How we decide how big a reward is...

Furlong and Opfer do a nice set of experiments showing that we can be lured into making decisions by numbers that seem bigger than they really are. We apparently go with numerical values rather than real economic values. They asked volunteers to take part in the prisoner’s dilemma behavioral test, in which two partners are offered various rewards to either work together or defect. The idea is that in the long term, the participants earn the most money by cooperating. But in any given round of play, they make the most if they decide to turn against their partner while he stays loyal. (The reward is lowest when both partners defect.) When the reward for cooperation was increased to 300 cents from 3 cents, the researchers found, the level of cooperation went up. But when the reward went from 3 cents to $3, it did not. Here is their abstract:

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¢) increased cooperation, whereas increasing economic values increased cooperation only when there were also numeric increases. Thus, changing rewards from 3¢ to 300¢ increased cooperation rates, but an economically identical change from 3¢ 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.