Caller Number Five: Timing Games that Morph from One Form to Another

25 Pages Posted: 19 May 2005

See all articles by Andreas Park

Andreas Park

University of Toronto - Finance Area

Lones Smith

University of Wisconsin at Madison - Department of Economics

Date Written: July 12, 2007

Abstract

There are two varieties of timing games in economics: In a war of attrition, more predecessors helps; in a pre-emption game, more predecessors hurts. In this paper, we introduce and explore a spanning class with 'rank-order payoffs' that subsumes both as special cases. In this environment with unobserved actions and complete information, there are endogenously-timed phase transition moments. We identify equilibria with a rich enough structure to capture a wide array of economic and social timing phenomena - shifting between phases of smooth and explosive entry.

We introduce a tractable general theory of this class of timing games based on potential functions. This not only yields existence by construction, but also affords rapid characterization results. We then flesh out the simple economics of phase transitions: Anticipation of later timing games influences current play - swelling pre-emptive atoms and truncating wars of attrition. We also bound the number of phase transitions as well as the number of symmetric Nash equilibria. Finally, we compute the payoff and duration of each equilibrium, which we uniformly bound. We contrast all results with those of the standard war of attrition.

Keywords: Games of timing, war of attrition, preemption game

JEL Classification: C73

Suggested Citation

Park, Andreas and Smith, Lones, Caller Number Five: Timing Games that Morph from One Form to Another (July 12, 2007). Cowles Foundation Discussion Paper No. 1554, Available at SSRN: https://ssrn.com/abstract=724403

Andreas Park (Contact Author)

University of Toronto - Finance Area ( email )

Toronto, Ontario M5S 3E6
Canada

Lones Smith

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

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