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Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…
This paper investigates the long-term behavior of an interacting particle system of interest in the hot topic of evolutionary game theory. Each site of the $d$-dimensional integer lattice is occupied by a player who is characterized by one…
An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (``mutant'') strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the…
In evolutionary game theory, it is customary to be partial to the dynamical models possessing fixed points so that they may be understood as the attainment of evolutionary stability, and hence, Nash equilibrium. Any show of periodic or…
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how…
Two families of denotational models have emerged from the semantic analysis of linear logic: dynamic models, typically presented as game semantics, and static models, typically based on a category of relations. In this paper we introduce a…
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…
In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play…
Quasi-stationary Mean Field Games models consider agents who base their strategies on current information without forecasting future states. In this paper we address the first-order quasi-stationary Mean Field Games system, which involves…
We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…
Evolutionary game theory combines game theory and dynamical systems and is customarily adopted to describe evolutionary dynamics in multi-agent systems. In particular, it has been proven to be a successful tool to describe multi-agent…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…
The replicator equation is a simple model of evolution that leads to stable form of Nash Equilibrium, Evolutionary Stable Strategy (ESS). It has been studied in connection with Evolutionary Game Theory and was originally developed for…
Evolution Strategies are inspired in biology and part of a larger research field known as Evolutionary Algorithms. Those strategies perform a random search in the space of admissible functions, aiming to optimize some given objective…
We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point…
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…
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…
This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living…
The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many…