Shipwrecks and Treasure Hunters

36 Pages Posted: 9 May 2017

See all articles by Nicolas de Roos

Nicolas de Roos

University of Liverpool; University of Sydney

Alexander Matros

Moore School of Business

Vladimir Smirnov

The University of Sydney - School of Economics

Andrew Wait

University of Sydney

Date Written: May 5, 2017


We examine dynamic search as a game in which two rivals explore (an island) for a hidden prize of known value. In every period until its discovery, the players decide how much of the unsearched area to comb. If a player finds the prize alone he wins it and the game ends. Players have a per-period discount factor and costs proportional to the area they search. First, as a benchmark for efficiency, we solve the monopoly problem. Second, in the duopoly setting we show that if players are sufficiently impatient they can inefficiently over-search in the unique symmetric Markov perfect equilibrium (SMPE) – a result akin to the tragedy of the commons. On the other hand, if players are patient: the SMPE is unique except for possibly one point; and either over- or under-search can result. Finally, with patient players, several counter-intuitive results can arise: for example, players might be better off searching a larger island or looking for a less valuable prize.

Keywords: R&D, search, uncertainty

JEL Classification: D21, D32, O32

Suggested Citation

de Roos, Nicolas and Matros, Alexander and Smirnov, Vladimir and Wait, Andrew, Shipwrecks and Treasure Hunters (May 5, 2017). Available at SSRN: or

Nicolas De Roos (Contact Author)

University of Liverpool ( email )

Chatham Street
Brownlow Hill
Liverpool, L69 7ZA
United Kingdom

University of Sydney ( email )

University of Sydney
Sydney NSW 2006

Alexander Matros

Moore School of Business ( email )

1014 Greene St
Columbia, SC 29208
United States

Vladimir Smirnov

The University of Sydney - School of Economics ( email )

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

Andrew Wait

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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