Convergence analysis for symmetric arbitration games final offer arbitration and delayed offer arbitration

Up to now, results on the existence of Nash equilibrium have required either continuity of payoff functions or compactness of strategy sets. However, in the arbitration game FOA and DOA, neither condition is satisfied. This paper first gives a new existence result for a general game. The result is then applied to the symmetric arbitration games FOA and DOA. The conclusions of this paper generalize the main result of Zeng, Nakamura and Ibaraki, that DOA leads to a convergence of offers but FOA does not.