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Cooperation among competitors-whether sharing the burden of wind resistance in the Tour de France, forming price-fixing cartels in economic markets, or adhering to arms-control agreements in international treaties-seldom spreads in proportion to the potential benefits. To gain insight into the minds of uncooperative agents, economists and social psychologists have used the prisoner's dilemma task to examine factors leading to cooperation among competitors. Two types of factors have emerged in these studies: the relative rewards of defecting versus cooperating and breakdowns in trust, forgiveness and communication. The generalizability of economic and social psychological factors, however, relies on the assumption that agents' comparisons of gains and losses (whether for themselves, others, or both) preserves ratio information over arbitrary units, such as dollars and cents, and real rewards, such as food. This assumption is inconsistent with psychophysical studies on how the brain represents quantitative information, which suggests that mental magnitudes increase logarithmically with actual value. Thus, discrimination of two numerical magnitudes improves as the numerical distance between them increases and decreases as the magnitudes increase. Here we show an important consequence of this representational system for economic decision making: in the prisoner's dilemma game, purely nominal increases in the numerical magnitude of payoffs (such as, converting dollar values to cents or whole grapes into grape-parts) has a large effect on cooperative behaviour. Moreover, a logarithmic scaling of the ratio of rewards for cooperation versus defection predicted 97% of variability in observed cooperation, whereas the objective ratio predicted 0% of variability. By linking the brain's system of representing the magnitude of rewards to motivations for cooperative behaviour, these findings suggest that the nature of numerical representations may also account for the subjective value function described by Bernoulli, in which the apparent value of monetary incentives increases logarithmically with actual value.

Numbers, not value, motivate cooperation in humans and orangutans