On the existence and heuristic computation of the solution for the commons game

It is well known that Game Theory can be used to capture and model the phenomenon of economic strategies, psychological and social dilemmas, and the exploitation of the environment by human beings. Many artificial games studied in Game Theory can be used to understand the main aspects of humans using/misusing the environment. They can be tools by which we can define the aggregate behavior of humans, which, in turn, is often driven by "short-term", perceived costs and benefits. 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 intrinsically hard because it is non-zero-sum, and involves multiple players, each of who can use any one of a set of strategies. It also could involve potential competitive and cooperative strategies. In the Commons Game, an ensemble of approaches towards the exploitation of the commons can be modeled by colored cards. This paper shows, in a pioneering manner, the existence of an optimal solution to Commons Game, and demonstrates a heuristic computation for this solution. To do this, 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 then 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 a heuristic algorithm which determines (locates in the corresponding space) feasible probability values to be used so as to obtain the maximum average score. This project has also involved the corresponding implementation of the game, and the output of the new algorithm enables the user to visualize the details