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Saliency of Outside Options in the Lost Wallet Game

Authors
Disciplines
  • Economics

Abstract

CERTIFICATES PAPER Saliency of Outside Options in the Lost Wallet Game By James C. Cox, Maroš Servátka, and Radovan Vadovič 1. Introduction In the lost wallet game (Dufwenberg and Gneezy, 2000), the first mover (FM) can choose between the actions Take and Leave. If FM chooses Take, her payoff is x and the payoff of the second mover (SM) is Alternatively, if FM chooses Leave then SM can divide the amount 0. π between the two players. So long as xπ > y , the FM’s choice of Leave generates a surplus for the two players. SM can choose any amount [0, ]π∈ for the FM payoff and yπ − for himself. If FM chooses Leave, she gains (resp. loses) money if SM c s hoose y x> sp. (re y x< ).1 Arguably, the size of the FM payoff x in the Take option provides a measure of the amount of trust the FM places in SM, hence reciprocal SMs will choose amounts for FM payoffs y that increase with x . Surprisingly, Dufwenberg and Gneezy (hereafter DG) report that the size of the foregone Outside Option x does not affect SM choices of payoff amounts y for FMs. A similar observation was made by Brandts, et al. (2006) in a pie-sharing game. We find this behavior puzzling for the following reasons. If SM views the Outside Option x as FM’s “investment” that is necessary in order for π to be made available to SM, then a higher forgone x implies that FM is willing to invest more, which should inspire SM to return more to FM. Our question about robustness of the reported invariance of y with x hinges on the perceived salience of the amount of the Outside Option. When making her choice, the SM must be aware of the amount of FM’s foregone payoff x if she is going to respond to the size of x. However, in DG (and also in Brands, et al.) the responses of SMs were obtained via the strategy method which does not allow SMs to observe FM choices before making their decisions. Thus the monetary consequences of the FMs’ actions, which are at the heart of this pu

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