The games that experimental subjects play: the utility of payoffs

Experiments have been used to study the behavioural validity of the predictions of game theory. Unfortunately, almost all of the games studied by experimental economists require at least one maintained assumptions in order to interpret the payoffs faced by subjects as utilities: that the subject has a linear utility function defined over monetary payoffs. With some notable exceptions, experimental games reward subjects by giving them money. Money is not the same as utility, which is what game theory assumes payoffs to be defined in terms of. Moreover, linear transformations of money do not accurately reflect linear transformations of utility unless the subject is risk neutral. Since there is evidence that experimental subjects tend to behave as if risk averse over the domain of income involved in most experiments, there is a potential confound in the interpretation of behaviour in experimental games. This point is well known, in the sense that it is easy to find occasional references to it by careful students of experimental games. And there are some remarkable experimental designs that attempt to control for this confound. But there are also many experimental games in which the possibility of risk aversion makes inferences difficult, to say the least. The problem is that the experimenter has lost control of one of the fundamentals of the game, and simply cannot know with any certainty what utility payoffs the subject is facing. We follow Goeree, Holt and Palfrey GEB 2003, and propose joint econometric estimation of the utility function of individuals from behavior in an individual lottery choice task and in strategic games, where behavior in the latter is constrained to be a Quantal Response Equilibrium. We develop computational tools using GAMBIT and Stata to facilitate the maximum likelihood estimation of behavior in experimental games defined over utility. These tools are applied to evaluate behavior over a wide range of experimental games. Our approach generalizes to also allow for other specifications in which utility might not be the same as own-payoff, such as an allowance for social preferences.