A noncooperative infinite game can be approached by a sequence of discrete games. For each game in the sequence, a Nash solution can be found as well as their limit. This idea and procedure was used before as a theoretical device to prove existence of solutions to games with continuous payoffs and recently even for a class of games with discontinuous ones (Dasgupta and Maskin, 1981). No one, however, used the method for the actual solution of a game. Here, an example demonstrates the method's usefulness in finding a solution to a two-person game on the unit square with discontinuous payoff functions.
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Bjork, T.,On the Existence of Equilibrium Points for Certain n-Person Games, FOA Reports, Vol. 7, No. 4, 1973.
Shilony, Y.,Mixed Pricing in Oligopoly, University of California, Berkeley, PhD Dissertation, 1975.
Dasgupta, P., andMaskin, E.,The Existence of Equilibrium in Discontinuous Economic Games, I: Theory, London School of Economics, ICERD Discussion Paper, 1982.
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The author wishes to thank D. McFadden for very useful discussions. Financial support was provided in part by NSF Grant No. SOC-72-05551A02 to the University of California, Berkeley, California.
Communicated by Y. C. Ho
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Shilony, Y. The sequence method for finding solutions to infinite games: A first demonstrating example. J Optim Theory Appl 46, 105–117 (1985). https://doi.org/10.1007/BF00938764
- Game theory
- infinite games
- discrete approximations