Evolutionary Random Access Game With Objective and Subjective Players

Abstract

We consider an evolutionary game on a graph under the condition that players perception of uncertainty and decision making can follow either an objective expected utility theory (EUT) model or a subjective prospect theory (PT) model. Each player chooses one of two strategies with probabilities x and 1-x, where the subjective players bias their choices of the probabilities to be w(x) and w(1-x) to reflect the probability weighting effect of PT. We derive the conditions to achieve a locally asymptotically stable Nash equilibrium (NE) and the necessary conditions to achieve an evolutionary stable strategy (ESS). We illustrate these results through a simple random access channel game. We find that players' behavior is affected by the total number of players as well as the number of each type of players (objective or subjective). We show that increasing the number of interacting players induces an aggressive transmission strategy and the behavior becomes similar for both types of players. Moreover, we let the objective and subjective players adjust their transmission under throughput rewards, delay penalties, and energy costs. The EUT players' throughput is higher than the PT players' throughput for a small number of interacting players and equal to if the number of interacting players increases.

Keywords

• Game theory
• evolutionary games
• prospect theory
• replicator dynamics
• random access wireless channel