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Treasure game

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  • Matros, Alexander
  • Smirnov, Vladimir

Abstract

A prize is located at an unknown point on an island. In each period, each of n players searches a subset of the as yet unsearched portion of the island. If one player alone finds the prize he wins it and the game ends. Players have a per-period discount factor and a search cost proportional to area searched. Efficient symmetric Markov perfect equilibria are characterized when search is observable. Equilibria for n ≥ 2 exhibit two types of inefficiency: a tragedy of the commons (for small islands) and free riding (for large islands). For n ≥ 3, equilibrium properties are non-monotonic: players may be better off searching larger islands, and larger islands may take less time to search. When search is unobservable and players are sufficiently impatient, multi-player search can be efficient. The model is very general: applications include R&D races, team production, and extraction of exhaustible resources.

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File URL: http://hdl.handle.net/2123/7867
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Bibliographic Info

Paper provided by University of Sydney, School of Economics in its series Working Papers with number 2011-10.

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Date of creation: Oct 2011
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Handle: RePEc:syd:wpaper:2123/7867

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Keywords: uncertainty; search; R&D;

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