Related papers: Stochasticity and evolutionary stability
Evolutionary game dynamics in finite populations is typically subject to noise, inducing effects which are not present in deterministic systems, including fixation and extinction. In the first part of this paper we investigate the…
We study the problem of stochastic stability for evolutionary dynamics under the logit choice rule. We consider general classes of coordination games, symmetric or asymmetric, with an arbitrary number of strategies, which satisfies the…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…
In order to better understand the impact of environmental stochastic fluctuations on the evolution of animal behavior, we introduce the concept of a stochastic Nash equilibrium (SNE) that extends the classical concept of a Nash equilibrium…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…
The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…
Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural…
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.…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
We consider coalition formation among players in an n-player finite strategic game over infinite horizon. At each time a randomly formed coalition makes a joint deviation from a current action profile such that at new action profile all…
Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players…
We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type…
Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding…
In this paper, we examine the robustness of Nash equilibria in continuous games, under both strategic and dynamic uncertainty. Starting with the former, we introduce the notion of a robust equilibrium as those equilibria that remain…
Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning…
As an equilibrium refinement of the Nash equilibrium, evolutionarily stable strategy (ESS) is a key concept in evolutionary game theory and has attracted growing interest. An ESS can be either a pure strategy or a mixed strategy. Even…
We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed…