Game Theory Concepts Research Articles

Game theoretic equilibria and the evolution of learning

Equilibrium concepts in game theory can be justified as the outcomes of some plausible learning rules. Some scholars have sought a deeper kind of justification arguing that learning rules which do not find equilibria of a game will not be evolutionarily successful. This article presents and examines a model of evolving learning rules. The results are mixed for learning rules that lead to equilibria, showing that they are often successful, but not strongly stable. It is also shown that evolved learning rules, when taken in isolation, may not lead to equilibria. This is a case of reflexive modelling; where game theoretic models are used to assess other features of game theory. I argue that it is possible for reflexive modelling to provide a weak form of justification, but that it falls short in this case.

A Simple but Efficient Scheme for Reliable Connectivity and High Performance in Ad-hoc Wireless Networks

This paper presents a simple but efficient scheme incorporating a reputation-based approach and a cross-layer approach, called the SIM scheme, for maintaining reliable connectivity and high performance in ad-hoc wireless networks. The SIM scheme incorporates the following two things: an ad-hoc routing scheme with a reputation-based approach exploiting the game theory concept based on an evolutionarily stable strategy, and a cross-layer approach between the network layer and the transport layer employing a reputation-based approach.

Evolutionary Games and Periodic Fitness

One thing that nearly all stability concepts in evolutionary game theory have in common is that they use a time-independent fitness matrix. Although this is a reasonable assumption for mathematical purposes, in many situations in real life it seems to be too restrictive. We present a model of an evolutionary game, driven by replicator dynamics, where the fitness matrix is a variable rather than a constant, i.e., the fitness matrix is time-dependent. In particular, by considering periodically changing fitness matrices, we model seasonal effects in evolutionary games. We discuss a model with a continuously changing fitness matrix as well as a related model in which the changes occur periodically at discrete points in time. A numerical analysis shows stability of the periodic orbits that are observed. Moreover, trajectories leading to these orbits from arbitrary starting points synchronize their motion in time. Several examples are discussed.

A Nonlinear Interval Model for Water and Waste Load Allocation in River Basins

In this paper, a new methodology is proposed for simultaneous allocation of water and waste load in river basins. A nonlinear interval number optimization model is used to incorporate the uncertainties of model inputs and parameters. In this methodology, the bounds of the uncertain inputs are only required, not necessarily knowing their probability density or fuzzy membership functions. In the proposed model, the existing uncertainties in water demands and monthly available water are considered in the optimization model. Also the economic and environmental impacts of water allocation to the agricultural water users are taken into account. To have an equitable water and waste load allocation, benefits are reallocated to water users using some solution concepts of the cooperative game theory. Results of applying the methodology to the Dez river system in south-western part of Iran show its effectiveness and applicability for water and waste load allocation in an uncertain environment.

Pay-as-bid versus marginal pricing: The role of suppliers strategic behavior

This paper illustrates how a generator profit may be affected by the pricing method of an oligopoly market model. Through utilizing a bilevel optimization technique and game theory concepts, Supply Function Equilibria (SFE) of pay-as-bid pricing (PABP) and marginal pricing (MP) mechanisms are derived. Theoretically, it is demonstrated that in the presence of strategic interaction, the generator optimal bidding strategy and the market clearing price are higher under PABP as compared with MP. In addition, the probability distribution patterns of expected loss and profit of each generator are constructed by simulating a multiperiod market under PABP and MP rules. It is shown that a generator has a higher expected loss or profit under PABP in unconstrained networks. However, the generator may gain less expected loss or profit if its physical location or transmission limitations are considered.

An integrative case study approach between game theory and Pareto frontier concepts for the transboundary water resources allocations

Summary In the context of transboundary issues, this paper introduces a composite water resources allocation approach that integrates both game theory and Pareto frontier concepts over the case of the Euphrates and Tigris Rivers. The proposed approach searches for an acceptable and viable solution set over the Pareto Frontier Surface via game theory based rationality constraints. For this purpose, the used base model is the Euphrates and Tigris River Basin Model, which is a linear programming model maximizing net economic benefits while optimally allocating scarce water resources in the basin. Results indicate that game theory based strategies and associated constraints provide a determinative backbone for an efficient and effective use of generated Pareto Frontier Surfaces. Additionally, estimated marginal values imply that the upstream countries have upper hand positions regarding their geographic and climatic contexts. After all the generation schemes, it appears that Turkey is the critical partner for inclusion into any form of coalition in the Euphrates and Tigris River Basin.

Cooperative Game Theory: Basic Concepts and Computational Challenges

Cooperative game theory studies situations in which agents can benefit by working together. This article outlines the key concepts of cooperative game theory, and discusess the challenges that arise in applying these in AI applications.

Application of strategic fuzzy games to wage increase negotiation and decision problems

We propose a flexible decision support scheme which could be used in managing the wage negotiation between employers and employees. This scheme uses fuzzy inference systems and game theory concepts in arriving at decisions on future wage increase which could be more mutually agreeable. For example, rather than specifying 5% yearly increase of wages, we propose that the uncertain factors which are mostly difficult to predict and that could affect wage decisions need to be taken into consideration by the wage formula. These include business revenues or (profit), inflation rate, number of competitors, cost of production, and other uncertain factors that may affect business operations. The accuracy of the fuzzy rule base and the game strategies will help to mitigate the adverse effects that a business may suffer from these uncertain factors. Based on our scheme, we propose that employers and employees should calculate their future wage by using a fuzzy rule base and strategies that take into consideration these uncertain variables. The proposed approach is illustrated with a case study and the procedure and methodology may be easily implemented by business organizations in their wage bargaining and decision processes.

Enhancing the Network Security Using Amalgam Games

This paper presents a new modeling method to enhance the network security using game theory. Reconnaissance is applied as a game strategy to obtain more information about the enemy’s strategic intentions. To model the framework and analyze to defend the network attacks using various game nets. The game issues are solved with the help of game theory concepts. The course of action for a player in multi-player game environment with the mixed strategy is determined. Finally, the Nash equilibrium is computed and best-response strategies for the players (administrator and attacker) are found. It proves how the strategies are realistic and how the administrators can use these results to enhance the security of their network .

The Structure of Financial Supervision: Consolidation or Fragmentation for Financial Regulators? A Game Theoretical Perspective

Consolidation or fragmentation for financial regulators? This debate has gained importance since the 2007-2009 financial crisis. The financial services sector has changed considerably over the last 25 years. Financial institutions have evolved from domestic firms engaged in distinct insurance, securities, and banking services into integrated financial services conglomerates offering a broad range of financial products across the globe. These conglomerates and their products now appear even in the most unexpected places, wearing all manner of disguises, and the task of regulating them has grown astronomically. Given these developments, an assessment of the architecture of financial regulators in different parts of the world is long overdue. This paper aims to assess the existing structures of financial supervision using game theory concepts. The paper develops a game theory matrix describing how two regulators working in the same field are expected to interact with each other. Possible market failures and possible solutions are identified and applied in order to assess the existing financial regulatory structures. The results of this analysis help shed light on why countries keep on switching, in what seems like a random move, from one financial supervisory structure to the other. The paper concludes with an application in Public Choice theory providing a possible solution to the problem of regulators’ incentives identified by this paper, a problem which might lead to lack of regulation which in turn could result in a financial crisis.

A new evolutionary approach for computing Nash equilibria in bimatrix games with known support

AbstractIn this paper, we present the application of the Differential Evolution (DE) algorithm to the problem of finding approximate Nash equilibria in matrix, non-zero sum games for two players with finite number of strategies. Nash equilibrium is one of the main concepts in game theory. It may be classified as continuous problem, where two probability distributions over the set of strategies of both players should be found. Every deviation from the global optimum is interpreted as Nash approximation and called ε-Nash equilibrium. The main advantage of the proposed algorithm is self-adaptive mutation operator, which direct the search process. The approach used in this article is based on the probability of chosing single pure strategy. In optimal mixed strategy, every strategy has some probability of being chosen. Our goal is to determine this probability and maximize payoff for a single player.

An Evolutionary Game Theory Approach for Intelligent Patrolling

In order to achieve a secure country, many security policies and strategies have been implemented and numerous security force s have been enlisted such as regular police forces, Army, and Navy, among others. Each security force has different roles and responsibilities. One important area of concern related to national security is border security. Border protection is a chall enging problem due to the different types of illegal activity that must to be controlled such as drug smuggling, terrorist attacks, illegal immigration, etc. One common approach to achieve border security is patrolling. Patrolling can be defined as the act of traveling an area in regular intervals in order to secure it against different threats. This paper presents a hybrid method that combines an evolutionary approach and game theory concepts in order to define the multi-agent patrolling strategy that simultaneously optimizes maximum idleness, infiltration ratio, and total patrolling cost.

A Decomposition of the Atkinson Index through the Shapley Value

This paper studies the economic inequality as a phenomenon resulting from two variables: The variable of responsibility which depends on the agents’ performance in the economy, and the variable of opportunity which is independent of the individuals’ performance in the economy. Identifying the contribution of the inequality of opportunity in the total inequality as the problem to be measured, we propose a decomposition of the Atkinson inequality index, by using one of the central solution concepts of cooperative game theory, called the Shapley value.

A survey on computation methods for Nash equilibrium

A dominant solution concept of non-cooperative game theory is the concept of Nash equilibrium. A Nash equilibrium is a strategy profile from where unilateral deviations do not pay. A nice property of this concept is the well known fact that every finite game has at least one Nash equilibrium. The proof given by Nash (1950) is based on Brouwer fixed point theorem which is very non-constructive. A natural question to ask is whether Nash equilibrium can be computed efficiently. This is still unknown in terms of complexity. Very recently (Daskalakis et al., 2006), it has been shown that the computation of Nash equilibrium is PPAD-complete; which is a new complexity class introduced by Papadimitriou (1994) mainly to capture the complexity of Nash equilibrium. This note tries to give a brief survey of the various algorithms that exist in the literature for computing the Nash equilibrium in finite games. Also, it will briefly touch upon the various existential conditions for Nash equilibrium for infinite games.

CONTRIBUTION-BASED PROFIT-SHARING SCHEME FOR JOINT VENTURES / PELNO PASIDALIJIMO TARP ĮMONIŲ SCHEMA, PAGRĮSTA PATIRTOMIS IŠLAIDOMIS

Along with globalization of the construction market, international construction firms often choose to cooperate with local construction firms in the form of Joint Ventures (JV) when they enter into the domestic markets of different countries. In this way, they cannot only reduce investment risks, but also enhance production efficiency, reduce costs and generate more profits. The conventional method of profit-sharing between JV firms is based on ratio of investment. However, as the firms make different contributions to the project, the rationality of such a profit-sharing method is often doubtful and thus is difficult to maintain a stable cooperative relationship for a JV team. Based on the concept of the cooperative game theory, this paper proposes a contribution-based profit-sharing model using Shapley Value. A case study is used to describe how firms can use this model to reach decisions of participation, and determine a fair profit-sharing rule after cooperation to enhance mutual trust and create the advantages of cooperation. Santrauka Vykstant statybos rinkos globalizacijai, tarptautinės statybos įmonės, patekusios į vietinę kitos šalies rinką, dažnai linkusios bendradarbiauti su vietos statybos įmonėmis. Jos gali ne tik sumažinti investicijos riziką, bet ir padidinti gamybos efektyvumą, sumažinti išlaidas ir gauti didesnį pelną. Tradicinis pelno pasidalijimo metodas tarp įmonių grindžiamas investicijų santykiu. Tačiau kai įmonių įnašas į projektą skirtingas, toks pelno metodo racionalumas dažnai abejotinas, todėl tokiu atveju yra sunku palaikyti stabilų įmonių bendradarbiavimą. Remiantis lošimų teorijos koncepcija, šiame darbe siūlomas pelno pasidalijimo modelis naudojant Shapley reikšmę. Skaitmeniniu pavyzdžiu rodoma, kaip įmonės gali taikyti šį modelį priimdamos sprendimus dėl dalyvavimo bendroje veikloje ir teisingo pelno pasidalijimo. Taip sustiprinamas tarpusavio pasitikėjimas ir sukuriamos bendradarbiavimo prielaidos.

Topological Implications of Cascading Interdomain Bilateral Traffic Agreements

The Internet uses a model in which Autonomous Systems (AS) peer bilaterally with each other, resulting in a cascaded connectivity model: the end-to-end service that an end-user sees is the result of this cascade of bilateral traffic agreements. As a result, the routing decisions at each AS beyond the next hop are implicitly delegated, so an AS has limited control over the remaining path. While this may be considered a key feature of the Internet (e.g., helps scalability), the impact of this cascading model on the structure of the Internet is not yet well understood. In this paper, we analyze this cascaded model using concepts of game theory. Although our model cannot capture the full complexity of the real Internet - we actually aim at simplicity and try to only isolate the cascading effect -, our results suggest that cascading bilateral agreements brings order to an arbitrary graph. In particular, it brings forward some well-known properties of the Internet topology, such as the current AS hierarchy and common peering models. Finally, we compare our results with topological and routing data, obtained from CAIDA, looking for experimental evidence of our results, while further exploring the insight obtained from our model.

Natural games

A course of a game is formulated as a physical process that will consume free energy in the least time. Accordingly, the rate of entropy increase is the payoff function that will subsume all forms of free energy that motivate diverse decisions. Also other concepts of game theory are related to their profound physical counterparts. When the physical portrayal of behavior is mathematically analyzed, the course of a game is found to be inherently unpredictable because each move affects motives in the future. Despite the non-holonomic character of the natural process, the objective of consuming free energy in the least time will direct an extensive-form game toward a Lyapunov-stable point that satisfies the minimax theorem.

Bargaining strategies designed by evolutionary algorithms

This paper explores the possibility of using evolutionary algorithms (EAs) to automatically generate efficient and stable strategies for complicated bargaining problems. This idea is elaborated by means of case studies. We design artificial players whose learning and self-improving capabilities are powered by EAs, while neither game-theoretic knowledge nor human expertise in game theory is required. The experimental results show that a co-evolutionary algorithm (CO-EA) selects those solutions which are identical or statistically approximate to the known game-theoretic solutions. Moreover, these evolved solutions clearly demonstrate the key game-theoretic properties on efficiency and stability. The performance of CO-EA and that of a multi-objective evolutionary algorithm (MOEA) on the same problems are analyzed and compared. Our studies suggest that for real-world bargaining problems, EAs should automatically design bargaining strategies bearing the attractive properties of the solution concepts in game theory.

Bidding strategy of generation companies using PSO combined with SA method in the pay as bid markets

This paper proposes a new method that uses the combination of particle swarm optimization (PSO) and simulated annealing (SA) to predict the bidding strategy of Generating Companies (Gencos) in an electricity market where they have incomplete information about their opponents and market mechanism of payment is pay as bid. In the proposed methodology, Gencos prepare their strategic bids according to Supply Function Equilibrium (SFE) model and they change their bidding strategies until Nash equilibrium points are obtained. Nash equilibrium points constitute a central solution concept in game theory and they are computed with solving a global optimization problem. In this paper a new computational intelligence technique is introduced that can be used to solve the Nash optimization problem. This new procedure, is based on the PSO algorithm, which uses SA method to avoid becoming trapped in local minima or maxima and improve the velocity’s function of particles. The performance of this procedure is compared with results of other computational intelligence techniques such as PSO, Genetic Algorithm (GA), and a mathematical method (GAMS/DICOPT). The IEEE 39-bus test system is employed to illustrate and verify the results of the proposed method.

Designing the conflict resolution machinery using game theory–based neural network

We consider some general and practical cases of conflicts and design a neural network that is able to solve these basic conflict problems. For the preliminary definition and concepts in game theory, neural network and optimization, such as pay off function, stable solutions, and linear programming see, Fundenberg and Tirole (Game theory, Massachusetts Institute of Technology, Cambridge, 1996), Gass (Linear programming, McGraw Hill, New York, 1958), Hertz et al. (Introduction to the theory of neural computation, Addison Wesley Company, Redwood City, 1991).