Comments on "Reverse auction: the lowest positive integer game"

TL;DR

This paper critiques previous analyses of the lowest unique positive integer game, showing the prior solutions are not Nash equilibria and providing improved solutions for small player numbers and approximations for larger groups.

Contribution

It demonstrates that earlier solutions are not Nash equilibria and offers exact solutions for three and four players, along with an approximate solution for many players.

Findings

Previous solutions are not Nash equilibria.

Exact solutions for 3- and 4-player cases.

Approximate solutions for many players.

Abstract

In Zeng et al. [Fluct. Noise Lett. 7 (2007) L439--L447] the analysis of the lowest unique positive integer game is simplified by some reasonable assumptions that make the problem tractable for arbitrary numbers of players. However, here we show that the solution obtained for rational players is not a Nash equilibrium and that a rational utility maximizer with full computational capability would arrive at a solution with a superior expected payoff. An exact solution is presented for the three- and four-player cases and an approximate solution for an arbitrary number of players.