Formalizing commitment-based deals in Boolean Games

Abstract

Boolean games (BGs) are a strategic framework in which agents' goals are described using propositional logic. Despite the popularity of BGs, the problem of how agents can coordinate with others to (at least partially) achieve their goals has hardly received any attention. However, negotiation protocols that have been developed outside the setting of BGs can be adopted for this purpose, provided that we can formalize (i) how agents can make commitments and (ii) how deals between coalitions of agents can be identified given a set of active commitments. In this paper, we focus on these two aims. First, we show how agents can formulate commitments that are in accordance with their goals, and what it means for the commitments of an agent to be consistent. Second, we formalize deals in terms of coalitions who can achieve their goals without help from others. We show that verifying the consistency of a set of commitments of one agent is Pi(P)(2)-complete while checking the existence of a deal in a set of mutual commitments is Sigma(P)(2)-complete. Finally, we illustrate how the introduced concepts of commitments and deals can be used to achieve game-theoretical properties of the deals and to configure negotiation protocols.