Cognitive constraints on how economic rewards affect cooperation

Cooperation often fails to spread in proportion to its potential benefits. This phenomenon is captured by prisoner's dilemma games, in which cooperation rates appear to be determined by the distinctive structure of economic incentives (e.g., $3 for mutual cooperation vs. $5 for unilateral defection). Rather than comparing economic values of cooperating versus not ($3 vs. $5), we tested the hypothesis that players simply compare numeric values (3 vs. 5), such that subjective numbers (mental magnitudes) are logarithmically scaled. Supporting our hypothesis, increasing only numeric values of rewards (from $3 to 300 cent) increased cooperation (Study 1), whereas increasing economic values increased cooperation only when there were also numeric increases (Study 2). Thus, changing rewards from 3 cent to 300 cent increased cooperation rates, but an economically identical change from 3 cent to $3 elicited no gains. Finally, logarithmically scaled reward values predicted 97% of variation in cooperation, whereas the face value of economic rewards predicted none. We conclude that representations of numeric value constrain how economic rewards affect cooperation.