Equilibrium solution to the lowest unique positive integer game

Details Equilibrium solution to the lowest unique positive integer game Equilibrium solution to the lowest unique positive integer game

2010-01-07

arxiv.org/abs/1001.1065v1

Fluctuation and Noise Letters, 9:1, pp. 61-68 (2010)

Mathematics

Combinatorics

8 pages, 3 figures

Scientific paper

10.1142/S0219477510000071

We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider become very much involved even for a small number of players, which has hindered a precise analysis in previous works. We here present a systematic way to reach the solution for a general number of players, and show that this game is an example of conflict between the group and the individual interests.

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