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The introduction of concepts of Game Theory and Ordinary Differential Equations into Biology gave birth to the field of Evolutionary Stable Strategies, with applications in Biology, Genetics, Politics, Economics and others. In special, the…
Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a…
The concept of evolutionarily stability and its relation with the fixed points of the replicator equation are important aspects of evolutionary game dynamics. In the light of the fact that oscillating state of a population and individuals…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some…
Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only…
We present an algorithm for computing all evolutionarily stable strategies in nondegenerate normal-form games with three or more players.
In evolutionary game theory an Evolutionarily Stable Strategy (ESS) is a refinement of the Nash equilibrium concept that is sometimes also recognized as evolutionary stability. It is a game-theoretic model, well known to mathematical…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective…
Evolutionary game theory has become one of the most diverse and far reaching theories in biology. Applications of this theory range from cell dynamics to social evolution. However, many applications make it clear that inherent…
Even though existence of non-convergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such outcomes are scarce in the literature of…
Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by…