.2. Model-to-Code Mapping

Behind each of the skill steps shown graphically above is C# code, which was added as part of this work. The parts listed above can be found in the source code using name mapping. Each space is replaced by an underscore (i.e., “_”), and “State” suffix is added at the end. Figure 8 below shows the comparison.

5.3.3. Code Documentation

The documentation is divided into two parts. The first part of the documentation provides the model explanation. Conversions that go beyond this are described directly in the code by the C# own XML convention. Figure 9 shows an example.

5.3.4. Test Results

The test setup consists of three parts: the package distribution (http request handler such as Postman Inc. [30]), the prototype propoed in this work [31], and a monitoring unit (a simple JSON viewer is also available at Wallner [31]). Two test cases are presented below. The first case involves the direct processing of the auction without a restart. The second comprises a restart of the auction. It is tested whether a result is achieved and whether the result is comprehensible.

In the first step, a package is created in the form of a JSON string. The package contains an ID for identification (UID), a sender (Sender), a receiver (Receiver), a weight, and the dimensions (Length, Width, Height). This data is independent of the test-case Listing 1.

Listing 1. Example JSON string.

This string is transmitted in JSON format in the HTTP body via an HTTP POST request to the HTTP input of the prototype implementation [31]. The auction result and the steps involved are returned. This is illustrated in the following excerpts, which correspond to the two test cases in the form of monitoring messages. These were received again via an HTTP POST request.

A monitoring message (see Figure 10) consists of information on the recorded action (SENT, RECEIVED, RUN <Service>), the status of the auction (Init New Auction, Init Auction, Ask For Bids, Received Bid, Continue, End), and the bid. A bid, in turn, consists of the bidder, the value (0 to 2,147,483,647), information on the parcel (sender, recipient, weight, and dimensions), and information on the whereabouts in the auction (true or false) and the timestamp (UTC). A special feature records the parcel information for distribution in the form of a bid object.

5.3.5. Test Without Restart

Figure 11 below shows the main results of the negotiation without a new start in the form of monitoring messages. In #1, the package that is called for auction is shown. The steps involved in determining the starting bid are shown in #2 to #4 (inclusive). In #5 to #8 (inclusive), the first auction round and its temporary result are shown. In #9 to #12 (inclusive), the second or final auction round is recorded. Finally, #13 shows the actual winning agent, including the lowest bid. Following the progression, one can see that the auction starts with a bid of 569. An agent is prepared to undercut this value. Therefore, the temporary best value is 378. This bid is called out again, only this time, no agent can deliver a lower value. The auction ends, and the agent with the value 378 wins the bid.

5.3.6. Test with Restart

Figure 12, Figure 13 and Figure 14 below show the main results of the negotiation with restart in the form of monitoring messages.

In #1, the package that is called for auction is shown. The steps involved in determining the starting bid are shown in #2 to #4 (inclusive). In #5 to #8 (inclusive), the first auction round and its temporary result are shown. In #9 to #13 (inclusive), the restart of the auction, including the redetermination of the starting bid, is shown. The new auction round and its temporary result are shown in #14 to #18 (inclusive). Round numbering continues with “2”. In Figure 14, the further steps of the auction are shown. The third auction round and its temporary result are shown in #19 to #22 (inclusive). In #13 to #26 (inclusive), the fourth auction round and its temporary result are shown. In #27 to #30 (inclusive), the fifth auction round and its temporary result are shown. In #31 to #34 (inclusive), the sixth and final auction round is shown. Finally, #35 shows the actual winning agent, including the lowest bid.

Following the process, one can see that the bid starts at 1018. None of the agents is willing to undercut this value. Therefore, the auction is restarted. The new starting bid is now 846, and both agents place the same bid. Therefore, the first bid received is determined to be the temporary best bid at 561. The auctionis not yet over, and bids are collected again. The steps are repeated until no agent can submit a lower bid. The agent with the value of 138 finally wins the bid. The performed tests show that a result was found in each case and that the result is comprehensible.

In summary, this section presents the prototypical implementation of a negotiation-based approach to distributing a task. The practical application of the research results can be demonstrated using the Compunity ToolSuite. Despite tool-related limitations, the performed tests ultimately proved the theoretical answer to the research question posed at the beginning.

6. Conclusions

This research focused on transparent and intelligible negotiation-based approaches to task distribution in multi-agent systems. The most promising algorithmic candidate was selected from existing findings, and its utility was demonstrated in a prototype implementation. An autonomous system in logistics served as a demonstrator and test case. Although a literature search revealed a variety of approaches for multi-agent systems, there is no universally applicable solution.

Although several authors have adopted a negotiation-based approach, confirming its suitability, there was a notable lack of structured evaluation criteria. Therefore, we needed to find an evaluation method to analyze the various approaches in more detail. We were able to apply the utility analysis proposed by Zangemeister [25] in reference to the addressed research question. Applying the developed evaluation scheme, the approach proposed by Fiedler [8] was the most suitable concerning the research question. This first part provided the theoretical basis for answering the research question. Consequently, this approach was selected for prototype implementation.

The Compunity ToolSuite was used for the practical demonstration and to create evidence. First, the theoretical process model was graphically transferred to the tool. Only in a further step were the individual steps implemented using C# code. It is worth mentioning that the theoretical process had to be adapted minimally, as the Compunity ToolSuite cannot receive or send messages dynamically and selectively. However, this did not pose a problem for the implementation, as all the processes under consideration leave some room for interpretation. For this reason, the edge case in which several agents deliver the same bid was solved by selecting the first agent as the temporary best bidder. The prototype was developed in incremental steps, with regular evaluations ensuring a close link to the research question.

The test results ultimately confirmed the functionality of the developed prototype. Auctions both with and without a restart led to successful results. The results were in line with theoretical expectations. Thus, they confirmed the selected approach in the context of a comprehensible distribution of tasks concerning parcel delivery with autonomous agents. The adapted process of Fiedler [8], including the various implementation-relevant extensions concerning traceability, represents the answer to the research question.

As a limitation of this work, it should be noted that other field tests of the implemented approach remain to be performed. Although some essential insights were gained in this first study, future research is required.

• A significant limitation of this work concerns the lack of in-the-field conditions. Future research projects could focus on applying and testing the selected approach under real-world conditions to validate its practical applicability and robustness in dynamic, real-world scenarios.
• This work focused on the multi-agent domain. Future studies need to extend the analysis to other areas.
• Prototype implementation was tested in a controlled environment. Further research could investigate the scalability of the approach and evaluate its performance in larger, more complex environments and with a larger number of agents.
• This work focused on parcel delivery with autonomous agents. Further research could explore the application of the approach in other industries and assess its versatility and impact in different sectors.

However, all future research can build on this work and contribute to a deeper understanding and broader application of negotiation-based approaches in the area of traceable task allocation.