In this article, we put forward the multi-objective matrix game model based on fuzzy payoffs. In order to solve the game model, we first discuss the relationship of two fuzzy numbers via the lower limit− 2 of the possibility degree. Then, utilizing this relationship, we conclude that the equilibrium solution of this game model and the optimal solution of multicriteria linear optimization proble...

This paper deals with the approximation of Nash-equilibria in m-player games. We present conditions under which an approximating sequence of games admits near-equilibria that approximate near equilibria in the limit game. We apply the results to two classes of games: (i) a duopoly game approximated by a sequence of matrix games; (ii) a stochastic game played under the S-adapted information stru...

A bimatrix game (A, B) is called a game of rank k if the rank of the matrix A + B is at most k. We consider the problem of enumerating the Nash equilibria in (non-degenerate) games of rank 1. In particular, we show that even for games of rank 1 not all equilibria can be reached by a Lemke– Howson path and present a parametric simplex-type algorithm for enumerating all Nash equilibria of a non-d...

Coevolutionary game dynamics is the result of players that may change their strategies and their network of interaction. For such games, and based on interpreting strategies as configurations, strategy– to–payoff maps can be defined for every interaction network, which opens up to derive game landscapes. This paper presents an analysis of these game landscapes by their information content. By t...

Here we will use results of Cox, Durrett, and Perkins [56] for voter model perturbations to study spatial evolutionary games on Zd, d ≥ 3 when the interaction kernel is finite range, symmetric, and has covariance matrix σ2I. The games we consider have payoff matrices of the form 1 + wG where 1 is matrix of all 1’s and w is small and positive. Since our population size N = ∞, we call our selecti...

Researchers often use normal-form games to model multiagent interactions. When a game model is based on observational or simulated data about agent payoffs, we call it an empirical game. The payoff matrix of an empirical game can be analyzed like any normal-form game, for example, by identifying Nash equilibria or instances of other solution concepts. Given the game model’s basis in sampled dat...

One thing that nearly all stability concepts in Evolutionary Game Theory have in common is that they use a time-independent fitness matrix. Although this is a reasonable assumption for mathematical purposes, in many situations in real life it seems to be too restrictive. We present a model of an evolutionary game, driven by replicator dynamics, where the fitness matrix is a variable rather than...

a {em roman dominating function} on a graph $g = (v ,e)$ is a function $f : vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. the {em weight} of a roman dominating function is the value $w(f)=sum_{vin v}f(v)$. the roman domination number of a graph $g$, denoted by $gamma_r(g)$, equals the...

The casino game of baccara chemin de fer is a bimatrix game, not a matrix game, because the house collects a five percent commission on Banker wins. We generalize the game, allowing Banker’s strategy to be unconstrained and assuming a 100α percent commission on Banker wins, where 0 ≤ α < 2/5. Assuming for simplicity that cards are dealt with replacement, we show that, with one exception at α = ...

The classic prisoner's dilemma model of game theory is modified by introducing occasional variations on the options available to players. Mutation and selection of game options reliably change the game matrix, gradually, from a prisoner's dilemma game into a byproduct mutualism one, in which cooperation is stable, and "temptation to defect" is replaced by temptation to cooperate. This result su...