Bulletin of the Korean Mathematical Society (대한수학회보)
- Volume 33 Issue 4
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- Pages.587-592
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- 1996
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- 1015-8634(pISSN)
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- 2234-3016(eISSN)
A new equilibrium existence via connectedness
- Rim, Dong-Il (Department of Mathematics and Department of Mathematics Education, Chungbuk National University, Cheongju 360-763) ;
- Im, Sung-Mo (Department of Mathematics and Department of Mathematics Education, Chungbuk National University, Cheongju 360-763) ;
- Kim, Won-Kyu (Department of Mathematics and Department of Mathematics Education, Chungbuk National University, Cheongju 360-763)
- Published : 1996.11.01
Abstract
In 1950, Nash [5] first proved the existence of equilibrium for games where the player's preferences are representable by continuous quasiconcave utilities and the strategy sets are simplexes. Next Debreu [3] proved the existence of equilibrium for abstract economies. Recently, the existence of Nash equilibrium can be further generalized in more general settings by several athors, e.g. Shafer-Sonnenschein [6], Borglin-Keiding [2], Yannelis-Prabhaker [8]. In the above results, the convexity assumption is very essential and the main proving tools are the continuous selection technique and the existence of maximal elements. Still there have been a number of generalizations and applications of equilibrium existence theorem in generalized games.