An Axiomatic Approach to Arbitration and its Application in Bargaining Games

We define an arbitration problem as the triplet of a bargaining set and the offers submitted by two players. We characterize the solution to a class of arbitration problems using the axiomatic approach. The axioms we impose on the arbitration solution are "Symmetry in Offers,'' "Invariance'' and "Pareto Optimality.'' The key axiom, "Symmetry in Offers,'' requires that whenever players' offers are symmetric, the arbitrated outcome should also be symmetric. We find that there exists a unique arbitration solution, called the symmetric arbitration solution, that satisfies all three axioms. We then analyze a simultaneous-offer game and an alternating-offer game. In both games, the symmetric arbitration solution is used to decide the outcome whenever players cannot reach agreement by themselves. We find that in both games, if the discount factor of players is close to 1, then the unique subgame perfect equilibrium outcome coincides with the Kalai-Smorodinsky solution outcome.