Evolutionary Game Theory

Articl

Evolutionary game theory

Game Theory

Escort Evolutionary Game Theory

A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations of basic concepts and constructions in evolutionary game theory are given, such as an escorted Fisher's Fundamental theorem and generalizations of the Shahshahani geometry.Comment: Minor typo correctio

Cycle frequency in standard Rock-Paper-Scissors games: Evidence from experimental economics

The Rock-Paper-Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained to be rather weak. In this work we performed laboratory experiments on the RPS game and analyzed the social-state evolutionary trajectories of twelve populations of N=6 players. We found strong evidence supporting the existence of persistent cycles. The mean cycling frequency was measured to be $0.029 \pm 0.009$ period per experimental round. Our experimental observations can be quantitatively explained by a simple non-equilibrium model, namely the discrete-time logit dynamical process with a noise parameter. Our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the RPS game.Comment: 7 Page, 3 figure; Keyword: Rock-Paper-Scissors game; cycle; social state; population dynamics; evolutionary trajector

On an Evolutionary Foundation of Neuroeconomics

Neuroeconomics focuses on brain imaging studies mapping neural responses to choice behavior. Economic theory is concerned with choice behavior but it is silent on neural activities. We present a game theoretic model in which players are endowed with an additional structure - a simple ``nervous system'' - and interact repeatedly in changing games. The nervous system constrains information processing functions and behavioral functions. By reinterpreting results from evolutionary game theory (Germano, 2007), we suggest that nervous systems can develop to ``function well'' in exogenously changing strategic environments. We present an example indicating that an analogous conclusion fails if players can influence endogenously their environment.Neuroeconomic Theory, Evolutionary Game Theory, Learning in Games,Neuroeconomic Theory, Evolutionary Game Theory, Learning in Games

Information Geometry and Evolutionary Game Theory

The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary game theory are realized information-theoretically. Results are extended to the Lotka-Volterra equation and to multiple population systems.Comment: Added reference

The evolution of social norms

Evolutionary game theory provides the tools to analyze which strategies, or patterns of behaviour, emerge over time through a process of adaptation. Social norms can be defined as patterns of behaviour with certain characteristics. Evolutionary game theory thus provides one perspective on how social norms are formed and maintained. Prisoner's dilemma games can be used to study the conditions under which cooperative norms emerge. Bargaining games can be used to address the formation of fairness norms. However, being more congenial to analyzing norms that somehow focus on material payoffs, it is not a given that evolutionary game theory can adequately address norms focusing on rights or virtues.Evolutionary game theory Social norms

Doves and hawks in economics revisited [An evolutionary quantum game theory-based analysis of financial crises]

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as the consequences of the financial crisis exhibit, it would be desirable to change the 'rules of the game' in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the in literature well-known Hawk-Dove game by a quantum approach, we can show that dependent on entanglement, also evolutionary stable strategies can emerge, which are not predicted by classical evolutionary game theory and where the total economic population uses a non aggressive quantum strategy.Evolutionary game theory; financial crisis; hawk-dove game; quantum game theory

Altruistic Duality in Evolutionary Game Theory

A game-theoretic model of social preference and enlightened self-interest is formulated. Existence of symmetry and duality in the game matrices with altruistic social preference is revealed. The model is able to quantitatively describe the dynamical evolution of altruism in prisoner's dilemma and the regime change in prey-predator dynamics.Comment: ReVTeX4, 4 papes, 2 ifigures, Typos corrected for publicatio