A reason for unreason: returns-based beliefs in game theory

Players cooperate in experiments more than game theory would predict. We introduce the ‘returns-based beliefs’ approach: the expected returns of a particular strategy in proportion to total expected returns of all strategies. Using a decision analytic solution concept, Luce’s (1959) probabilistic choice model, and ‘hyperpriors’ for ambiguity in players’ cooperability, our approach explains empirical observations in various classes of games including the Prisoner’s and Traveler’s Dilemmas. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2 × 2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts.

Human pavlovian-instrumental transfer.

The vigor with which a participant performs actions that produce valuable outcomes is subject to a complex set of motivational influences. Many of these are believed to involve the amygdala and the nucleus accumbens, which act as an interface between limbic and motor systems. One prominent class of influences is called pavlovian-instrumental transfer (PIT), in which the motivational characteristics of a predictor influence the vigor of an action with respect to which it is formally completely independent. We provide a demonstration of behavioral PIT in humans, with an audiovisual predictor of the noncontingent delivery of money inducing participants to perform more avidly an action involving squeezing a handgrip to earn money. Furthermore, using functional magnetic resonance imaging, we show that this enhanced motivation was associated with a trial-by-trial correlation with the blood oxygenation level-dependent (BOLD) signal in the nucleus accumbens and a subject-by-subject correlation with the BOLD signal in the amygdala. Our data dovetails well with the animal literature and sheds light on the neural control of vigor.