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Hot versus cold behavior in centipede games

Abstract

There is a long-standing unresolved debate in game theory and experimental economics regarding the behavioral equivalence of the direct-response method (hot play) and the strategy method (cold play). Using a unified experimental framework, we compare behavior elicited via both methods in four different Centipede Games that differ in their incentives to take or pass, in the evolution of those incentives over decision nodes, and in the asymmetry of the incentives across the two player roles. Out of the four Centipede Games, we find that both methods yield statistically different behavior in two of them, while in the remaining two we cannot reject the same behavior across the hot and cold methods. Whenever the behavior diverges, hot play consistently makes individuals stop earlier. These findings should shift the question from whether both methods are generically behaviorally equivalent to under which conditions they are (not) and why.

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Notes

  1. Kawagoe and Takizawa (2012) scale the payoffs in the constant CG up to balance the incentives across the two CGs.

  2. Given the matching protocol in this treatment, the number of participants did not have to be even.

  3. The distributions of behavior do not differ between the two places, in which we conducted our experiment. We performed two different tests of independence of the two samples for each game: Fisher's exact test of independence and two-sample Kolmogorov-Smirnov test. No test rejects the equality of both distributions (\(p=0.14\) and \(p=0.22\) for CG1; \(p=1.00\) and \(p=1.00\) for CG2; \(p=1.00\) and \(p=1.00\) for CG3; \(p=0.8\) and \(p=1.00\) for CG4).

  4. In all rounds, there are five independent observations (different matching groups) for each CG.

  5. Figure A.3 in Online Supplement A.1 reports stopping probabilities conditional on reaching a particular decision node (rather than the distribution of reached decision nodes) showing similar results.

  6. Tests of proportions in Table A.1 in Online Supplement A.1 corroborate the results reported in the main text.

  7. We find little evidence of learning over rounds in the hot treatment. See the additional analysis in Online Supplement A.2.

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Funding

Financial support from the Departamento Vasco de Educación, Política Linguística y Cultura (IT1367-19 and IT1336-19), Ministerio de Economía y Competividad and Fondo Europeo de Desarrollo Regional (ECO 2015-64467-R, ECO 2015-66027-P, PID2019-106146GB-I00, and PID2019-108718GB-I00 MINECO/FEDER), and GAČR (17-25222S) is gratefully acknowledged.

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Correspondence to Jaromír Kovářík.

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N. Iriberri: IKERBASQUE, Basque Foundation for Research.

J. Kovářík: CERGE-EI, a joint workplace of Charles University in Prague and the Economics Institute of the Czech Academy of Sciences, Politických vĕznů 7, 111 21 Prague, Czech Republic.

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García-Pola, B., Iriberri, N. & Kovářík, J. Hot versus cold behavior in centipede games. J Econ Sci Assoc 6, 226–238 (2020). https://doi.org/10.1007/s40881-020-00096-z

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Keywords

  • Centipede games
  • Direct method
  • Strategy method
  • Experiments

JEL Classification

  • C72
  • C91
  • D91