The optimal strategy in the minimum effort game

A simple expression is derived for the optimal strategy in the minimum effort game. This maps from player beliefs to an optimal effort level. From this expression the set of Nash equilibria in the game is fully characterized. All Nash equilibria are symmetric and involve at most two actions being played with positive probability. We discuss how our expression for the optimal strategy can help inform on the comparative statics of a change in the number of players and effort cost benefit ratio.