Copyright © 2013 Jie Ren et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 fundamen-tal difference from the standard Nash and Stackelberg games. Then we show that the players ’ belief functions can be re-garded as the optimizatio...
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