A Strategic Model of Magical Thinking: Axioms and Analysis

53 Pages Posted: 10 Oct 2014

See all articles by Philipp Sadowski

Philipp Sadowski

Duke University - Department of Economics

Brendan Daley

Johns Hopkins University

Date Written: September 26, 2014

Abstract

This paper seeks to make two contributions. First, we propose and analyze a tractable model of strategic play in which players behave as if their expectations about their opponents' behavior vary with their own choices. We refer to this nonstandard updating as magical thinking. The model provides a unified view of documented behavior in a range of often-studied games, such as the Prisoners' Dilemma, the Battle of the Sexes, Hawk-Dove, and the Stag Hunt. Second, we provide axioms applied to the behavior of the collection of players in symmetric 2x2 games, and a representation theorem that establishes these axioms to be the precise behavioral content of the model. We thereby suggest a novel way to import the axiomatic methodology of individual decision theory to strategic settings and demonstrate the benefits of this approach.

In the model, the degree to which players exhibit magical thinking is heterogeneous in the population and is captured by players' types. All players perceive types to be i.i.d. draws from a common distribution. We show that the model's parameters, namely these individual types and the commonly perceived distribution, can be (essentially) identified from behavior in games, allowing for tractable comparative statics. Finally, the model generates novel predictions across games. For example, the ability of a collection of players to coordinate on Pareto superior Nash equilibria in coordination games is positively correlated with their degree of cooperation in Prisoners' Dilemma games.

The supplement for this paper are available at the following URL: http://ssrn.com/abstract=2507394

Keywords: Prisoners' dilemma, coordination games, magical thinking, cooperation

JEL Classification: C7, D8

Suggested Citation

Sadowski, Philipp and Daley, Brendan, A Strategic Model of Magical Thinking: Axioms and Analysis (September 26, 2014). Economic Research Initiatives at Duke (ERID) Working Paper No. 173, Available at SSRN: https://ssrn.com/abstract=2507377 or http://dx.doi.org/10.2139/ssrn.2507377

Philipp Sadowski (Contact Author)

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States
919-660-1800 (Phone)

Brendan Daley

Johns Hopkins University ( email )

Baltimore, MD 20036-1984
United States

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