Abstract
The purpose of this study is to present an analysis of the applicability of an analytical solution to the $N-$person social dilemma game. Such solution has been earlier developed for Pavlovian agents in a cellular automaton environment with linear payoff functions and also been verified using agent based simulation. However no discussion has been offered for the applicability of this result in all Prisoners 'Dilemma game scenarios or in other $N-$person social dilemma games such as Chicken or Stag Hunt. In this paper it is shown that the analytical solution works in all social games where the linear payoff functions are such that each agent's cooperating probability fluctuates around the analytical solution without cooperating or defecting with certainty. The social game regions where this determination holds are explored by varying payoff function parameters. It is found by both simulation and a special method that the analytical solution applies best in Chicken when the payoff parameter $S$ is slightly negative and then the analytical solution slowly degrades as $S$ becomes more negative. It turns out that the analytical solution is only a good estimate for Prisoners' Dilemma games and again becomes worse as $S$ becomes more negative. A sensitivity analysis is performed to determine the impact of different initial cooperating probabilities, learning factors, and neighborhood size.
Highlights
Agent based social simulation is a common method to analyze N-person social dilemma games
In this paper the applicability of the analytical solution of such games with Pavlovian agents in a two dimensional cellular automaton environment is explored when the agents’ decision to cooperate or defect is based on reinforcement learning with linear payoff functions
In the Prisoners’ Dilemma plateau each agent’s cooperating probability fluctuates around a steady state equilibrium. These agents are called bipartisan since they are willing to change their minds from iteration to iteration
Summary
Agent based social simulation is a common method to analyze N-person social dilemma games. In this figure each mesh intersection represents the percentage of cooperators at the end of a simulation run on a 50 × 50 cellular automaton grid with each Pavlovian agent having an initial cooperating probability 0.5 and equal learning factors 0.05. This paper is intended to be a follow-up to the works of Szilagyi [12] and Merlone et al [9] In these papers analytical solutions are presented with verification using agent based simulation for some specific Prisoner’s Dilemma examples, no exhaustive analysis is given on the conditions where it is applicable.
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