Answers set programs for non-transferable utility games: Expressiveness, complexity and applications

Abstract

Coalitional games are mathematical models suited to study payoff distribution problems in cooperative scenarios. In abstract terms, a coalitional game can be specified by explicitly listing all possible—in fact, exponentially many—coalitions with their associated distributions. This naïve representation, however, quickly becomes infeasible over games involving many agents, thereby calling for suitable compact representations, that is, encoding mechanisms that (on some specific classes of games of interest) take an amount of space that grows polynomially with the number of agents. To date, a plethora of compact encodings have been already introduced and analyzed from the algorithm and computational viewpoints. Despite their specific technical differences, these encodings typically share the assumption that the utility associated with a coalition can be freely transferred among agents. Indeed, designing encoding mechanisms for the non-transferable utility (NTU) setting is a research issue that has been largely unexplored so far.The paper addresses this issue by proposing a compact encoding for representing and reasoning about the outcomes of NTU coalitional games founding on answer set programming. By exploiting the expressiveness of this well-known knowledge representation formalism, it is shown that the proposed representation can succinctly encode several games of interest within a wide range of application domains. Computational issues arising in the setting have been studied too, by addressing questions related to certain payoff distributions enjoying desirable stability properties. Eventually, a prototype system supporting the proposed framework has been implemented by leveraging a state-of-the-art answer set engine, and results of a thorough experimental activity conducted on top of it have been discussed.