Social Motives and Expectations in One-Shot Asymmetric Prisoner's Dilemmas

Abstract

We propose a formal-behavioral framework with 3 components: nonselfish motives, expectations about others' nonselfish motives, and a game-theoretic component. For nonselfish motives, 3 nonstandard utility models representing altruism, inequality aversion, and norms are considered. Expectations are modeled as certain versus uncertain expectations. The game-theoretic component predicts behavior of actors and actors' expectations about behaviors of others. This framework is applied to asymmetric one-shot prisoner's dilemmas; predictions are tested experimentally. Formal analyses show that asymmetry provides new predictions through which nonstandard utility-expectation models can be distinguished. Empirical tests show that the inequality aversion model does considerably worse than altruistic and normative variants. Statistical tests for own motives, expected motives, and the association between the two are provided, while accounting for decision noise.

Keywords:

• cooperation
• game theory
• rational choice

Acknowledgments

We thank Vincent Buskens, Rens van de Schoot, participants of the ICS Cooperative Relations Seminars, the June 2009 Maastrict Behavioral and Experimental Economics symposium, and the June 2008 International Institute of Sociology congress for helpful comments.

Notes

¹This does not apply to intention based models that employ psychological game theory (e.g., Rabin; 1993), which include beliefs about others' intentions in the equilibrium solution. In this article we do not include intention based models because of their high degree of complexity owing to the use of psychological game theory with multiple free parameters and multiple equilibrium predictions (see Fehr and Schmidt; 2006). Moreover, we investigate simultaneous play one-shot games with limited feedback where there is no opportunity to observe intentions.

²This representation is mathematically equivalent to the representation U(x, y; w _i ) = w _i1 x + w _i2 y, given that utility is defined up to increasing affine transformations and w _i1 > 0; that is, people prefer more for self than less. The social orientation model is a special case of the utility model of Charness and Rabin (2002).

³In this article, we also exclude interdependent utility; that is, a player is interested in the “utility” of the other player not just the outcomes (Becker, 1993).

⁴In fact, it also predicts all higher order expectations about behavior.

⁵In the social orientation and normative models, multiple equilibria may arise, but only in cases where an actor is indifferent between cooperating and defecting, which yields an infinite number of equilibria. These cases can be ignored since they happen only for actors with specific values of social motive parameters.

Note. Observed cooperation rates and the Spearman's rank correlations (ρ) between observed and predicted rates are also included. N = 268 for Γ₅; N = 134 for all other games. CSE = certain symmetric expectations; USE = uncertain symmetric expectations.

Note. Observed percentages of ego's expectations about alter's cooperative behavior and the Spearman's rank correlations (ρ) between observed and predicted rates are also included. N = 134 for Γ₅; N = 67 for all other games. CSE = certain symmetric expectations; USE = uncertain symmetric expectations.

Note. Pr(H _i |H ₀ is the PMP of the model, given the unconstrained model and Pr(H _i |H _All is the PMP of the model, given all of the models in the table plus the unconstrained model. CSE = certain symmetric expectations; USE = uncertain symmetric expectations.

Note. Differences between own and expected social motives, covariance, and correlation between own and expected θ, and their standard errors are also given.

**p(2-sided) < 0.05. ***p(2-sided) < 0.01 for Wald tests.

⁶She uses the term “commitment theories” as a generic term for Kantian/normative theories.