Distributed welfare games with applications to sensor coverage

Jason R. Marden, Adam Wierman

Abstract: Traditionally resource allocation problems are approached in a centralized manner; however, often centralized control is impossible. We consider a distributed, non-cooperative approach to resource allocation. In particular, we consider the situation where the global planner does not have the authority to assign players to resources; rather, players are self-interested. The question that emerges is how can the global planner entice the players to settle on a desirable allocation with respect to the global welfare? To study this question, we focus on a class of games that we refer to as distributed welfare games. Within this context, we investigate how the global planner should distribute the global welfare to the players. We measure the efficacy of a distribution rule in two ways: (i) Does a pure Nash equilibrium exist? (ii) How efficient are the Nash equilibria as compared with the global optimum? We derive sufficient conditions on the distribution rule that ensures the existence of a pure Nash equilibrium in any single-selection distributed welfare game. Furthermore, we derive bounds on the efficiency of these distribution rules in a variety of settings. Lastly, we highlight the implications of these results in the context of the sensor coverage problem.