The Social Will-Testing Game and its Solution

TL;DR

This paper analyzes a two-player game called Will-Testing, revealing a unique equilibrium distribution of strategies among many players, which may explain social hierarchies in animals.

Contribution

It introduces the Will-Testing game, proves the existence of a strategy distribution equilibrium among large populations, and suggests biological implications.

Findings

No equilibrium exists for the two-player game.

An equilibrium distribution exists for large populations playing all pairings.

The equilibrium involves all players adopting different strategies.

Abstract

We examine a two-person game we call Will-Testing in which the strategy space for both players is a real number. It has no equilibrium. When an infinitely large set of players plays this in all possible pairings, there is an equilibrium for the distribution of strategies which requires all players to use different strategies. We conjecture this solution could underlie some phenomena (like pecking orders) observed in animals.