Game Theory Problem Research Articles

The Limits of Our Explanation: A Case Study in Myxococcus xanthus Cooperation

AbstractIn this article, I demonstrate two ways in which our major theories of the evolution of cooperation may fail to capture particular social phenomena. The first shortcoming of our current major theories stems from the possibility of mischaracterizing the cooperative problem in game theory. The second shortcoming of our current major theories is the insensitivity of these explanatory models to ecological and genomic context. As a case study to illustrate these points, I will use the cooperative interaction of a species of myxobacteria called Myxococcus xanthus. M. xanthus cooperate in many areas of their life cycle—in quorum sensing, social motility, fruiting body formation, and predation. I focus in particular on predation as we have not yet discovered an adequate explanation of how they sustain cooperative predation in the face of developmental cheats. In explaining why we have not, I draw generalizable conclusions that shed light on our use of simplified models to explain real-world behaviors in a variety of organisms.

THE PROBLEM OF MODEL ADEQUACY IN THE APPLICATION OF GAME THEORY IN INTERNATIONAL RELATIONS

The article considers the use of game theory in international relations and the risks associated with it. An analysis is made of the possibility of reflecting the same real situations using different game models with different connotations. The concept of the adequacy of the model in relation to the situation is considered, as well as the necessary logical stage of proving this adequacy and the risk of manipulative influence in the absence of such proof. Attention is paid to the phenomenon of the model itself and its relation to the real object of modeling.The opinion is argued about the need to prove the similarity before using the analogy as an argument for attempts to persuade on the basis of this similarity. The mechanism of manipulation is considered in which, by skipping the discussion of the adequacy of the model, it is automatically considered adequate, so the author of the model can impose his own forecasts on the consumer of information regarding the development of events, as well as his own subjective vision of the positivity of the results.As an example, two well-known problems in game theory are considered, actively used for modeling international relations: the Prisoner's Dilemma and the Chicken game. An example of modeling the same hypothetical situation using both games and differences in subjective perception of the same results, which are manifested in the choice of which of these games to use, is given. The opinion is given that although both games can be very useful in the field of international relations, when consuming information which incorporates these and other games, it is necessary to carefully check not only the author's forecasts regarding the development of events, but also the assessment of the positivity of the results in the model.

Vibration based single-objective finite element model updating using cooperative game theory approach

This paper introduces a novel approach that focuses on application of cooperative game theory model for automated finite element model updating. The approach involves transforming the conventional single-objective optimization finite element model updating problem into a game theory problem. Among the different alternatives, a cooperative game model is considered to solve the transformed updating problem. This new approach overcomes the limitations of the conventional single-objective optimization formulation, which include challenges related to selecting appropriate weighting factor of residuals and analysing their influence on optimization results. To demonstrate the effectiveness of the proposed approach, an ultralight fibre reinforced polymer footbridge is considered. The numerical model of the footbridge is updated using the experimentally determined inherent properties (natural frequencies and mode shapes) using the proposed approach. A comparison with the conventional sensitivity-based weighted single objective method reveals that the inclusion of the weighting factor in the optimization process under the cooperative game model method allows for more efficient solution of the single-objective updating optimization problem, while maintaining accuracy and quality in the updated model.

Game Theory and Game Mechanics Design

This paper focuses on the significance of game balance in games and explores the application of game theory concepts for designing and analyzing balanced gameplay. When analyzing instances of games, the paper initially presents the renowned prisoner’s dilemma, a prominent problem in game theory, and delves into diverse strategies along with their corresponding advantages, thereby enabling readers to appreciate the captivating essence of game theory. After that, the paper respectively mentions two individual cases from two different forms of games. The well-known game Rock-Paper-Scissors is a simple strategy game. FPS (First Person Shooter) game is a sort of video game that is a complex strategy game. In analyzing this type of game, the paper draws images to show the imbalance in the game. In the end, the article puts forward the prospect that game theory can contribute to game design. The approach adopted in this study integrates existing research in game theory with practical insights from game design, without delving into extensive theoretical derivations or complex formulas.

ВОПРОСЫ ПРИМЕНЕНИЯ ЧИСЛЕННЫХ И ВЫЧИСЛИТЕЛЬНЫХ МЕТОДОВ В МАТЕМАТИЧЕСКОМ И ТЕОРЕТИКО-ИГРОВОМ МОДЕЛИРОВАНИИ

Computational methods are widely used in mathematical modeling to identify sequences necessary for the desired quantities. Logical and computational operations are used in programming to create computer programs that work with the model in a technical plane. Numerical methods are equally widespread in problems of game theory, where they are used to calculate optimal strategies, display winning probabilities and calculate the effectiveness of selected methods, in order to proceed to a solution using computational methods, the original problem is replaced by a computational algorithm. Mathematical modeling is a theoretical tool and allows you to describe in theory the trends of a particular phenomenon or process, track development trends, outline the relationships and behavior of objects within the desired model. Mathematical modeling can be attributed to experimental scientific methods, since using computer technologies and tools it allows you to conduct a huge number of experiments with models, which in turn allows you to work through many scenarios with different introductory ones.

Quantum 2-Player Games and Realizations with Circuits.

Game theory problems are widely applied in many research areas such as computer science and finance, with the key issue being how to quickly make decisions. Here, we present a novel quantum algorithm for game theory problems based on a continuous quantum walk. Our algorithm exhibits quantum advantage compared to classical game algorithms. Furthermore, we exploit the analogy between the wave function of the Schrödinger equation and the voltage in Kirchhoff's law to effectively translate the design of quantum game trees into classical circuit networks. We have theoretically simulated the quantum game trees and experimentally validated the quantum functionality speedup on classical circuit networks. Due to the robust scalability and stability inherent in classical circuit networks, quantum game trees implemented within this framework hold promise for addressing more intricate application scenarios.

The Prisoner's Dilemma is an Innovative Tool Valid in the Most Varied Situations: some Applications

The paper was born from the intent to highlight the importance of the prisoner's dilemma and its applications. Prisoner's Dilemma is a comprehensive information game proposed in the 1950s by Albert Tucker as a game theory problem. In addition to being extensively studied in this context, the "dilemma" is also quite well known to the non-technical public as an example of a paradox. John Von Neumann, creator of game theory, was also interested in this dilemma, presented to him by the two creators while working at RAND in 1948. In this article, we have applied the prisoner's dilemma to three very different events: the writing of the thesis, its application in the tobacco manufacturers and the role of pricing policies and the prisoner's dilemma.

Optimal Selection and Tracking Of Generalized Nash Equilibria in Monotone Games

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.

Overview of selected reinforcement learning solutions to several game theory problems

This paper collects several applications of reinforcement learning in solving some problems related to game theory. The methods were selected to possibly show variety of problems and approaches. Selections includes Thompson Sampling, Q-learning, DQN and AlphaGo Zero using Monte Carlo Tree Search algorithm. Paper attempts to show intuition behind proposed algorithms with shallow explaining of technical details. This approach aims at presenting overview of the topic without assuming deep knowledge about statistics and artificial intelligence.

A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory

A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory

Consideration of hotspots in the selection of supervision schemes to reduce illegal dumping of construction and demolition waste.

Illegal dumping of construction and demolition waste continues to be a problem hindering circular economy efforts. Controlling illegal dumping necessitates establishing an effective surveillance scheme and investigating the proper penalty value. This problem has previously been described as a game theory problem, with the government and construction contractors as the players. Taking into account illegal dumping hotspots, which can often be identified through topographical and geographical characteristics, is also important when establishing supervision strategies. This study develops an evolutionary game-theoretic model that can assist in devising effective supervision strategies to control the spread of illegal dumping, while taking into consideration hotspots. In specific, this study investigates the suitability of two alternative strategies: police patrols and hybrid monitoring through both patrols and the installation of closed-circuit television cameras in hotspots. The model was applied to two case studies, using parameters informed by real-world contexts, to demonstrate its potential for selecting suitable strategies according to local situations. The results suggest that nine possible scenarios govern the stable evolutionary strategies of game players, with five scenarios in which contractors converge to adopt legal dumping. Accordingly, based on the parameters of the region (hotspot areas, cost of supervision, efficiency of patrols, penalties, etc.), governments would be able to assess which of the strategies would lead to long-term compliance of contractors while also increasing their payoffs. Further analysis allowed to determine the minimum efficiency required, and simulations were performed to demonstrate the influence of different supervision efficiencies and penalties on the evolutionary strategies.

Integrated preference argumentation and applications in consumer behaviour analyses

Consumer preference studies in economics rest heavily on the behavioural interpretation of preference especially in the form of Revealed Preference Theory (RPT). Viewing purchasing decisions as a kind of human reasoning, in this paper we are interested in generalising behaviourism to preference-based argumentation where existing frameworks are arguably governed by the opposing mentalistic interpretation of preference. Concretely our contributions are three-fold. First we re-construct and unify two main approaches to RPT in argumentation terms by developing a Revealed Preference Argumentation (RPA) framework. We show that key RPT-based consumer analyses such as different rationality checks of a consumer behaviour and various kinds of such behaviour's extrapolations can be translated to computational tasks in RPA. RPA is in turn subsumed by the second contribution - an Integrated Preference Argumentation (IPA) framework which fully integrates mentalism and behaviourism. In particular we show that RPA is just a special case of IPA with only revealed preference, while existing preference-based argumentation frameworks can be viewed as IPA frameworks with only stated preference. As the third contribution, we develop a complete set of IPA algorithms and establish their correctness and termination for a general class of IPA frameworks. For demonstration we implement the algorithms in Prolog to obtain an IPA reasoning engine and test the engine with various RPT-based consumer behaviour analyses. In sum, it is argued that the current paper provides not only a theory of Integrated Preference Argumentation, but also a related development tool for future applications of argumentation to behavioural economics - a largely unexplored area so far though Dung used the stable marriage problem in microeconomic game theory to partly motivate the argumentation theory.

Nonlocal fully nonlinear parabolic differential equations arising in time-inconsistent problems

We prove the local well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter t on top of the temporal and spatial variables (s,y) and thus the problem could be considered as a flow of equations. The nonlocality comes from the dependence on the unknown function and its first- and second-order derivatives evaluated at not only the local point (t,s,y) but also at the diagonal line of the time domain (s,s,y). Such equations arise from time-inconsistent problems in game theory or behavioral economics, where the observations and preferences are (reference-)time-dependent. We first study the linearized version of the nonlocal PDEs with an innovative construction of appropriate norms and Banach spaces and contraction mappings over which. With fixed-point arguments, we obtain the solvability of nonlocal linear PDEs and establish a Schauder-type prior estimate for the solutions. Then, by the linearization method, we establish the well-posedness under the fully nonlinear case. Moreover, we reveal that the solution of a nonlocal fully nonlinear parabolic PDE is an adapted solution to a flow of second-order forward-backward stochastic differential equations.

A hybrid optimisation method for intercepting satellite trajectory based on differential game

AbstractThis study addresses orbit design and optimisation for the situation of satellite interception in which the target spacecraft is capable of manoeuvring using continuous magnitude restricted thrust. For the purpose of designing a long-range continuous thrust interception orbit, the orbit motion equations of two satellites with J2 perturbation are constructed. This problem is assumed to be a typical pursuit-evasion problem in differential game theory; using boundary constraint conditions and a performance index function that includes time and fuel consumption, the saddle point solution corresponding to the bilateral optimal is derived, and then this pursuit-evasion problem is transformed into a two-point boundary value problem. A hybrid optimisation method using a genetic algorithm (GA) and sequential quadratic programming (SQP) is derived to obtain the optimal control strategy. The proposed model and algorithm are proved to be feasible for the given simulation cases.

Decision-Focused Learning for Inverse Noncooperative Games: Generalization Bounds and Convergence Analysis

Finding the equilibrium strategy of agents is one of the central problems in game theory. Perhaps equally intriguing is the inverse of the above problem: from the available finite set of actions at equilibrium, how can we learn the utilities of players competing against each other and eventually use the learned models to predict their future actions? Instead of following an estimate-then-predict approach, this work proposes a decision-focused learning (DFL) method that directly learns the utility function to improve prediction accuracy. The game's equilibrium is represented as a layer and integrated into an end-to-end optimization framework. We discuss the statistical bounds of covering numbers for the set of solution functions corresponding to the solution of a generic parametric variational inequality. Also, we establish the generalization bound for the set of solution functions with respect to the smooth loss function with an improved rate. Moreover, we proposed an algorithm based on the iterative differentiation strategy to forward and backpropagate through the equilibrium layer. The convergence analysis of the proposed algorithm is established. Finally, We numerically validate the proposed framework in the utility learning problem among the agents whose utility functions are approximated by partially input convex neural networks (PICNN).

Game theory-based maximum likelihood method for finite-element-model updating of civil engineering structures

Finite element modelling is performed to numerically predict the behaviour of civil engineering structures. Due to the different assumptions adopted during the modelling phase, this initial model does not always reflect adequately the actual structural behaviour. In this context, the results of experimental structural dynamic properties can be used to improve initial numerical model via the implementation of the so-called finite element model updating method. After this process, the updated model better reflects the actual structural behaviour. Due to its simplicity, for practical engineering applications, the updating process is usually performed considering the maximum likelihood method. According to this approach, the updating problem may be formulated as the combination of two sub-problems: (i) a bi-objective optimization sub-problem; and (ii) a decision-making sub-problem. The bi-objective function is usually defined in terms of the residuals between the experimental and numerical modal properties. As optimization method, nature-inspired computational algorithms have been usually considered due to their high efficiency to cope with non-linear optimization problems. Despite this extensive use, this method presents two main limitations: (i) the high simulation time required to compute the Pareto optimal front; and (ii) the necessity of solving a subsequent decision making problem (the selection of the best solution among the different elements of the Pareto front). In order to overcome these limitations, in this paper game theory has been adopted as computational tool to improve the performance of the updating process. For this purpose, the updating problem has been re-formulated as a game theory problem considering three different game models: (i) non-cooperative; (ii) cooperative; and (iii) evolutionary. Finally, the performance of proposal has been assessed when it is implemented for the model updating of a laboratory footbridge. As result of this study, game theory has been shown up as efficient tool to improve the performance of the updating process under the maximum likelihood method since it allows a direct estimation of the solution reducing the simulation time without compromising the accuracy of the result.

Complex interactions promote the frequency of cooperation in snowdrift game

The emergence and maintains of cooperation in social dilemmas is one of the most popular problem in evolutionary game theory. In this paper, we consider the influence of complex interactions in evolutionary game theory. We consider a situation that some individuals may get additional benefits in snowdrift game without the detriment of the co-player because of difference in status, like good reputation of assisting the weak. We find that the replicator dynamics of asymmetric snowdrift game have one boundary stable equilibrium, which is affected by the asymmetry of the interaction and the proportion of strong individuals. The stable equilibrium shows that strong individuals are willing to choose cooperation and weak individuals are willing to choose defection. In this case, the average frequency of cooperation is not less than the equilibrium frequency of cooperators with only symmetric interactions. In addition, complex interactions in spatially organized populations causes weak individuals to mimic the strategies of strong neighbors. Strong individuals with great benefit are willing to choose cooperation, and cooperators create a cluster with a core of strong cooperators and weak cooperators outside. For a wide range of parameters, the frequency of cooperation among weak individuals grows dramatically. Complex interactions frequently improves the frequency of cooperation while decreasing the frequency of cooperation slightly only over a narrow range of parameter. Because of the high frequency of cooperation, complex interactions can roughly solve the paradox in the snowdrift game.

The Costliness of US Residency Applications: Moving Toward Preference Signaling and Caps.

The Costliness of US Residency Applications: Moving Toward Preference Signaling and Caps.

Regret-Based Nash Equilibrium Sorting Genetic Algorithm for Combinatorial Game Theory Problems with Multiple Players.

We introduce a regret-based fitness assignment strategy for evolutionary algorithms to find Nash equilibria in noncooperative simultaneous combinatorial game theory problems where it is computationally intractable to enumerate all decision options of the players involved in the game. Applications of evolutionary algorithms to non-cooperative simultaneous games have been limited due to challenges in guiding the evolutionary search toward equilibria, which are usually inferior points in the objective space. We propose a regret-based approach to select candidate decision options of the players for the next generation in a multipopulation genetic algorithm called Regret-Based Nash Equilibrium Sorting Genetic Algorithm (RNESGA). We show that RNESGA can converge to multiple Nash equilibria in a single run using two- and three- player competitive knapsack games and other games from the literature. We also show that pure payoff-based fitness assignment strategies perform poorly in three-player games.

Back Cover

Previous article FreeBack CoverPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreOr: The Game within the GameThe final week of the NFL’s first 17-game regular season includes a set of circumstances that could descend the sport into the absurd. The Indianapolis Colts and the Jacksonville Jaguars play on Sunday afternoon. The Las Vegas Raiders and the Los Angeles Chargers play on Sunday night. Either the Raiders or Chargers would make the playoffs by winning. But if the Jaguars beat the Colts, both the Chargers and Raiders would advance in the event of a tie. It raises the outlandish possibility that both teams could spend the game kneeling, punting or spiking the football with designs of a 0–0 tie. To football fans, it’s a ridiculous scenario in which two teams could make a behind the scenes deal to secure a tie and playoff spot. To economists, it’s a game theory problem known as a prisoner’s dilemma. “It’s really, really hard to sustain this collusion,” said Benjamin Polak, an economics professor at Yale. “There’s an incentive to defect from that agreement and try and win at the last minute.”(Suggested by Allen Sanderson) Previous article DetailsFiguresReferencesCited by Journal of Political Economy Volume 130, Number 7July 2022 Article DOIhttps://doi.org/10.1086/721277 Views: 394Total views on this site © 2022 The University of Chicago. All rights reserved.PDF download Crossref reports no articles citing this article.