Several extensions of the Abian-Brown Fixed Point Theorem and their applications to extended and generalized Nash equilibria on chain-complete posets

In this paper, we provide several extensions of the Abian-Brown Fixed Point Theorem from single-valued mappings to set-valued mappings on chain-complete posets. Then we examine some non-monetized, non-cooperative games where both the collections of the strategies and the ranges of the utilities for the players are posets. By applying the extensions of the Abian-Brown Fixed Point Theorem and by applying the order-preserving property of mappings, we prove some existence theorems of extended and generalized Nash equilibria for non-monetized, non-cooperative games on chain-complete posets. (C) 2013 Elsevier Inc, All rights reserved.