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We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T),…
Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…
The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended…
We investigate the effects of update rules on the dynamics of an evolutionary game-theoretic model - the N-player evolutionary trust game - consisting of three types of players: investors, trustworthy trustees, and untrustworthy trustees.…
A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…
A partial differential equation is derived, describing the replicator dynamics with mutations of games with a continuous strategy space. This equation is then applied to continuous versions of symmetric 2x2 games, such as the Prisoners…
Spatial evolutionary games are studied with myopic players whose payoff interest, as a personal character, is tuned from selfishness to other-regarding preference via fraternity. The players are located on a square lattice and collect…
In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or…
The importance of microscopic details on cooperation level is an intensively studied aspect of evolutionary game theory. Interestingly, these details become crucial on heterogeneous populations where individuals may possess diverse traits.…
This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We…
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between…
We introduce a mean-field term to an evolutionary spatial game model. Namely, we consider the game of Nowak and May, based on the Prisoner's dilemma, and augment the game rules by a self-consistent mean-field term. This way, an agent…
Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
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…
Discrete-time replicator map is a prototype of evolutionary selection game dynamical models that have been very successful across disciplines in rendering insights into the attainment of the equilibrium outcomes, like the Nash equilibrium…