Search Results (109)

The concept of Nash equilibria in pure strategies for quantum extensions of the general form of the Prisoner’s Dilemma game is investigated. The process of quantization involves incorporating two additional unitary strategies, which effectively expand the classical game. We consider five classes of such quantum games, which remain invariant under isomorphic transformations of the classical game. The resulting Nash equilibria are found to be more closely aligned with Pareto-optimal solutions than those of the conventional Nash equilibrium outcome of the classical game. Our results demonstrate the complexity and diversity of strategic behavior in the quantum setting, providing new insights into the dynamics of classical decision-making dilemmas. In particular, we provide a detailed characterization of strategy profiles and their corresponding Nash equilibria, thereby extending the understanding of quantum strategies’ impact on traditional game-theoretical problems. Full article

In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash equilibriums for such games and efficient algorithms to find them. For continuous priors, we suggest a methodology to perform Nash equilibrium searches in simple cases. For discrete priors, we present algorithms that can handle two-action and two-player games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash equilibrium. We illustrate our results with several examples like the double-game prisoner’s dilemma (DGPD), the game of chicken, and the sustainable adoption decision problem (SADP). Full article

Objective: Marital infidelity significantly impacts both the community and the institution of marriage. This study aims to develop a theoretical framework for analyzing marital infidelity through a game-theoretic lens. Methodology/Design/Approach: This research employs a game-theoretic model to predict the decision-making processes of unfaithful partners. Static game models are utilized to explore the interactions between spouses, focusing on identifying Nash equilibria that encapsulate the complexities and uncertainties inherent in infidelity-related decisions, whether through pure or mixed strategies. Results: The analysis reveals strategic dynamics in marital infidelity, where Nash equilibria indicate scenarios where one or both partners may engage in extramarital affairs. A Nash equilibrium is established when both partners perceive the benefits of infidelity as outweighing the costs, leading to diminished trust and communication. The Mixed-Strategy Nash Equilibrium (MSNE) hypothesis suggests that spouses may oscillate between fidelity and infidelity based on probabilistic strategies. Research Implications: This study provides a game-theoretic perspective on marital infidelity, whose findings may be used to inform legal frameworks and social policies addressing the consequences of infidelity, potentially impacting family counseling and legal services. Value/Originality: This research introduces a game-theoretic approach to understanding trust and transgression in marriages, identifying two primary categories of Nash equilibria. It fills a theoretical gap while providing practical insights into marital behavior. 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

Since high complexity and uncertainty is inherent in real-world environments that can influence the strategies choices of agents, we introduce a stochastic perturbation term to characterize the interference caused by uncertain factors on multi-agent systems (MASs). Firstly, the stochastic Q learning is designed by introducing stochastic perturbation term into Q learning, and the corresponding replicator dynamic equations of stochastic Q learning are derived. Secondly, we focus on two-agent games with two and three action scenarios, analyzing the impact of learning parameters on agents’ strategy selection and demonstrating how the learning process converges to its Nash equilibria. Finally, we also conduct a sensitivity analysis on exploration parameters, demonstrating how exploration rates affect the convergence process in potential games. The analysis and numerical experiments offer insights into the effectiveness of different exploration parameters in scenarios involving uncertainty. Full article

The engagement of emerging market participants in electricity markets exerts dual influences on price formation mechanisms and operational dynamics. To quantify the impacts on locational marginal prices and stakeholders’ economic interests when EV aggregators (EVAs), cloud energy storage operators (CESSOs), and load aggregators (LAs) collectively participate in market competition, this study develops a bi-level game-theoretic framework for market equilibrium analysis. The proposed architecture comprises two interdependent layers: The upper-layer Stackelberg game coordinates strategic interactions among EVA, LA, and CESSO to mitigate bidding uncertainties through cooperative mechanisms. The lower-layer non-cooperative Nash game models competition patterns to determine market equilibria under multi-agent participation. A hybrid solution methodology integrating nonlinear complementarity formulations with genetic algorithm-based optimization was developed. Extensive numerical case studies validate the methodological efficacy, demonstrating improvements in solution optimality and computational efficiency compared to conventional approaches. Full article

Policy space response oracles (PSRO) is an important algorithmic framework for approximating Nash equilibria in two-player zero-sum games. Enhancing policy diversity has been shown to improve the performance of PSRO in this approximation process significantly. However, existing diversity metrics are often prone to redundancy, which can hinder optimal strategy convergence. In this paper, we introduce the policy similarity measure (PSM), a novel approach that combines Gaussian and cosine similarity measures to assess policy similarity. We further incorporate the PSM into the PSRO framework as a regularization term, effectively fostering a more diverse policy population. We demonstrate the effectiveness of our method in two distinct game environments: a non-transitive mixture model and Leduc poker. The experimental results show that the PSM-augmented PSRO outperforms baseline methods in reducing exploitability by approximately 7% and exhibits greater policy diversity in visual analysis. Ablation studies further validate the benefits of combining Gaussian and cosine similarities in cultivating more diverse policy sets. This work provides a valuable method for measuring and improving the policy diversity in two-player zero-sum games. Full article

In this paper, we focus on developing self-organizing algorithms aimed at solving, in a distributed way, the coverage problem in Wireless Sensor Networks (WSNs). For this purpose, we apply a game-theoretical framework based on an application of a variant of the Spatial Prisoner’s Dilemma game. The framework is used to build a multi-agent system, where agent-players in the process of iterated games tend to achieve a Nash equilibrium, providing them the possible maximal values of payoffs. A reached equilibrium corresponds to a global solution for the coverage problem represented by the following two objectives: coverage and the corresponding number of sensors that need to be turned on. A multi-agent system using the game-theoretic framework assumes the creation of a graph model of WSNs and the further interpretation of nodes of the WSN graph as agents participating in iterated games. We use the following two types of reinforcement learning machines as agents: Learning Automata (LA) and Cellular Automata (CA). The main novelty of the paper is the development of a specialized reinforcement learning machine based on the application of ($ϵ,h$)-learning automata. As the second model of an agent, we use the adaptive CA that we recently proposed. While both agent models operate in discrete time, they differ in the way they store and use available information. LA-based agents store in their memories the current information obtained in the last h-time steps and only use this information to make a decision in the next time step. CA-based agents only retain information from the last time step. To make a decision in the next time step, they participate in local evolutionary competitions that determine their subsequent actions. We show that agent-players reaching the Nash equilibria corresponds to the system achieving a global optimization criterion related to the coverage problem, in a fully distributed way, without the agents’ knowledge of the global optimization criterion and without any central coordinator. We perform an extensive experimental study of both models and show that the proposed learning automata-based model significantly outperforms the cellular automata-based model. Full article

This paper introduces an enhanced algorithm for computing generalized Nash equilibria for multiple player nonlinear games, which degenerates in a gradient algorithm for single player games (i.e., optimization problems) or potential games (i.e., equivalent to minimizing the respective potential function), based on the Rosen gradient algorithm. Analytical examples show that it has similar theoretical guarantees of finding a generalized Nash equilibrium when compared to the relaxation algorithm, while numerical examples show that it is faster. Furthermore, the proposed algorithm is as fast as, but more stable than, the Rosen gradient algorithm, especially when dealing with constraints and non-convex games. The algorithm is applied to an electricity market game representing the current electricity market model in Brazil. Full article

This paper investigates the effectiveness of centrality measures for the influence maximization problem in competitive social networks (SNs). We consider a framework, which we call “I-Game” (Influence Game), to conceptualize the adoption of competing products as a strategic game. Firms, as players, aim to maximize the adoption of their products, considering the possible rational choice of their competitors under a competitive diffusion model. They independently and simultaneously select their seeds (initial adopters) using an algorithm from a finite strategy space of algorithms. Since strategies may agree to select similar seeds, it is necessary to include an initial seed tie-breaking rule into the game model of the I-Game. We perform an empirical study in a two-player game under the competitive independent cascade model with three different seed-tie-breaking rules using four real-world SNs. The objective is to compare the performance of centrality-based strategies with some state-of-the-art algorithms used in the non-competitive influence maximization problem. The experimental results show that Nash equilibria vary according to the SN, seed-tie-breaking rules, and budgets. Moreover, they reveal that classical centrality measures outperform the most effective propagation-based algorithms in a competitive diffusion setting in three graphs. We attempt to explain these results by introducing a novel metric, the Early Influence Diffusion (EID) index, which measures the early influence diffusion of a strategy in a non-competitive setting. The EID index may be considered a valuable metric for predicting the effectiveness of a strategy in a competitive influence diffusion setting. Full article

This paper examines manipulation games through the lens of Machiavellianism, a psychological theory. It analyzes manipulation dynamics using principles like hierarchical perspectives, exploitation tactics, and the absence of conventional morals to interpret interpersonal interactions. Manipulators intersperse unethical behavior within their typical conduct, deploying deceptive tactics before resuming a baseline demeanor. The proposed solution leverages Lyapunov theory to establish and maintain Stackelberg equilibria. A Lyapunov-like function supports each asymptotically stable equilibrium, ensuring convergence to a Nash/Lyapunov equilibrium if it exists, inherently favoring no-regret strategies. The existence of an optimal solution is demonstrated via the Weierstrass theorem. The game is modeled as a three-level Stackelberg framework based on Markov chains. At the highest level, manipulators devise strategies that may not sway middle-level manipulated players, who counter with best-reply strategies mirroring the manipulators’ moves. Lower-level manipulators adjust their strategies in response to the manipulated players to sustain the manipulation process. This integration of stability analysis and strategic decision-making provides a robust framework for understanding and addressing manipulation in interpersonal contexts. A numerical example focusing on the oil market and its regulations highlights the findings of this work. Full article

The integration of Connected Vehicles into conventional traffic systems presents significant challenges due to the diverse behaviors and objectives of different drivers. Conventional vehicle drivers typically follow User Equilibrium principles, aiming to minimize their individual travel times without considering the overall network impact. In contrast, Connected Vehicle drivers, guided by real-time information from central authorities or private service providers, can adopt System Optimum strategies or Cournot-Nash oligopoly behaviors, respectively. The coexistence of these distinct player classes in mixed-traffic environments complicates the task of achieving optimal traffic flow and network performance. This paper presents a comprehensive framework for optimizing mixed-traffic road networks through a multiclass traffic assignment model. The framework integrates three distinct types of players: conventional vehicle drivers adhering to User Equilibrium principles, Connected Vehicle drivers following System Optimum principles under a central governing authority, and Connected Vehicle drivers operating under Cournot-Nash oligopoly conditions with access to services from private companies. The methodology includes defining a model to achieve optimal mixed equilibria, designing an algorithm for multiclass traffic assignment, formulating strategic games to analyze player interactions, and establishing key performance indicators to evaluate network efficiency and effectiveness. The framework is applied to a real-world road network, validating its practicality and effectiveness through computational results. The extraction and analysis of computational results are used to propose optimal traffic management policies for mixed-traffic environments. The findings provide significant insights into the dynamics of mixed traffic networks and offer practical recommendations for improving traffic management in increasingly complex urban transportation systems. Full article

The deepening implementation of the energy and carbon market imposes trading requirements on multiple regional integrated energy system participants, including power generation plants, industrial users, and carbon capture, utilization, and storage (CCUS) facilities. Their diverse roles in different markets strengthen the interconnections among these subsystems. On the other hand, the operation of CCUS, containing carbon capture (CS), power-to-hydrogen (P2H), and power-to-gas (P2G), results in the coupling of regional carbon reduction costs with the operation of electricity and hythane networks. In this paper, we propose a regional economic dispatching model of an integrated energy system. The markets are organized in a centralized form, and their clearing conditions are considered. CCUS is designed to inject hydrogen or natural gas into hythane networks, operating more flexibly. A generalized Nash game is applied to analyze the multiple trading equilibria of different entities. Simulations are carried out to derive a different market equilibrium regarding network scales, seasonal load shifts, and the ownership of CCUS. Simulation results in a 39-bus/20-node coupled network indicate that the regional average carbon prices fluctuate from ¥1078.82 to ¥1519.03, and the organization of independent CCUS is more preferred under the proposed market structure. Full article

We start from the fundamental premise that any physical interaction can be interpreted as a game. To demonstrate this, we draw upon the free energy principle and the theory of quantum reference frames. In this way, we place the game-theoretic Nash Equilibrium in a new light in so far as the incompleteness and undecidability of the concept, as well as the nature of strategies in general, can be seen as the consequences of certain no-go theorems. We show that games of the generic imitation type follow a circularity of idealization that includes the good regulator theorem, generalized synchrony, and undecidability of the Turing test. We discuss Bayesian games in the light of Bell non-locality and establish the basics of quantum games, which we relate to local operations and classical communication protocols. In this light, we also review the rationality of gaming strategies from the players’ point of view. Full article

In this study, we examine how the strategies of the players over multiple time scales impact the decision making, resulting payoffs and the costs in non-cooperative strategic games. We propose a dynamic generalized Nash equilibrium problem for non-cooperative strategic games which evolve in multidimensions. We also define an equivalent dynamic quasi-variational inequality problem. The existence of equilibria is established, and a spot electricity market problem is reformulated in terms of the proposed dynamic generalized Nash equilibrium problem. Employing the theory of projected dynamical systems, we illustrate our approach by applying it to a 39-bus network case, which is based on the New England system. Moreover, we illustrate a comparative study between multiple time scales and a single time scale by a simple numerical experiment. Full article