Search Results (101)

This paper analyzes the pricing dynamics of product warranties by developing a three-player hierarchical game model involving a manufacturer, an independent service agent, and a consumer. The model provides a scenario where the manufacturer and the agent form a coalition to coordinate pricing strategies, while interacting non-cooperatively with the consumer. In this framework, the manufacturer sets the product’s sale price, including the base warranty, while the agent determines the price of extended maintenance services. The key contribution is the application of the Shapley value to equitably distribute the coalition’s profits based on each member’s contribution—a novel approach in the warranty pricing literature. We detail the characteristic functions that define the coalition’s structure and present computer simulations to estimate the expected costs associated with maintenance services. A comprehensive sensitivity analysis is applied to report how changes in parameters influence equilibrium strategies and players’ payoffs. The results provide strategic insights into how manufacturers and agents can coordinate to optimize pricing, capture consumer surplus, and improve decision-making in warranty service markets. Full article

Non-cooperative games in normal form are specified by a player set, sets of player strategies, and payoff functions. Cooperative games, meanwhile, are specified by a player set and a worth function that maps coalitions of players to payoffs they can feasibly achieve. Although these games study distinct aspects of social behavior, this paper proposes a novel attempt at relating the two models. In particular, cooperative games may be represented by a non-cooperative game in which players can freely sign binding agreements to form coalitions. These coalitions inherit a joint strategy set and seek to maximize collective payoffs. When these coalitions play against one another, the equilibrium payoffs for each coalition coincide with what is predicted by the worth function. This paper proves sufficient conditions under which cooperative games can be represented by non-cooperative games. This paper finds that all strictly superadditive partition function form (PFF) games can be represented under Nash equilibrium (NE) and rationalizability; that all weakly superadditive characteristic function form (CFF) games can be represented under NE; and that all weakly superadditive PFF games can be represented under trembling hand perfect equilibrium (THPE). Full article

I consider an underexplored possible explainer of the “surprising” results of Ultimatum Game experiments, namely, that Proposers and Recipients consider following only some of all the logically possible strategies of their Ultimatum Game. I present an evolutionary analysis of different games having the same set of allowable Proposer offers and functions that determine Proposer and Recipient payoffs. For Unrestricted Ultimatum Games, where Recipients may choose from among any of the logically possible pure strategies, populations tend to evolve most often to Nash equilibria where Proposers make the lowest allowable offer. However, for Threshold Reduced Ultimatum Games, where Recipients must choose from among minimum acceptable offer strategies, and for Range Reduced Ultimatum Games, where Recipients must choose from among pure strategies that spurn offers that are “too high” as well as “too low”, populations tend to evolve most often to Nash equilibria where Proposers offer substantially more than the lowest possible offer, a result that is consistent with existing Ultimatum Game experimental results. Finally, I argue that, practically speaking, actual Proposers and Recipients will likely regard some reduction of the Unrestricted Ultimatum Game as their game because, for them, the strategies of this reduction are salient. Full article

Federated Learning (FL), a key paradigm in privacy-preserving and distributed machine learning (ML), enables collaborative model training across decentralized data sources without requiring raw data exchange. FL enables collaborative model training across decentralized data sources while preserving privacy. However, selecting appropriate clients remains a major challenge, especially in heterogeneous environments with diverse battery levels, privacy needs, and learning capacities. In this work, a centralized reward-based payoff strategy (RBPS) with cooperative intent is proposed for client selection. In RBPS, each client evaluates participation based on locally measured battery level, privacy requirement, and the model’s accuracy in the current round computing a payoff from these factors and electing to participate if the payoff exceeds a predefined threshold. Participating clients then receive the updated global model. By jointly optimizing model accuracy, privacy preservation, and battery-level constraints, RBPS realizes a multi-objective selection mechanism. Under realistic simulations of client heterogeneity, RBPS yields more robust and efficient training compared to existing methods, confirming its suitability for deployment in resource-constrained FL settings. Experimental analysis demonstrates that RBPS offers significant advantages over state-of-the-art (SOA) client selection methods, particularly those relying on a single selection criterion such as accuracy, battery, or privacy alone. These one-dimensional approaches often lead to trade-offs where improvements in one aspect come at the cost of another. In contrast, RBPS leverages client heterogeneity not as a limitation, but as a strategic asset to maintain and balance all critical characteristics simultaneously. Rather than optimizing performance for a single device type or constraint, RBPS benefits from the diversity of heterogeneous clients, enabling improved accuracy, energy preservation, and privacy protection all at once. This is achieved by dynamically adapting the selection strategy to the strengths of different client profiles. Unlike homogeneous environments, where only one capability tends to dominate, RBPS ensures that no key property is sacrificed. RBPS thus aligns more closely with real-world FL deployments, where mixed-device participation is common and balanced optimization is essential. Full article

This paper demonstrates that perfectly calibrating a multi-asset model to observed market prices of all basket call options is insufficient to uniquely determine the price of a best-of call option. Previous research on multi-asset option pricing has primarily focused on complete market settings or assumed specific parametric models, leaving fundamental questions about model risk and pricing uniqueness in incomplete markets inadequately addressed. This limitation has critical practical implications: derivatives practitioners who hedge best-of options using basket-equivalent instruments face fundamental distributional uncertainty that compounds the well-recognized non-linearity challenges. We establish this non-uniqueness using convex analysis (extreme ray characterization demonstrating geometric incompatibility between payoff structures), measure theory (explicit construction of distinct equivalent probability measures), and geometric analysis (payoff structure comparison). Specifically, we prove that the set of equivalent probability measures consistent with observed basket prices contains distinct measures yielding different best-of option prices, with explicit no-arbitrage bounds $[a_K,b_K]$ quantifying this uncertainty. Our theoretical contribution provides the first rigorous mathematical foundation for several empirically observed market phenomena: wide bid-ask spreads on extremal options, practitioners’ preference for over-hedging strategies, and substantial model reserves for exotic derivatives. We demonstrate through concrete examples that substantial model risk persists even with perfect basket calibration and equivalent measure constraints. For risk-neutral pricing applications, equivalent martingale measure constraints can be imposed using optimal transport theory, though this requires additional mathematical complexity via Schrödinger bridge techniques while preserving our fundamental non-uniqueness results. The findings establish that additional market instruments beyond basket options are mathematically necessary for robust exotic derivative pricing. Full article

According to the Federal Reserve of the United States, in the second quarter of 2024, American credit card debt reached USD 1.14 trillion, the highest balance ever recorded. In an age of high-interest, complex credit cards, how does financial literacy affect credit card debt repayment? Also, how could financial literacy and education stop the rise in credit card debt in America? To answer these questions, we use microdata from the latest wave of the Survey of Consumer Finances for 2022. We aim to capture the likelihood of credit card repayment behaviors related to the monthly balances owed by 3865 credit card holders. We consider three categories of self-reported credit card payoff behavior: hardly ever, sometimes, and always or almost always. Given the ordinal nature of our outcome variable, we perform a series of likelihood-ratio and Brant tests to assess the assumption of the proportionality of odds across response categories. Following the failure of the tests, we conclude with the selection of a generalized ordered logit/partial proportional odds model that allows us to relax the parallel lines constraint for those variables for which it is not justified. In our logistic regressions, we account for a comprehensive set of demographic characteristics, and from our results, we highlight the following: For credit card holders with low financial literacy, we find that the odds of moving to a higher category of payoff behavior are 21% and significantly lower than those of high financial literacy respondents. Further, for college-educated card holders, the odds of paying off always or almost always versus sometimes and hardly ever are 2.49 times and significantly greater than the odds for credit card holders without a college education. Credit card holders who are minority group members, female, under 45, have dependents, or earn less than USD 50,000 demonstrate a tendency for poor credit card payoff behavior. In our conclusion, we discuss how to improve credit card repayments. We stress the importance of monitoring people closely. We also aim to provide better financial advice to certain groups. Lastly, we present a more realistic approach to building and sustaining financial literacy. Full article

This paper defines stubbornness as an optimal feedback Nash equilibrium within a dynamic setting. Stubbornness is treated as a player-specific parameter, with the team’s coach initially selecting players based on their stubbornness and making substitutions during the game according to this trait. The payoff function of a soccer player is evaluated based on factors such as injury risk, assist rate, pass accuracy, and dribbling ability. Each player aims to maximize their payoff by selecting an optimal level of stubbornness that ensures their selection by the coach. The goal dynamics are modeled using a backward parabolic partial stochastic differential equation (BPPSDE), leveraging its theoretical connection to the Feynman–Kac formula, which links stochastic differential equations (SDEs) to partial differential equations (PDEs). A stochastic Lagrangian framework is developed, and a path integral control method is employed to derive the optimal measure of stubbornness. The paper further applies a variant of the Ornstein–Uhlenbeck BPPSDE to obtain an explicit solution for the player’s optimal stubbornness. Full article

In this paper, in order to enhance the autonomous operation capabilities of aircraft and ensure their operational safety and efficiency, we propose an autonomous decision-making framework based on target motion state prediction combined with the Markov Decision Process, namely IMM-MDP architecture. Firstly, our own aircraft utilizes the IMM algorithm to achieve the state prediction of the target; building upon the existing algorithmic structure, the proposed framework improves model sets within the IMM algorithm by incorporating climb and turn models and refines the motion modes of aircraft during the cruise phase, gathering corresponding sub-models to predict different motion modes and enhance the prediction accuracy of the target. Secondly, we adopt the Markov Decision Process as the autonomous decision-making method for the own aircraft, proposing a method by which to calculate the optimal decision sequence based on the prediction scenarios of the IMM algorithm; that is, in both multi-step prediction and single-step prediction scenarios, the payoff values of different action strategies at each decision moment are calculated to obtain the optimal decision sequence. The experimental results show that the IMM algorithm with the improved model set, described in this paper, is more accurate than the IMM algorithm and prediction results of the current statistical model, as described in the literature. We also set up a multi-aircraft operation scenario, comparing the IMM-MDP decision framework proposed in this paper with the Monte Carlo and MPC decision models, thus demonstrating that the proposed framework provides better decisions while ensuring safety. Due to the target state prediction and updating, this method also demonstrates better real-time performance and practicality. Full article

Decision-making involves selecting the best alternative based on evaluation criteria while considering environmental impacts. The translation of environmental factors into quantifiable mathematical expressions is challenging due to the inherent uncertainties. Decision-makers can address the subjective characteristics of alternatives by incorporating fuzzy set theory into decision-making processes where uncertainty and ambiguity exist. Game theory is introduced as another approach to enhance the robustness of decision-making models, leading to more informed and flexible decision outcomes. This approach promotes strategic thinking and aids decision-making by allowing individuals to visualize the potential consequences of different decisions under various conditions. This study proposes a fuzzy multi-criteria decision support system that provides a structured framework to address the complexities of agricultural land selection. The decision support system employs a two-person zero-sum game to identify the optimal land management option, considering the strategic interactions between players. The results from the payoff matrix reveal the equilibrium point, providing an ideal solution for more effective land use planning decisions. Full article

The paper proposes a technique for protecting reconfigurable networks that implements topology rebuilding, which combines immunization and network gaming methods, as a solution for maintaining cyber resilience. Immunization presumes an adaptive set of protective reconfigurations destined to ensure the functioning of a network. It is a protective reconfiguration aimed to preserve/increase the functional quality of the system. Network nodes and edges are adaptively reorganized to counteract an invasion. This is a functional component of cyber resilience. It can be implemented as a global strategy, using knowledge of the whole network structure, or a local strategy that only works with a certain part of a network. A formal description of global and local immune strategies based on hierarchical and peer-to-peer network topologies is presented. A network game is a kind of the well-defined game model in which each situation generates a specific network, and the payoff function is calculated based on the constructed networks. A network game is proposed for analyzing a network topology. This model allows quickly identifying nodes that require disconnection or replacement when a cyber attack occurs, and understanding which network sectors might be affected by an attack. The gaming method keeps the network topology resistant to unnecessary connections. This is a structural component of cyber resilience. The basic network game method has been improved by using the criterion of maximum possible path length to reduce the number of reconfigurations. Network optimization works together with immunization to preserve the structural integrity of the network. In an experimental study, the proposed method demonstrated its effectiveness in maintaining system quality within given functional limits and reducing the cost of system protective restructuring. Full article

The literature on strategic ambiguity in classical games provides generalized notions of equilibrium in which each player best responds to ambiguous or imprecise beliefs about his opponents’ strategic choices. In a recent paper, strategic ambiguity has been extended to psychological games, by taking into account ambiguous hierarchies of beliefs and max–min preferences. Given that this kind of preference seems too restrictive as a general method to evaluate decisions, in this paper we extend the analysis by taking into account $\alpha$-max–min preferences in which decisions are evaluated by a convex combination of the worst-case (with weight $\alpha$) and the best-case (with weight $1-\alpha$) scenarios. We define the $\alpha$-max–min psychological Nash equilibrium; an illustrative example shows that the set of equilibria is affected by the parameter $\alpha$ and the larger the ambiguity, the greater the effect. We also provide a result of stability of the equilibria with respect to perturbations that involve the attitudes toward ambiguity, the structure of ambiguity, and the payoff functions: converging sequences of equilibria of perturbed games converge to equilibria of the unperturbed game as the perturbation vanishes. Surprisingly, a final example shows that the existence of equilibria is not guaranteed for every value of $\alpha$. Full article

Integrating large language model (LLM) agents within game theory demonstrates their ability to replicate human-like behaviors through strategic decision making. In this paper, we introduce an augmented LLM agent, called the private agent, which engages in private deliberation and employs deception in repeated games. Utilizing the partially observable stochastic game (POSG) framework and incorporating in-context learning (ICL) and chain-of-thought (CoT) prompting, we investigated the private agent’s proficiency in both competitive and cooperative scenarios. Our empirical analysis demonstrated that the private agent consistently achieved higher long-term payoffs than its baseline counterpart and performed similarly or better in various game settings. However, we also found inherent deficiencies of LLMs in certain algorithmic capabilities crucial for high-quality decision making in games. These findings highlight the potential for enhancing LLM agents’ performance in multi-player games using information-theoretic approaches of deception and communication with complex environments. Full article

The pinning control of complex networks is a hot topic of research in network science. However, most studies on pinning control ignore the impact of external interference on actual control strategies. To more comprehensively evaluate network synchronizability via pinning control in the attack–defense confrontation scenario, the paper constructs an attacker-defender game model. In the model, the attacker needs to control nodes in the network as much as possible. The defender will do their best to interfere with the attacker’s control of the network. Through a series of experiments, we find that the random attack strategy is always the dominant strategy of the attacker in various equilibriums. On the other hand, the defender needs to constantly change dominant strategy in equilibrium according to the set of defense strategies and cost constraints. In addition, scale-free networks with different network metrics can also influence the payoff matrix of the game. In particular, the average degree of the network has an obvious impact on the attacker’s payoff. Moreover, we further verify the correctness of the proposed attacker-defender game through a simulation based on the specific network synchronization dynamics. Finally, we conduct a sensitivity analysis in different network structures, such as the WS small-world network, the ER random network, and the Google network, to comprehensively evaluate the performance of the model. Full article

The greatest source of failure in portfolio analytics is not individual models that perform poorly, but rather an inability to integrate models quantitatively across management functions. The separable components of age–period–cohort models provide a framework for integrated credit risk modeling across an organization. Using a panel data structure, credit risk scores can be integrated with an APC framework using either logistic regression or machine learning. Such APC scores for default, payoff, and other key rates fit naturally into forward-looking cash flow estimates. Given an economic scenario, every applicant at the time of origination can be assigned profit and profit volatility estimates so that underwriting can truly be account-level. This process optimizes the most fallible part of underwriting, which is setting cutoff scores and assigning loan pricing and terms. This article provides a summary of applications of APC models across portfolio management roles, with a description of how to create the models to be directly integrated. As a consequence, cash flow calculations are available for each account, and cutoff scores can be set directly from portfolio financial targets. Full article

Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered in terms of a possible range of acceptance and nonacceptance by players rather than specific values. Furthermore, decision makers exhibit some hesitancy regarding this information. In such a situation, all the aforementioned expansions of fuzzy sets are unable to accurately represent the scenario. The purpose of this article is to present asymmetric information situations in which the range of choices takes into account the hesitancy of players in accepting or not accepting information. To illustrate these problems, we develop matrix games that consider the payoffs of interval-valued intuitionistic hesitant fuzzy elements (IIHFEs). Dealing with these types of fuzzy programming problems requires a significant amount of effort. To solve these matrix games, we formulate two interval-valued intuitionistic hesitant fuzzy programming problems. Preserving the hesitant nature of the payoffs to determine the optimal strategies, these two problems are transformed into two nonlinear programming problems. This transformation involves using mathematical operations for IIHFEs. Here, we construct a novel aggregation operator of IIHFEs, viz., min-max operators of IIHFEs. This operator is suitable for applying the developed methodology. The cogency and applicability of the proposed methodology are verified through a numerical example based on the situation of conflict between hackers and defenders to prevent damage to cybersecurity. To validate the superiority of the proposed model along with the computed results, we provide comparisons with the existing models. Full article