The Logic of Bargaining

This paper reexamines the game-theoretic bargaining theory from logic and Artificial Intelligence perspectives. We present an axiomatic characterization of the logical solutions to bargaining problems. A bargaining situation is described in propositional logic with numerical representation of bargainers' preferences. A solution to the n-person bargaining problems is proposed based on the maxmin rule over the degrees of bargainers' satisfaction. The solution is uniquely characterized by four axioms collective rationality, scale invariance, symmetry and mutually comparable monotonicity in conjunction with three other fundamental assumptions individual rationality, consistency and comprehensiveness. The Pareto efficient solutions are characterized by the axioms scale invariance, Pareto optimality and restricted mutually comparable monotonicity along with the basic assumptions. The relationships of these axioms and assumptions and their links to belief revision postulates and game theory axioms are discussed. The framework would help us to identify the logical reasoning behind bargaining processes and would initiate a new methodology of bargaining analysis.