TITLE:
A Forward-Looking Nash Game and Its Application to Achieving Pareto-Efficient Optimization
AUTHORS:
Jie Ren, Kai-Kit Wong, Jianjun Hou
KEYWORDS:
Belief; Cognition; Iterative Algorithm; Nash Equilibrium; Pareto-Optimality; Stackelberg
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.12,
November
20,
2013
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.