Hide&Seek

Hide&Seek - Fatal Attraction: Focality, Naivete,...

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Fatal Attraction: Focality, Naivete, and Sophistication in Experimental "Hide-and-Seek" Games Vincent P. Crawford and Nagore Iriberri 1 University of California, San Diego 20 August 2004; revised 15 September 2004 Abstract: Rubinstein, Tversky, and Heller elicited subjects' initial responses to games in which a Hider and a Seeker choose simultaneously among four locations, with the Seeker winning a given amount if he chooses the same location as the Hider and the Hider otherwise winning that amount. The game has a unique equilibrium, in which both players randomize uniformly over locations; but the design framed locations non-neutrally and subjects deviated systematically from equilibrium in ways that were highly sensitive to the framing. This paper compares alternative explanations of the results and proposes a structural non-equilibrium model of initial responses to explain them. Keywords: experimental game theory, framing effects, focal points, bounded rationality, strategic sophistication JEL classification numbers: C70, C92 1 Email: vcrawfor@weber.ucsd.edu and niriberr@weber.ucsd.edu . We are grateful to the National Science Foundation (Crawford) and the Centro de Formacion del Banco de España (Iriberri) for research support; to Miguel Costa-Gomes, Victor Ferreira, Barry Nalebuff, Steven Scroggin, Ricardo Serrano-Padial, David Swinney, Joel Sobel, Joel Watson, and Mark Voorneveld for helpful comments or discussions; to Dale Stahl for providing a copy of Bacharach and Stahl (1997a); to Stahl and Daniel Zizzo for searching for Bacharach and Stahl (1997b); and to Ariel Rubinstein for providing a copy of Rubinstein and Tversky (1993), searching for additional data, and a helpful discussion. Glenn Close and Michael Douglas were no help at all. 1
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1. Introduction Game theorists and economists have been intrigued by "Hide-and-Seek" games for more than 50 years (von Neumann (1953)). Rubinstein and Tversky (1993; henceforth "RT") and Rubinstein, Tversky, and Heller (1996; "RTH") were perhaps the first to study such games experimentally; see also Rubinstein (1999; "R"). RT, RTH, and R (collectively "RTH" from now on) elicited subjects' initial responses to several closely related Hide-and-Seek games. In a leading example of their games, one player, the Hider, hides a "treasure" or "prize" in one of four locations; and the other player, the Seeker, looks in one of the locations. Because the Seeker looks without observing the Hider's choice, their choices are strategically simultaneous. If the Seeker chooses the same location as the Hider he wins a given amount; if not, the Hider wins that amount. Instead of giving subjects a payoff matrix, RTH explained the Hide-and-Seek games in "stories," probably increasing comprehension. Their key innovation was to present the games with non-neutral framing of the locations. R, for example, told Seekers: "You and another student are playing the following game: Your opponent has hidden a prize in one of four boxes arranged in a row. The boxes are marked as follows: A, B, A, A. Your goal is, of course, to find the prize. His goal is that you will not find it. You are allowed to open only one box. Which box are you going to
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Hide&Seek - Fatal Attraction: Focality, Naivete,...

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