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

No 1554, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

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: timing game; war of attrition; pre-emption game; potential function; Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C73 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2006-01
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Working Paper: Caller Number Five: Timing Games that Morph From One Form to Another (2004)
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