First Uploaded: Oct. 19, 2017; This version: Oct. 19, 2017

Abstract: In this paper we build upon the work of Stanford in analyzing the distribution of the number of pure Nash equilibria in "random" two player finite common payoff games. By utilizing a combinatorial framework, complete distribution information for the cases of 2 by n games are found. Larger games can be analyzed in the same fashion, though the complexity is best handled through the use of compute algebra systems, such as Maple(TM). We also show the lack of need for this information for practical purposes by casting the problem into an experimental framework, collecting data on both two player and three player games with small strategy sets.

Maple Packages, Scripts, and Data

• CommonPayoffNash.txt, a small Maple package that contains procedures for computing random multi-player finite common payoff games and their Nash equilibria.

• MakeCommonPayoffData.txt, a small script for generating data on the distribution of the number of Nash equilibria in random multi-player finite common payoff games. Contains comments on parameter choices.

• CommonPayoffDataL44N3000000.m, a Maple data file containing the variable CommonPayoffDataL44N3000000, which stores the results of 3000000 trials of 4 by 4 common payoff games.

• CommonPayoffDataL44N3000000.txt, a text file which accompanies CommonPayoffDataL44N3000000.m that can be referred to without starting Maple.

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