Duplicative search

Abstract

In this paper we examine the dynamic search of two rivals looking for a prize of known value that is hidden in an unknown location, modeled as search for treasure on an island. In every period, the players choose how much to search of the previously unsearched portion of the island in a winner-takes-all contest. If the players cannot coordinate so as to avoid searching the same locations, the unique equilibrium involves complete dissipation of rents. On the other hand, if the players have some (even limited) ability to coordinate so as to avoid duplicative search and the search area is sufficiently small, there is a unique equilibrium in which the full area is searched and each player earns a positive expected return.

Shipwrecks and treasure hunters

“…When δ = 1/4, these expressions are defined by their limits as δ → 1/4. Note also that this theorem corrects the critical points derived in Proposition 3 of Matros and Smirnov (2016).…”

“…isfactory; it is the welfare analysis of two-player search in a dynamic environment that is a key contribution of the model in this paper. The setup we use here is similar to Matros and Smirnov (2016), who analyze duplication in search. 8 They find that with independent search, all rents are dissipated.…”

“…The following Lemma proved in Matros and Smirnov (2016) implies value iteration can be used to solve (6). With the help of Lemma 2, one can construct the sequence {Ψ s } and find all SMPE.…”

Social Welfare in Search Games with Asymmetric Information

“…5 In addition, each finder's private value is multiplied by a duplication factor ρ ∈ [0, 1] if two or more players find the prize simultaneously. The case in which ρ = 0 corresponds to setups in which a price (Bertrand) competition between the pharmaceutical firms or a "credit war" between the research labs (see Example 1) destroys the finder's private value in case of a simultaneous discovery (e.g., Chatterjee & Evans, 2004;Matros & Smirnov, 2016;de Roos et al, 2018). The opposite case of ρ = 1 may correspond to a setup in which one of the players who search in the prize's location is randomly chosen to be its undisputed owner, and she gains the prize's full value (e.g., Fershtman & Rubinstein, 1997;Konrad, 2014;Chen et al, 2015).…”

“…These situations (henceforth, search games) are common in various important areas such as R&D races in oligopolistic markets (e.g., Loury et al, 1979;Fershtman & Rubinstein, 1997;Chatterjee & Evans, 2004;Konrad, 2014;Akcigit & Liu, 2015;Letina, 2016;Liu & Wong, 2019), design of innovation contests (e.g., Che & Gale, 2003;Adamczyk et al, 2012, Erat & Krishnan, 2012Bryan & Lemus, 2017;Letina & Schmutzler, 2019;Mihm & Schlapp, 2019;Matros et al, 2019), pharmaceutical research (e.g., Matros & Smirnov, 2016;de Roos et al, 2018), academic research (e.g., Kleinberg & Oren, 2011), and product design within a firm (e.g., Loch et al, 2001). Most of the existing literature assumes that all agents have symmetric information regarding the prize's location.…”