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A Forward-Looking Nash Game and Its Application to Achieving Pareto-Efficient Optimization
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, China
Department of Electronic and Electrical Engineering, University College London, Torrington Place, London, UK
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, China
- 1 School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, China
- 2 Department of Electronic and Electrical Engineering, University College London, Torrington Place, London, UK
- 3 School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing, China
Applied Mathematics·Volume 04 (2013)·Pages 1609–1615·Published 8 November 2013·DOI10.4236/am.2013.412218
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Abstract
Recognizing the fact that a player’s cognition plays a defining role in the resulting equilibrium of a game of competition, this paper provides the foundation for a Nash game with forward-looking players by presenting a formal definition of the Nash game with consideration of the players’ belief. We use a simple two-firm model to demonstrate its fundamental difference from the standard Nash and Stackelberg games. Then we show that the players’ belief functions can be regarded as the optimization parameters for directing the game towards a much more desirable equilibrium.
KeywordsBeliefCognitionIterative AlgorithmNash EquilibriumPareto-OptimalityStackelberg
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