A Fast Heuristic Solution for the Commons Game

Abstract

Game Theory can be used to capture and model the phenomenon of the exploitation of the environment by human beings. The Commons Game is a simple and concise game that elegantly formulates the different behaviors of humans toward the exploitation of resources (also known as “commons”) as seen from a game-theoretic perspective. The game is particularly difficult because it is a multi-player game which requires both competition and cooperation. Besides, to augment the complexity, the various players are unaware of the moves made by the others – they merely observe the consequences of their respective moves. This makes the game extremely difficult to analyze, and there is thus no known method by which one can even understand whether the game has has an equilibrium point or not. In the Commons Game, an ensemble of approaches towards the exploitation of the commons can be modeled by colored cards. In this paper, we consider the cases when, with some probability, the user is aware of the approach (color) which the other players will use in the exploitation of the commons. We investigate the problem of determining the best probability value with which a specific player can play each color in order to maximize his ultimate score. Our solution to this problem is an “intelligent” heuristic algorithm which determines (i.e., locates in the corresponding space) feasible probability values to be used so as to obtain the maximum average score. The basis for such a strategy is that we believe that results obtained in this manner can be used to work towards a “expectiminimax” solution, or for a solution which utilizes such values for a UCT-type algorithm. The solution has been rigorously tested by simulations, and the results obtained are, in our opinion, quite impressive. Indeed, as far as we know, this is a pioneering AI-based heuristic solution to the game under the present model of computation.