General Timing Games with Multiple Players

34 Pages Posted: 29 Apr 2022

See all articles by Vladimir Smirnov

Vladimir Smirnov

The University of Sydney - School of Economics

Andrew Wait

University of Sydney

Date Written: April 22, 2022


We examine innovation in an $n$-player market-entry timing game with complete information and observable actions. In our novel multi-player setup, we allow for heterogeneous payoffs between players and for a leader's payoff
functions to be multi-peaked and non-monotonic, only requiring that followers' payoffs are non-increasing with the time of the leader's entry. We provide conditions for when equilibrium actions do not depend on historic payoffs, showing in this case that the $n$-player asymmetric game generates standard leader-maximized or preemption equilibria. In the two-player game we provide a complete characterization of the pure-strategy equilibria for when historic payoffs affect equilibrium actions (including the possibility of no equilibria in pure strategies). Finally, we relate our results to three applications from the literature.

Keywords: timing games, preempting entry, innovation

JEL Classification: C72, L13, O31, O33

Suggested Citation

Smirnov, Vladimir and Wait, Andrew, General Timing Games with Multiple Players (April 22, 2022). Available at SSRN: or

Vladimir Smirnov

The University of Sydney - School of Economics ( email )

Rm 370 Merewether (H04)
The University of Sydney
Sydney, NSW 2006 2008

Andrew Wait (Contact Author)

University of Sydney ( email )

School of Economics
University of Sydney, NSW 2006
+61-2-9351-3060 (Phone)
+61-2-9351-4341 (Fax)


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