Equilibrium solution to the lowest unique positive integer game

TL;DR

This paper derives the equilibrium solution for the lowest unique positive integer game, providing a systematic approach to analyze strategic behavior in complex multi-player reverse auction scenarios.

Contribution

It introduces a novel systematic method to determine equilibrium strategies for any number of players in the game, overcoming previous analytical challenges.

Findings

Equilibrium strategies are explicitly characterized for the game.

The game exemplifies conflict between individual and group interests.

Abstract

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.