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Evolution by natural selection can be seen an algorithm for generating creative solutions to difficult problems. More precisely, evolution by natural selection is a class of algorithms that share a set of properties. The question we address…
Synchronization, cooperation, and chaos are ubiquitous phenomena in nature. In a population composed of many distinct groups of individuals playing the prisoner's dilemma game, there exists a migration dilemma: No cooperator would migrate…
We study evolutionary games in a spatial diluted grid environment in which agents strategically interact locally but can also opportunistically move to other positions within a given migration radius. Using the imitation of the best rule…
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…
Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with…
We have proposed two new evolutionary rules on spatio-iterated games that is not mimic evolution of strategies, and mainly discussed the Prisoner's Dilemma game \cite{toyota2} by the two evoutionary rules \cite{toyota3}. In this paper we…
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…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
Evolutionary game theory has been an important tool for describing economic and social behaviour for decades. Approximate mean value equations describing the time evolution of strategy concentrations can be derived from the players'…
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 propose a model for evolutionary game dynamics with three strategies $A$, $B$ and $C$ in the framework of Moran process in finite populations. The model can be described as a stochastic process which can be numerically computed from a…
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…
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 factors contributing to the persistence and stability of life are fundamental for understanding complex living systems. Organisms are commonly challenged by harsh and fluctuating environments that are suboptimal for growth and…
Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We…
We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…
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…
Conways Game of Life is a cellular automaton noted for its rich, complex, and emergent behavior, which seems qualitatively lifelike it exists within a wider space of different rule-sets of cellular automata none of which have been found to…
The serious games between humans and AI have only just begun. Evolutionary Game Theory (EGT) models the competitive and cooperative strategies of biological entities. EGT could help predict the potential evolutionary equilibrium of humans…
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…