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Interactions among multiple self-interested agents may not necessarily yieldsocially desirable behaviors. While static games offer a pragmatic model forsuch interactions, and modifying the utilities of the agents in such gamesprovides a means toward achieving socially desirable behavior, manipulating theutilities is hard-if not impossible-after the system is deployed. Weinvestigate an alternative means where each agent incorporates others'utilities into its own utility based on a relationship network, whichcharacterizes how much one agent cares about another and hence the extent oftheir utility incorporation. We introduce the notion of a relationship game, astatic game with a set of weighted relationship networks and a social costfunction. The main problem we study is the design of the weight vector on therelationships such that the Nash equilibrium of the associated game is sociallydesirable. We propose an ordering-based exact method and a gradient-basedapproximate method to solve this problem. We show theoretically that the exactsolution scales exponentially with the number of players. Empirical resultsshow both methods are effective and scale exponentially, with the runtime ofgradient-based solution growing slower.

Relationship Design for Socially Desirable Behavior in Static Games