Game Theoretic Modeling and Computational Analysis for N-Players with Conflicts over Resources

Abstract

This paper considers the problem of n-player conflict modeling, arising due to competition over resources. Each player represents a distinct group of people and has some resource and power. A player may either attack other players (i.e., groups) to obtain their resources or do nothing. We present a game-theoretical model for interaction between the players, and show that key questions of interest to policy makers can be answered efficiently, i.e., in polynomial time in the number of players. They are: (1) Given the resources and the power of each group, is no-war a stable situation? and (2) Assuming there are some conflicts already in the society, is there a danger of other groups not involved in the conflict joining the conflict and further degrading the current situation? We show that the pure strategy Nash equilibrium is not an appropriate solution concept for our problem and introduce a refinement of the Nash equilibrium called the asymmetric equilibrium. We also provide an algorithm (that is exponential in the number of players) to compute all the asymmetric equilibria and propose heuristics to improve the performance of the algorithm.