Stable utility design for distributed resource allocation

The framework of resource allocation games is becoming an increasingly popular modeling choice for distributed control and optimization. In recent years, this approach has evolved into the paradigm of game-theoretic control, which consists of first modeling the interaction between the distributed agents as a strategic form game, and then designing local utility functions for these agents such that the resulting game possesses a stable outcome (e.g., a pure Nash equilibrium) that is efficient (e.g., good “price of anarchy” properties). One then appeals to the large, existing literature on learning in games for distributed algorithms for agents that guarantee convergence to such an equilibrium. An important first problem is to obtain a characterization of stable utility designs, that is, those that guarantee equilibrium existence for a large class of games. Recent work has explored this question in the general, multiselection context, that is, when agents are allowed to choose more than one resource at a time, showing that the only stable utility designs are the so-called “weighted Shapley values”. It remains an open problem to obtain a similar characterization in the single-selection context, which several practical problems such as vehicle target assignment, sensor coverage, etc. fall into. We survey recent work in the multi-selection scenario, and show that even though other utility designs become stable for specific single-selection applications, perhaps surprisingly, in a broader context, the limitation to “weighted Shapley value” utility design continues to prevail.