Nash equilibrium in games with incomplete preferences

摘要: This paper investigates Nash equilibrium under the possibility that preferences may be incomplete. I characterize Nash-equilibrium-set of such a game as union Nash-equilibrium-sets certain derived games with complete preferences. These can from original by simple linear procedure, provided admit concave vector-representation. theorems extend some results on finite Shapley and Aumann. The applicability theoretical is illustrated examples oligopolistic theory, where firms are modelled to aim at maximizing both profits sales (and thus have multiple objectives). Mixed strategy trembling hand perfect equilibria also discussed.