N-Person Cooperative Game Theory Solutions, Coalitions, and Applications

This study explores the topic of N-person cooperative game theory. The following paper begins with an introduction to the basic definitions and the- orems of game theory. These definitions and theorems are then used to in- troduce various solution methods and methods of coalition formation. These results are then applied to the airport game, to the supplier-firm-buyer game, and to evolutionary games

On the Truly Noncooperative Game of Island Life II: Evolutionary Stable Economic Development Strategy in Brief

This paper offers a solution to 'The Problem of Sustainable Economic Development' on islands. This hypothesis offers a foundational, sub-game solution to The Island Survival Game, a counterintuitive, dominant economic development strategy for ‘islands’ (and relatively insular states). This discourse also tables conceptual building blocks, prerequisite analytical tools, and a guiding principle for The Earth Island Survival Game, a bounded delay supergame which models 'The Problem of Sustainable Economic Development' at the global level. We begin our exploration with an introduction to The Principle of Relative Insularity, a postulate which informs ESS for ‘island’ and ‘continental’ players alike. Next, we model ‘island’ economic development with two bio-geo-politico-economic models and respective strategies: The Mustique Co. Development Plan, and The Prince Edward Island Federal-Provincial Program for Social and Economic Advancement. These diametrically opposed strategies offer an extraordinary comparative study. One island serves as a highly descriptive model for 'The Problem of Sustainable Economic Development'; the other model informs ESS. 'The Earth Island Survival Game' serves as a remarkable learning tool, offering lessons which promote islander survival, resource holding power, cooperative behaviour, and independence by illuminating the illusive path toward sustainable economic development.Non-cooperative games, evolutionary game theory, relative insularity, islands, tragedy of the commons, sustainable economic development, theory of value, resource holding power, evolutionary stable strategy, natural selection, long distance dispersal

Evolution and Walrasian Behavior in Market Games

We revisit the question of price formation in general equilibrium theory. We explore whether evolutionary forces lead to Walrasian equilibrium in the context of a market game, introduced by Shubik (1972). Market games have Pareto inferior (strict) Nash equilibria, in which some, and possibly all, markets are closed. We introduce a strong version of evolutionary stable strategies (SESS) for finite populations. Our concept requires stability against multiple, simultaneous mutations. We show that the introduction of a small number of ``trading mutants'' is sufficient for Pareto improving trade to be generated. Provided that agents lack market power, Nash equilibria corresponding to approximate Walrasian equilibria constitute the only approximate SESS.

Roles of mutation rate and co-existence of multiple strategy updating rules in evolutionary prisoner's dilemma games

The emergence and maintenance of cooperation has attracted intensive scholarly interest and has been analysed within the framework of evolutionary game theory. The role of innovation, which introduces novel strategies into the population, is a relatively understudied aspect of evolutionary game theory. Here, we investigate the effects of two sources of innovation---mutation and heterogeneous updating rules. These mechanisms allow agents to adopt strategies that do not rely on the imitation of other individuals. The model introduces---in addition to canonical imitation-based strategy updating---aspiration-based updating, whereby agents switch their strategy by referring solely to the performance of their own strategy; mutation also introduces novel strategies into the population. Our simulation results show that the introduction of aspiration-based rules into a population of imitators leads to the deterioration of cooperation. In addition, mutation, in combination with heterogeneous updating rules, also diminishes cooperators. This phenomenon is prominent when a large proportion of the population consists of imitators rather than adopters of aspiration-based updating. Nevertheless, a high mutation rate, in combination with a low aspiration level, has positive nonlinear effects, and a heterogeneous population achieves a higher level of cooperation than the weighted average of homogeneous populations. Our results demonstrate the profound role of innovation in the evolution of cooperation.Comment: 7 pages, 8 figures, Figs 3(b) and 8 were added following the reviewers' comment

Self-Enforcing Climate Change Treaties: A Generalized Differential Game Approach with Applications

Based on recent proposals on non cooperative dynamic games for analysing climate negotiation outcomes, such as Dutta and Radner (2004, 2006a), we generalize a specific framework for modelling differential games of this type and describe the set of conditions for the existence of closed loop dynamics and its relation to adaptive evolutionary dynamics. We then show that the Dutta and Radner (2004, 2006a) discrete time dynamic setup is a specific case of that generalization and describe the dynamics both analytically and numerically for closed loop feedback and perfect state patterns. Our discussion is completed with the introduction of a cooperative differential framework for welfare analysis purposes, within our non cooperative proposal for climate negotiations.Differential Game Theory, Environmental Economics, Evolutionary Dynamics, Climate Change Treaties

Probabilistic memory-one strategies to dominate the iterated prisoner’s dilemma over networks

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGThe Iterated Prisoner’s Dilemma (IPD) has been a classical game theoretical scenario used to model behaviour interactions among agents. From the famous Axelrod’s tournament, and the successful results obtained by the Tit for Tat strategy, to the introduction of the zerodeterminant strategies in the last decade, the game theory community has been exploring the performance of multiple strategies for years. This article grounds on such previous work, studying probabilistic memory-one strategies (PMO) and using evolutionary game theory, to analyse the criteria to find the most successful set of strategies in networked topologies. The results are nearly deterministic in discrete PMO scenarios. However, results become much more complex when moving to continuous ones, and there is no optimal strategy for a given scenario. Finally, this article describes how, using machine learning and evolutionary techniques; a cluster of agents, playing synchronously and adaptively, is able to dominate the rest of the populatio

Evolutionary Game Dynamics with Non-Uniform Interaction Rates

The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to non-linear fitness functions. We show that a strict Nash equilibrium remains uninvadable for non-uniform interaction rates, but the conditions for evolutionary stability need to be modified. We analyze all games between two strategies. If the two strategies coexist or exclude each other, then the evolutionary dynamics do not change qualitatively, only the location of the equilibrium point changes. If, however, one strategy dominates the other in the classical setting, then the introduction of non-uniform interaction rates can lead to a pair of interior equilibria. For the Prisoner's Dilemma, non-uniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, non-uniform interaction rates change the equilibrium frequency of cooperators.Human Evolutionary BiologyMathematic

Economics and mathematical theory of games

The theory of games is a branch of applied mathematics that is used in economics, management, and other social sciences. Moreover, it is used also in military science, political science, international relations, computer science, evolutionary biology, and ecology. It is a field of mathematics in which games are studied. The aim of this article is to present matrix games and the game theory. After the introduction, we will explain the methodology and give some examples. We will show applications of the game theory in economics. We will discuss about advantages and potential disadvantages that may occur in the described techniques. At the end, we will represent the results of our research and its interpretation

Research on Cooperative Innovation Behavior of Industrial Cluster Based on Subject Adaptability

From the perspective of the interactive cooperation among subjects, this paper portrays the process of cooperative innovation in industrial cluster, in order to capture the correlated equilibrium relationship among them. Through the utilization of two key tools, evolutionary stable strategy and replicator dynamics equations, this paper considers the cost and gains of cooperative innovation and the amount of government support as well as other factors to build and analyze a classic evolutionary game model. On this basis, the subject’s own adaptability is introduced, which is regarded as the system noise in the stochastic evolutionary game model so as to analyze the impact of adaptability on the game strategy selection. The results show that, in the first place, without considering subjects’ adaptability, their cooperation in industrial clusters depends on the cost and gains of innovative cooperation, the amount of government support, and some conditions that can promote cooperation, namely, game steady state. In the second place after the introduction of subjects’ adaptability, it will affect both game theory selection process and time, which means that the process becomes more complex, presents the nonlinear characteristics, and helps them to make faster decisions in their favor, but the final steady state remains unchanged