Procedurally Rational Volunteers

Abstract

The mixed-strategy equilibrium applied to the volunteer's dilemma (Diekmann, 1985) predicts that the probability that at least 1 bystander volunteers decreases, if the number of bystander increases. I argue that this prediction lacks empirical support and demonstrate that an alternative solution concept from the literature on bounded rationality, the procedurally rational equilibrium (Osborne & Rubinstein, 1998), yields alternative predictions. I supply some empirical evidence that the alternative solution concept fares better in explaining observed behavior in the volunteer's dilemma.

Keywords:

• bounded rationality
• experimental economics
• procedurally rational equilibrium
• volunteer's dilemma

ACKNOWLEDGMENTS

I thank the editor and the referees for very helpful comments that considerably improved the paper. Thanks also to Stefan Wehrli whose talk on the volunteer's dilemma set me on this track.

Notes

¹Strictly speaking, the situation in which only 1 recipient receives the e-mail does not amount to a volunteer's dilemma. However, we can use the 57% helping subjects as an estimate for the proportion of subjects having preferences as assumed in the volunteer's dilemma, which imply that a bystander prefers to help in the absence of other bystanders. Then 45/57 ≈ 79% of all subjects having preferences as assumed in the volunteer's dilemma help in the situation in which there are 5 recipients of the e-mail. This proportion is far too high to support ABE.

²Closer inspection reveals that this result is due to the artificial assumption that the order in which the decision maker perceives the alternatives is constant across all choice problems. Still, it holds that this kind of analysis of decision procedures yields counterintuitive and profound results. For a deeper discussion of the benefits of such behavioral characterizations the reader is referred to Spiegler (2008).

³We adopt the following notational convention regarding u: If and , then is the payoff to a player who chooses s, while the other players choose strategies as described in .

⁴This condition is satisfied in the volunteer's dilemma, since for all it holds

The condition merely simplifies the definition of w(·,·), since ties in random variables r(·,·) are ruled out; that is, there is no pair s, s′ ∈ S, s ≠ s′ such that r(s, p) = r(s′, p).

⁵ N : Number of subjects participating in games of size n. G : Number of observed games of size n. Since each subject participated in 20 games, we have G = (N · 20)/n. q : Observed rate of defectors computed over all games of size n. r: Rate of games of size n in which at least 1 bystander volunteers. S E _q : Standard error of q, i.e., . S E _r : Standard error of r, i.e., .

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/gmas.