Problems and Pseudo-Problems in Understanding Cooperation in Social Dilemmas

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Acknowledgments

We gratefully acknowledge support from the Leicester Judgment and Decision Making Endowment Fund and from the University of Leicester for granting study leave to the second author.

Notes

The “last-minute intrigue” experimental data in the target article are interpreted in terms of theoretical predictions that begin with “a player who has chosen to cooperate, who believes that the other player will probably [emphasis added] cooperate too.” This player is given the opportunity to switch unilaterally to defection and “now faces a choice between the value of p_cR and p_cT.” The player actually faces a choice between expected payoffs of p_cR + (1 – p_c )S and p_cT + (1 – p_c )P, respectively, and correct predictions require expressions of this form. However, from that point on, the probabilities disappear entirely and the analysis proceeds, in effect, with the tacit assumption that the other player chooses the same strategy with certainty, so that, given a last-minute opportunity for a bilateral switch: “Now, the projection hypothesis advises against switching because it would suggest trading the anticipated R payoff for the P payoff,” and so on. A bilateral switch from joint cooperation to joint defection is thus a reduced game consisting of just the top-left and bottom-right cells of Figure 1, and a rational (individual payoff-maximizing) player will obviously decline to switch, because the choice is simply between R and P, and R > P. Similarly, for Player I, a unilateral switch from joint cooperation reduces the game to the left-hand column in Figure 1, and a rational Player I will switch, because T > R. For similar reasons, a rational player will accept a bilateral switch and decline a unilateral switch from joint defection. These are the choices that most of the experimental participants predicted, but it is not correct to say that “the results uniquely supported the projection hypothesis,” because they support game theory (and common sense).