Evolutionary games: Natural selection of strategies

2007

Abstract. Evolutionary games have developed in biological sciences to study equilibrium behavior (called Evolutionary Stable Strategies–ESS) between large populations. ESS are more adapted than the standard Nash equilibrium to predict the evolution of large homogeneous or heterogeneous populations. While rich theoretical foundations of evolutionary games allow biologist to explain past and present evolution and predict future evolution, it can be further used in Engineering to architect evolution.

1982

Evolutionary Game Theory - V. Zeigler-Hill, T. K. Shackelford (eds.), Encyclopedia of Personality and Individual Differences, 2019

Journal of Theoretical Biology, 2014

Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption that the population size is infinite. However, in reality, population sizes are finite. Recently, stochastic processes in finite populations have been introduced into evolutionary games in order to study finite size effects in evolutionary game dynamics. However, most of these studies focus on populations playing only single games. In this study, we investigate a finite population with two games and show that a finite population playing two games tends to evolve toward a specific direction to form particular linkages between the strategies of the two games.

Journal of Economic Behavior & Organization, 1996

The paper analyzes the evolution of strategy profiles in a population of finitely many players where each player interacts only with a subset of the population. Conditions are given which guarantee that the strategy profiles converge globally resp. locally to an equilibrium state. The results, derived by using methods from the theory of iterated discrete functions, are illustrated by several examples, e.g. coordination and hawk-dove games. JEL classifcution: C62; C72; D83

Econometrica, 1995

BY KLAus RITZBERGER AND JORGEN W. WEIBULL1 This paper investigates stability properties of evolutionary selection dynamics in normal-form games. The analysis is focused on deterministic dynamics in continuous time and on asymptotic stability of sets of population states, more precisely of faces of the mixed-strategy space. The main result is a characterization of those faces which are asymptotically stable in all dynamics from a certain class, and we show that every such face contains an essential component of the set of Nash equilibria, and hence a strategically stable set in the sense of Kohlberg and Mertens (1986).

EPL (Europhysics Letters), 2008

How did cooperative behavior evolve is a big open question in both biology as well as in social sciences. This problem is frequently addressed through the evolutionary game theory. However, very often it is not obvious which game is the more appropriate to use. Furthermore, an empirical determination of the payoffs can be very difficult while variations in the payoff values can dramatically alter theoretical predictions. Here, to overcome the above difficulties, I propose a very minimal model without payoff parameters. Instead, starting with random heterogeneous distributions of payoffs, by the process of natural selection itself, definite payoff matrices are produced. The system evolves from a completely heterogeneous distribution of payoffs to a situation in which very few payoff matrices coexist. When the initial set of games consists of dilemma games, the emerging game is the "Stag Hunt". The fraction of cooperator agents converges in all the cases examined to non-zero values.

数理解析研究所講究録, 2009

This study examines the impacts of environmental variation on the game. Here, environmental variation corresponds to the fitness/payoff variation. In mathematical biology, if the fitness is " geometric mean," we know that the player chooses a Bet-Hedging strategy in the stochastic environment, and if it is "arithmetic average," the player does not. ([4, 5]) In addition, Selten [11] shows that no mixed equilibria, i.e., Bet-Hedging strategy, are evolutionarily stable when players can condition their strategies on their roles in a game. On the other hand, we know that Nash Equilibrium in the game with randomly disturbed payoffs is aJways mixed strategy ([3]). Thus, these results show a discrepancy, in spite of the similar model. This study examines and clarifies this discrepancy with Replicator equation.

Proceedings of the Royal Society B: Biological Sciences, 2011

In frequency-dependent games, strategy choice may be innate or learned. While experimental evidence in the producer–scrounger game suggests that learned strategy choice may be common, a recent theoretical analysis demonstrated that learning by only some individuals prevents learning from evolving in others. Here, however, we model learning explicitly, and demonstrate that learning can easily evolve in the whole population. We used an agent-based evolutionary simulation of the producer–scrounger game to test the success of two general learning rules for strategy choice. We found that learning was eventually acquired by all individuals under a sufficient degree of environmental fluctuation, and when players were phenotypically asymmetric. In the absence of sufficient environmental change or phenotypic asymmetries, the correct target for learning seems to be confounded by game dynamics, and innate strategy choice is likely to be fixed in the population. The results demonstrate that und...

Physica A: Statistical and Theoretical Physics, 1997

PLOS Computational Biology, 2015

Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner's Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games.

International Game Theory Review, 2000

A two-decision competition model is developed where players may choose different strategies at different decisions knowing that their payoff at one decision is not affected by their performance at the other. It is shown that both static solution concepts of Nash and evolutionarily stable equilibria for the two-decision model are directly related to those of the separate decisions. Furthermore, if there are at most two pure strategies at each decision, dynamic stability can also be characterised through a separate analysis of each decision. However, when there are more than two strategies, this last statement is not always true.

Bulletin of mathematical biology

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA E-mail: [email protected] ... DREW FUDENBERG Department of Economics, Harvard University, Cambridge, MA 02138, USA E-mail: dfudenberg@ ...

Philosophy of Science, 1994

The proper treatment of correlation in evolutionary game theory has unexpected connections with recent philosophical discussions of the theory of rational decision. The Logic of Decision (Jeffrey 1983) provides the correct framework for correlated evolutionary game theory and a variant of "ratifiability" is the appropriate generalization of "evolutionarily stable strategy". The resulting theory unifies the treatment of correlation due to kin, population viscosity, detection, signaling, reciprocal altruism, and behavior-dependent contexts. It is shown that (1) a strictly dominated strategy may be selected, and (2) under conditions of perfect correlation a strictly efficient strategy must be selected.

Wiley-VCH Verlag GmbH & Co. KGaA eBooks, 2010

Game theory and evolution Modern game theory goes back to a series of papers by the mathematician John von Neumann in the 1920s. This program started a completely new branch of social sciences and applied mathematics. This early work on game theory is summarized in the seminal book "The Theory of Games and Economic Behavior" by John von Neumann and Oskar Morgenstern [115]. Initially, game theory was primarily focused on cooperative game theory, which analyzes optimal strategies assuming that individuals stick to previous agreements. In the 1950's, the focus shifted to non-cooperative games in which individuals act selfish to get the most out of an interaction. At that time, game theory had matured from a theoretical concept to a scientific field influencing political decision making, mainly in the context of the arms race of the cold war. The basic assumption was that individuals act rationally and take into account that their interaction partners know that their decisions are rational and vice versa. Based on a common utility function that individuals maximize, the actions of others can be predicted and the optimal strategy can be chosen. However, the underlying assumption of rationality is often unrealistic. Even in simple interactions between two individuals A and B, it is difficult to imagine fully rational decision making, as this often leads to an infinite iteration: A thinks of B, who is thinking of A, who is thinking of B and so on. One way to avoid this situation in economy is the idea of bounded rationality [32, 91]. If the cost of acquiring and processing information is taken into account, individuals can no longer be assumed to do a fully rational analysis