A New Friedman’s Model for Evolutionary Game Problem

Abstract

The term game in game theory means a problem, where some of the people or groups (players) share a set of rules and regulations that create the conditions and events that make up the beginning of the game. For instance, in the trade market, the buyers and sellers of some commodities interact in a random way. The reputation of sellers effects on increasing of selling. e.g., honest sellers are more attractive than cheaters for the buyers and the buyers can examine the products or unexamined. In this paper, a non-linear discrete dynamical system of Friedman model was considered. Also, we proposed a new model of interaction between these two populations (buyers and sellers). investigate its limit run behavior where we found the limit converges to a fixed point (0,0) i.e., the sellers will always cheat and the sellers will not examine according to Friedman’s model which is denoted by the fixed point (0.0).