Related papers: Evolutionary Games on the Torus with Weak Selectio…

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a…

This study investigates simple games. A fundamental research question in this field is to determine necessary and sufficient conditions for a simple game to be a weighted majority game. Taylor and Zwicker (1992) showed that a simple game is…

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a…

Non-ergodic convergence of learning dynamics in games is widely studied recently because of its importance in both theory and practice. Recent work (Cai et al., 2024) showed that a broad class of learning dynamics, including Optimistic…

We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…

We study fixation in large, but finite, populations with two types, and dynamics governed by birth-death processes. By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation…

In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal…

Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy…

Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the…

In this paper we study the minority game in the presence of evolution. In particular, we examine the behavior in games in which the dimension of the strategy space, m, is the same for all agents and fixed for all time. We find that for all…

In [12] we formulated an evolutionary game theory model as a dynamical system on the state space of finite signed Borel measures under the weak* topology. The focus of this paper is to extend the analysis to include the long-time behavior…

We investigate the toric geometry of two families of generalised determinantal varieties arising from permutations: Matrix Schubert varieties ($\overline{X_w}$) and Kazhdan-Lusztig varieties ($\mathcal{N}_{v,w}$). Matrix Schubert varieties…

In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…

Consider a strongly monotone game where the players' utility functions include a reward function and a linear term for each dimension, with coefficients that are controlled by the manager. Gradient play converges to a unique Nash…

We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As the offspring distribution is varied, a game can undergo a phase transition, in which…

In this paper, we consider a fitness-level model of a non-elitist mutation-only evolutionary algorithm (EA) with tournament selection. The model provides upper and lower bounds for the expected proportion of the individuals with fitness…

We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\to \infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths…

We investigate spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the…

We study a modification of the Evolutionary Minority Game (EMG) in which agents are placed in the nodes of a regular or a random graph. A neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics…

We discover the mechanism for the transition from self-segregation (into opposing groups) to clustering (towards cautious behaviors) in the evolutionary minority game (EMG). The mechanism is illustrated with a statistical mechanics analysis…