Order-clustered fixed point theorems on chain-complete preordered sets and their applications to extended and generalized Nash equilibria
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Open Access
- 22 July 2013
- journal article
- Published by Springer Nature in Fixed Point Theory and Applications
- Vol. 2013 (1) , 192
Abstract
In this paper, we introduce the concept of order-clustered fixed point of set-valued mappings on preordered sets and give several generalizations of the extension of the Abian-Brown fixed point theorem provided in (Mas-Colell et al. in Microeconomic Theory, 1995), which is from chain-complete posets to chain-complete preordered sets. By using these generalizations and by applying the order-increasing upward property of set-valued mappings, we prove several existence theorems of the extended and generalized Nash equilibria of nonmonetized noncooperative games on chain-complete preordered sets. MSC:46B42, 47H10, 58J20, 91A06, 91A10.Keywords
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