The Logic of Bargaining

Abstract

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.