Game-theoretic Concepts Research Articles

Computational Game Unit Balancing based on Game Theory

Optimizing game elements through iterative human playtests can be time-consuming and insufficient for games with complex intransitive mechanics. Imbalances in games often require the release of numerous balance patches. We present a computational method for making each game unit equally preferable against a uniform play strategy. We leverage concepts from game theory to model intricate relationships among intransitive entities. Matching units against each other is modeled as a symmetric zero-sum game, where unit selection represents a strategy and the error is quantified using payoff values derived from unit parameters. The algorithm takes the initial unit parameters provided by the game designer and optimizes them with minimal changes using gradient descent. Consequently, the payoff matrix converges to a state where a uniform strategy is a near Nash equilibrium, ensuring that each unit is equally preferable under the optimized condition. We implemented a testing environment based on fictitious play and verified our results on different scenarios. While the majority of game theory research focuses on finding optimal strategies given specific environmental conditions, this paper takes a different perspective within the context of game design. We explore game theoretic concepts to address the goal of designing environments that lead to desired strategy choices.

Evolutionary Game Theory: A General Review

This article explores the Evolutionary Game Theory (now EGT), encompassing its historical underpinnings, recent advancements, and future potential. Originating in the 1970s through the pioneering work of John Maynard Smith and George R. Price, EGT leverages game-theoretic concepts to elucidate the evolution of strategies within various populations across biological, economic, and social domains. Notably, recent progress has seen the integration of advanced large language models (LLMs) such as GPT-3.5 and GPT-4 into agent-based simulations, thereby enriching the authenticity and intricacy of strategic interactions. Additionally, the study addresses the complexities associated with modeling diverse behaviors and bridging the insights derived from LLMs to practical applications in fields like biology, healthcare, education, and social sciences. Furthermore, it underscores the significance of interdisciplinary collaboration and innovative methodologies in addressing the multifaceted challenges within EGT. Finally, the article contemplates the potential avenues for future research, emphasizing the fusion of EGT with real-world applications and the necessity for comprehensive models that encompass the complexities of evolutionary dynamics in adaptive systems.

Limited trust in social network games.

We consider agents in a social network competing to be selected as partners in collaborative, mutually beneficial activities. We study this through a model in which an agent i can initiate a limited number k_{i}>0 of games and selects partners from its one-hop neighborhood. Each agent can accept as many games offered by its neighbors. Each game signifies a productive joint activity, and the players attempt to maximize their individual utilities. Unsurprisingly, more trustworthy agents, as measured by the game-theoretic concept of limited-trust, are more desirable as partners. Agents learn about their neighbors' trustworthiness through interactions and their behaviors evolve in response. Empirical trials conducted on realistic social networks show that when given the option, many agents become highly trustworthy; most or all become highly trustworthy when knowledge of their neighbors' trustworthiness is based on past interactions rather than known a priori. This trustworthiness is not the result of altruism; instead, agents are intrinsically motivated to become trustworthy partners by competition. Two insights are presented: First, trustworthy behavior drives an increase in the utility of all agents, where maintaining a relatively minor level of trustworthiness may easily improve net utility by as much as 14.5%. If only one agent exhibits a small degree of trustworthiness among self-centered ones, then it can increase its personal utility by up to 25% in certain cases. Second, and counterintuitively, when partnership opportunities are abundant, agents become less trustworthy.

Modeling Rationality: Toward Better Performance Against Unknown Agents in Sequential Games.

Opponent modeling is necessary for autonomous agents to capture the intents of others during strategic interactions. Most previous works assume that they can access enough interaction history to build the model. However, it may not be realistic. To solve this problem, we present a novel rationality-consistent opponent modeling (ROM) method for games with imperfect information. In our approach, a game-theoretical concept of consistence about rationality is proposed to take advantage of the characteristic of imperfect information sequential games that rational behavior at disjoint information sets is correlated through anticipated opponent's behavior. With the correlation between different information sets, agents could infer the opponents' strategies at information sets correlated to observed behavior. To exploit the correlation, ROM attempts to conduct reasoning from the opponent's perspective and rationalize its past behavior. In this way, ROM acquires the ability to better adapt to different opponents and achieves a more accurate opponent model with insufficient observation history, which is verified by experiments in different settings. A heuristic adaptation approach is also applied in ROM, which updates the opponent model in an online manner and significantly reduces the computation cost. We evaluate ROM in both a grid world game and a poker game. Compared with other opponent modeling methods, ROM shows better performance and has more accurate predictions in both games against different types of opponents with limited action interactions. Experimental results also show that ROM's time cost is significantly reduced through heuristic adaptation.

How flexible parasites can outsmart their hosts for evolutionary dominance

Antagonistic coevolution between hosts and parasites substantially impacts community structure, with parasites displaying fluctuating selection or arms race dynamics during coevolution. The traditional matching alleles (MA) and gene-for-gene (GFG) models have been used to describe the dynamics and interaction of host-parasite coevolution, with these models assuming that parasites adopt a single strategy when competing with other parasites. We present a nonlinear dynamic population model that challenges this assumption, showing how a parasite that is disadvantaged under either the MA or the GFG model can win the competition by switching between the two losing strategies based on an external environmental cue, internal processes, or stochastic decision-making. This counterintuitive outcome is analogous to Parrondo's paradox, a game-theoretic concept that shows how alternating between two losing strategies can result in a winning outcome. Our numerical experiments support the validity of this model, suggesting that parasites can greatly benefit from maximum flexibility in their interactions with hosts. The flexibility of successful parasites puts an extra burden on the host defenses that have to adapt to different strategies of the parasites. These findings contribute to a deeper understanding of the coevolution of parasites and hosts, with broad implications for the evolution of complex ecological systems. Published by the American Physical Society 2024

FairPlay: A Multi-Sided Fair Dynamic Pricing Policy for Hotels

In recent years, popular touristic destinations face overtourism. Local communities suffer from its consequences in several ways. Among others, overpricing and profiteering harms local societies and economies deeply. In this paper we focus on the problem of determining fair hotel room prices. Specifically, we put forward a dynamic pricing policy where the price of a room depends not only on the demand of the hotel it belongs to but also on the demand of: (i) similar rooms in the area and (ii) their hotels. To this purpose, we model our setting as a cooperative game and exploit an appropriate game theoretic solution concept that promotes fairness both on the customers' and the providers' side. Our simulation results involving price adjustments across real-world hotels datasets, confirm that ours is a fair dynamic pricing policy, avoiding both over- and under-pricing hotel rooms.

Maxileximin Envy Allocations and Connected Goods

Fair allocation of indivisible goods presents intriguing challenges from both a social choice perspective and an algorithmic standpoint. Due to the indivisibility of goods, it is common for one agent to envy the bundle of goods assigned to another agent and, indeed, envy-free solutions do not exist in general. In line with the classical game-theoretic concept of Nucleolus in coalitional games, we propose that a fair allocation should minimize the agents’ dissatisfaction profile in a lexicographic manner, where the dissatisfaction of an agent is defined as her maximum envy towards other agents. Therefore, we seek allocations that minimize the maximum envy. In cases where multiple solutions have an equal maximum value, we minimize the second-worst value, and so on. Additionally, as is customary in fair division problems, we also consider an efficiency requirement: among the allocations with the best agents’ dissatisfaction profile, we prioritize those that maximize the sum of agents’ utilities, known as maximum social welfare. Such allocations, referred to as maxileximin allocations, always exist. In this study, we analyze the computational properties of maxileximin allocations in the context of fair allocation problems with constraints. Specifically, we focus on the Connected Fair Division problem, where goods correspond to the nodes of a graph, and a bundle of goods is allowed if the subgraph formed by those goods is connected. We demonstrate that the problem is F∆P2 -complete, even for instances with simple graphical structures such as path and star graphs. However, we identify islands of tractability for instances with more intricate graphs, such as those having bounded treewidth, provided that the number of agents is bounded by a fixed number and utility functions use small values.

Automated workflow generation supporting the value stream design of reconfigurable robot assembly cells

The paper addresses the automated generation of value stream optimized assembly workflows for reconfigurable robot cells. The focus is on the generation of asynchronous concurrent action workflows from assembly task descriptions. The main motivation is to enable automated search for optimized solutions within the enormous design spaces of these systems which results from their structural and procedural configurability. The proposed approach conducts task assignment, task sequencing and logical task planning (AI Planning) for multiple agents. The approach combines existing methods from the distinct research fields of robot task sequencing and discrete task planning. The contribution of the research is twofold. Firstly, the paper proposes a generic domain meta model enabling automated workflow generation for multi-agent assembly tasks. Secondly, a workflow generation approach based on artificial intelligence planning combined with the game-theoretic concept of extensive form games is presented. The approach iteratively generates a cooperative strategy for acting agents which is subsequently optimized in terms of individual strategies. The obtained logical action plans are further transformed into parametric concurrent action schedules to support downstream design activities. Both the meta model and the workflow generation approach are applied in a case study and provide valuable information on achievable assembly speedup.

Cost allocation in CO2 transport: A multi-actor perspective: A general model to evaluate costs in infrastructure construction

This paper provides a multi-actor perspective on the realization of new infrastructures, motivated by the necessity for infrastructures to support the ongoing climate and energy transition in general, and CO2 transport infrastructures for carbon capture, utilization and storage (CCUS) in particular. We develop a general model to represent infrastructures that allows for a unique decomposition into ‘elementary infrastructure components’ based on heterogeneous user requirements. Notably, it incorporates a cost function with a very generic and adaptable structure, for which we can still explicitly determine the costs of each individual component. As a direct consequence an intuitive cost allocation rule is obtained: equal component cost sharing. This allocation rule is in line with existing game-theoretic concepts and satisfies the desirable properties of advantageous scaling and coalitional rationality. Advantageous scaling guarantees that the costs allocated to each existing user do not increase if the number of users grows larger and coalitional rationality ensures that there is no subgroup of infrastructure users that would have a financial reason to object to the cost allocation. Additionally, we examine the application of our model to a prospective CO2 transport infrastructure for CCUS in the port of Rotterdam and the adjoining industry area.

Explainable Machine Learning for Credit Risk Management When Features are Dependent

ABSTRACT Complex Machine Learning (ML) models used to support decision-making in peer-to-peer (P2P) lending often lack clear, accurate, and interpretable explanations. While the game-theoretic concept of Shapley values and its computationally efficient variant Kernel SHAP may be employed for this aim, similarly to other existing methods, the latter makes the assumption that the features are independent. The assumption of uncorrelated features in credit risk management is fairly restrictive and, thus, prediction explanations coming from correlated features might result in highly misleading Shapley values, even when considering simple models. We therefore propose an evaluation of different dependent-feature estimation methods of Kernel SHAP for classification purposes in credit risk management. We show that dependent-feature estimation of Shapley values can improve the understanding of true prediction explanations, their robustness and is essential for better identifying the most relevant variables to default predictions coming from black-box ML models.

Fair collaborative vehicle routing: A deep multi-agent reinforcement learning approach

Collaborative vehicle routing occurs when carriers collaborate through sharing their transportation requests and performing transportation requests on behalf of each other. This achieves economies of scale, thus reducing cost, greenhouse gas emissions and road congestion. But which carrier should partner with whom, and how much should each carrier be compensated? Traditional game theoretic solution concepts are expensive to calculate as the characteristic function scales exponentially with the number of agents. This would require solving the vehicle routing problem (NP-hard) an exponential number of times. We therefore propose to model this problem as a coalitional bargaining game solved using deep multi-agent reinforcement learning, where – crucially – agents are not given access to the characteristic function. Instead, we implicitly reason about the characteristic function; thus, when deployed in production, we only need to evaluate the expensive post-collaboration vehicle routing problem once. Our contribution is that we are the first to consider both the route allocation problem and gain sharing problem simultaneously — without access to the expensive characteristic function. Through decentralised machine learning, our agents bargain with each other and agree to outcomes that correlate well with the Shapley value — a fair profit allocation mechanism. Importantly, we are able to achieve a reduction in run-time of 88%.

Shapley-Value-Based Hybrid Metaheuristic Multi-Objective Optimization for Energy Efficiency in an Energy-Harvesting Cognitive Radio Network

Energy efficiency and throughput are concerns for energy-harvesting cognitive radio networks. However, attaining the maximum level of both requires optimization of sensing duration, harvested energy, and transmission time. To obtain the optimal values of these multiple parameters and to maximize the average throughput and energy efficiency, a new hybrid technique for multi-objective optimization is proposed. This hybrid optimization algorithm incorporates a Shapley value and a game theoretic concept into metaheuristics. Here, particle swarm optimization grey wolf optimization (PSOGWO) is selected as the source for the advanced hybrid algorithm. The concept of the unbiased nature of wolves is also added to PSOGWO to make it more efficient. Multi-objective optimization is formulated by taking a deep look into combined spectrum sensing and energy harvesting in a cognitive radio network (CSSEH). The Pareto optimal solutions for the multi-objective optimization problem of energy efficiency and throughput can be obtained using PSOGWO by updating the velocity with the weights. In the proposed Shapley hybrid multi-objective optimization algorithm, we used Shapley values to set up the weights that, in turn, updated the velocities of the particles. This updated velocity increased the ability of particles to reach a global optimum rather than becoming trapped in local optima. The solution obtained with this hybrid algorithm is the Shapley–Pareto optimal solution. The proposed algorithm is also compared with state-of-the-art PSOGWO, unbiased PSOGWO, and GWO. The results show a significant level of improvement in terms of energy efficiency by 3.56% while reducing the sensing duration and increasing the average throughput by 21.83% in comparison with standard GWO.

Game Theory Classification in Cybersecurity: A Survey.

Cyber security is a field designed to protect computers connected to the internet from attacks, and hence prevent unauthorized users from accessing the sensitive data present in it. Lately, it has witnessed intensified research from both academia and the industry. However, traditional cyber security technologies still face inadequacies in tackling the ever-dynamic frontier of cyber-attacks as a result of inability to incorporate behavioral tendencies of adaptive and intelligent adversaries in their security models. Game theory is often the first choice as a mathematical tool among researchers and industry practitioners for modeling conflict and cooperation among intelligent and rational actors. With its rich modeling and analytical techniques, and ability to forecast cyber-attacks and optimal defense strategies accurately, cyber security attacks are much easier to mitigate than traditional approaches. This paper reviews several game theoretic concepts and applications in the never-ending dynamic contradiction between the defender and the attacker. These concepts are classified according to applications and scenarios. Present research challenges are discussed and future directions for the need to incorporate attackers risk attitude as a determinant factor of the Nash Equilibrium is emphasized in the malicious insider threat scenario.

Good-for-Game QPTL: An Alternating Hodges Semantics

An extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in game-theory and allows the resulting logic to naturally express game-theoretic concepts. Inspired by the work on logics of dependence and independence, we provide a new compositional semantics for QPTL that allows for expressing such functional dependencies among variables. The fragment where only restricted quantifications are considered, called behavioral quantifications , allows for linear-time properties that are satisfiable if and only if they are realisable in the Pnueli-Rosner sense. This fragment can be decided, for both model checking and satisfiability , in 2 Exp Time and is expressively equivalent to QPTL , though significantly less succinct.

On the solution of games with arbitrary payoffs: An application to an over‐the‐counter financial market

AbstractThis paper defines a variety of game theoretic solution concepts in the language of soft set theory. We begin by defining the Nash equilibrium in pure strategies. We assume that the gains of the players are totally ordered and non‐desirable alternatives are absent. Moreover, we introduce the notions of strong and semi‐strong utility. These two completely new notions, serve as a mechanism for converting non‐ordered gains into totally ordered ones. We define the Nash equilibrium in mixed strategies in a general framework by introducing the notion of an extended game and strategy space. We finally define the Nash solution to cooperative bargaining games within the framework of soft set theory, illustrate a practical application to an over‐the‐counter financial market, and provide a detailed numerical example.

Understanding the compositional control on electrical, mechanical, optical, and physical properties of inorganic glasses with interpretable machine learning

Despite the use of inorganic glasses for more than 4500 years, the composition–property relationships in these materials remain poorly understood. Here, exploiting largescale experimental data and machine learning, we develop composition–property models for twenty five properties, which are interpreted using game-theoretic concepts. Specifically, we use a dataset consisting of ∼275,000 glass compositions comprising of 221 different components and 25 properties. This is by far the largest model developed in the literature. The analysis reveals that the glass components, such as network formers, modifiers, and intermediates, play distinct roles in governing the optical, physical, electrical, and mechanical properties of glasses. Interestingly, these components exhibit interdependence, the magnitude of which is different for different properties. While the physical origins of some of these interdependencies could be explained using known phenomena, the majority of the remaining ones remain to be explored. Thus, our work paves the way for decoding the “glass genome”, which can provide the recipe for discovering novel glasses while also shedding light on the fundamental factors governing the composition–structure–property relationships.

Challenges and review of goal-oriented requirements engineering based competitive non-functional requirements analysis

Modelling and analysis in software system development can be especially challenging in early requirements engineering (RE), where high-level system non-functional requirements are discovered. In the early stage, hard to measure non-functional requirements are critical; understanding the interactions between systems and stakeholders is key to system success. Goal-oriented requirements engineering (GORE) has been successful in dealing with the issues that may arise during the analysis of requirements. While assisting in the analysis of requirements, i* goal model is the only framework available among the many GORE models, emphasising socio-technical domains such as stakeholders/actors/players, goals/objectives, dependencies and design options/alternatives. Most current approaches to goal-model analysis use quantitative methods or formal information that is hard to gather in early RE, or produce analysis results automatically over models. In real-time competitive applications, the goals of various stakeholders are conflicting in complex systems. Also, each of the system goals have various alternative design options for the systems and optimal selection of goal-oriented requirements faces several challenges in requirements-based engineering. Hence, effective decision-making frameworks are necessary to capture the real issues to achieve multi-objective optimisation of interdependent actors. To obtain an optimum strategy for interdependent actors in the i* goal model must balance the opposing goals reciprocally. To achieve this, the model needs to go beyond the analytical decision-making tools such as sensitivity analysis tasks, cost-effective analysis process, game-theoretic concepts and analytical hierarchical process. To address these requirements, this paper discusses the design of novel frameworks for an agent-based goal model analysis in requirements engineering. The objective of this paper is to provide a brief and comprehensive review of the major efforts undertaken along this line of research. In this paper we have prepared literature review of the concepts, terminology, significance and techniques of Goal oriented requirements engineering in the context of non-functional requirements analysis.

Distributed Games and Nash Equilibrium Seeking in Multiagent Systems Over Networks: An Introduction to the Special Issue

This special issue provides an introduction to game-theoretic decision making in multiagents over networks—a research area that has exploded in the systems and control community over the past few years. There has been an almost exponentially growing interest in the application of game-theoretic concepts and tools in control, multiagent systems, and networks. This is partly due to their wide application: from smart grids, road traffic control, communication networks, and network congestion control, to social networks and sensor networks.

A Methodological Framework for Parametric Combat Analysis

This work proposes, explains, and demonstrates a methodological framework which affords decision-makers and policy-makers the opportunity to accelerate the tempo and enhance the quality of the U.S. Department of Defense acquisitions community. The effective implementation of this framework will augment the warfighting capability of the U.S. Department of Defense against peer competitors and advance the security posture of the United States. This work provides a theoretical foundation for explaining the distribution of potential outcomes for certain types of warfare while contextualizing the research to the space domain. This framework utilizes reliability models to account for natural attrition while using combat models to account for induced attrition. The use of game-theoretic concepts enables the evaluation of heterogeneous force structures.

A Methodological Framework for Parametric Combat Analysis

This work proposes, explains, and demonstrates a methodological framework which affords decision-makers and policy-makers the opportunity to accelerate the tempo and enhance the quality of the U.S. Department of Defense acquisitions community. The effective implementation of this framework will augment the warfighting capability of the U.S. Department of Defense against peer competitors and advance the security posture of the United States. This work provides a theoretical foundation for explaining the distribution of potential outcomes for certain types of warfare while contextualizing the research to the space domain. This framework utilizes reliability models to account for natural attrition while using combat models to account for induced attrition. The use of game-theoretic concepts enables the evaluation of heterogeneous force structures.