Fatal Attraction: Salience, Naïveté, and Sophistication in Experimental “Hide-and-Seek” Games

Abstract

" Hide-and-seek" games are zero-sum two-person Game theorists have been intrigued by hideand-seek games-zero-sum two-person games in which one player wins by matching the other's decision and the other wins by mismatching-for more than 50 years (John von Neumann 1953). These games cleanly model a strategic problem that is central to many economic, political, and social settings, as well as the obvious military and security applications. Examples include entry games where entry requires a differentiated product, and blocking it requires matching the entrant's design; election campaigns in which a challenger can win only by campaigning in different areas from those of the incumbent; and fashion games in which hoi polloi wish to mimic the elite but the elite prefer to distinguish themselves.Although zero-sum two-person games are one of game theory's success stories, equilibrium analysis of hide-and-seek games is not very helpful as a guide to prediction or decision making. There seem to be two main reasons for this, both illustrated by our epigraphs: hide-and-seek games are often played without clear precedents, so equilibrium depends on strategic thinking rather than learning; but such thinking may not follow the fixed-point logic of equilibrium. A game theorist would reply to our first epigraph, "But if investigators thought that way, a meeting with government officials is precisely where a government would try to kill an opponent." Further, hide-and-seek games are usually played on naturally occurring cultural * Crawford: University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (e-mail: vcrawfor@ dss.ucsd.edu); Iriberri: Departament d'Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain (e-mail: nagore.iriberri@upf. edu). Most of Iriberri's work on this paper was completed at the University of California, San Diego. We are grateful to the National Science Foundation (Crawford), the Centro de Formación del Banco de España (Iriberri), and the Barcelona Economics Program of CREA (Iriberri) for research support; to Miguel Costa-Gomes, Victor Ferreira, Navin Kartik, Barry Nalebuff, Steven Scroggin, Ricardo Serrano-Padial, Joel Sobel, David Swinney, Mark Voorneveld, Mark Walker, Joel Watson, and three anonymous referees for helpful comments or discussions; to Dale Stahl for helpful discussions and for providing a copy of Michael Bacharach and Stahl (1997a); to Stahl and Daniel Zizzo for searching for Bacharach and Stahl (1997b); to Barry O'Neill and Amnon Rapoport (with the help of Ido Erev and Mark Walker, respectively) for providing data from their experiments; and to Ariel Rubinstein for providing a copy of Rubinstein and Amos Tversky (1993), searching for additional data, and helpful discussions. Glenn Close and Michael Douglas (http://www.imdb.com/title/tt0093010/) were no help at all.

On Public Opinion Polls and Voters' Turnout

“…In particular, the provision of information signi…cantly raises the participation of voters supporting the slightly larger team relative to the participation of voters supporting the smaller team, thus a¤ecting the election's results. 7 The correlation between closeness and turnout observed in the laboratory is consistent with results in the related empirical literature [see, for example, Shachar and Nalebu¤ (1999)]. Feddersen and Sandroni (2006) show that this correlation can be explained using a model where voters have ethical preferences.…”

“…For closely divided preferences, on the contrary, we observe important quantitative di¤erences between the subjects'turnout and the predictions of the theoretical model underlying the experiment. 7 Although Figure 1 reveals a clear and signi…cant e¤ect of closeness on participation, the …gure masks important and unexpected di¤erences between teams for a given distribution of preferences. The heterogeneous e¤ect of closeness between teams is presented in Figure 2, which decomposes turnout as a function of the size of the teams.…”

Heterogeneous quantal response equilibrium and cognitive hierarchies

“…This difference in beliefs results in equilibrium strategies (and induced mixed 4 While the assumptions of the F i above preclude this case, it can be approximated arbitrarily closely by F i that do satisfy the assumptions. 5 Recall that strategies are maps from type to choice probabilities.…”

Coordination when there are restricted and unrestricted options

“…This counts against H3. 5 We test H4 by first estimating what weights, when attached to each rule for each category, can best explain the choice of labels in Experiment I under the assumption that each rule yields the distribution of choices revealed by Experiment II (see Crawford and Iriberri 2007, for a similar approach). Using maximum likelihood, we estimate these for each category individually as well as in the aggregate by pooling all the decision problems.…”