Integer game with delay

Abstract

In this note, we study a version of a war of attrition, in which the players pick delays and the player with the longest delay wins. Unlike the war of attrition, all players have to experience the longest delay before the consumption takes place. We show that the game has no mixed strategy Nash equilibria. The game can be seen as a re-interpretation of the integer game, which is one of the most important and most criticized constructions in the full implementation literature. Unlike the integer game, it has a well-defined best response against any mixed strategy.