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In this paper, we consider finite-strategy approximations of infinite-strategy evolutionary games. We prove that such approximations converge to the true dynamics over finite-time intervals, under mild regularity conditions which are…

This paper deals with modeling of network's dynamic using evolutionary games approach. Today there are many different protocols for data transmission through the Internet, providing users with better or worse service. The process of…

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature, and have shown profound effects on the resulting eco-evolutionary dynamics. Incorporating linear environmental…

Evolutionary game theory is a common framework to study the evolution of cooperation, where it is usually assumed that the same game is played in all interactions. Here, we investigate a model where the game that is played by two…

Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we…

There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…

We consider a class of continuous-time dynamic games involving a large number of players. Each player selects actions from a finite set and evolves through a finite set of states. State transitions occur stochastically and depend on the…

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces…

A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…

Environmental changes play a critical role in determining the evolution of social dilemmas in many natural or social systems. Generally, the environmental changes include two prominent aspects: the global time-dependent fluctuations and the…

Evolutionary game dynamics describes not only frequency dependent genetical evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update…

In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the…

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the possibility to use conditional strategies that depend on the outcome of…

The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic…

A novel mathematical framework is proposed to describe the ecological and evolutionary consequences of consumer--resource interactions. Both the consumer and resource are assumed to consist of several (sub)species, which interact between…

Age-structured models capture the dynamic behavior of populations over time and result in nonlinear integro-partial differential equations (IPDEs). These processes arise in various fields such as biotechnology, economics, or demography.…

Models in evolutionary game theory traditionally assume symmetric interactions in homogeneous environments. Here, we consider populations evolving in a heterogeneous environment, which consists of patches of different qualities that are…

Evolutionary dynamics provides an iconic relationship --- the periodic frequency of a game is determined by the payoff matrix of the game. This paper reports the first experimental evidence to demonstrate this relationship. Evidence comes…

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…

We examine the problem of the existence of optimal deterministic stationary strategiesintwo-players antagonistic (zero-sum) perfect information stochastic games with finitely many states and actions.We show that the existenceof such…