Abstract to "Simplifying Timing Games" Christopher K. Butler

Game theorists have examined various versions of timing games, the most notable of which is the game of duel. Early in the history of game theory, there was a proliferation of research extending the zero-sum game of duel in several directions. There has also been research modeling non-zero-sum timing games. Timing games are not, however, widely employed in game theory and are rarely seen in applied models. Two factors explain this under use of timing games. First, the most developed timing games are zero-sum and are viewed as having only tactical applications (e.g., strategic decisions on the battlefield). Second, the mathematics of timing games--especially of the non-zero-sum variants--is rather complicated and, hence, difficult to interpret in substantive applications.

In this paper I present a non-zero-sum timing game that is simple in form and solution and yet flexible enough to be used in conjunction with applied modeling. The game has only two players and each player has a decision of when to act. I make extremely simplifying assumptions for the base model and show that the timing decision often collapses into one of acting immediately or waiting forever--i.e., waiting until the circumstances of the game change.

I then explore extensions to the model that demonstrate its theoretical and applied value. For example, adding symmetrical subgames to the timing game's terminal nodes in order to endogenize who goes first in an existing extensive-form game. This extension allows for an examination of initiation problems; for instance, what is the equilibrium of strategic timing when there are multiple legislative proposers and who goes first matters?