This paper uses data from the popular television game-show, "Deal or No Deal?", to
analyse the way individuals make choices under risk. In a unique approach to the problem, I present a formal game-theoretical model of the show in which both the contestant and the banker are modelled as strategic players. I use standard techniques to form hypotheses of how rational expected utility-maximisers would behave as players in the game and I test these hypotheses with the relevant choice data. The main result is that an increasing offer function is the result of optimal behaviour when the banker is uncertain about the contestant’s risk attitudes. This result provides a theoretical foundation to the empirical model of the banker that pervades the literature. Estimates of the coefficient of relative risk aversion are consistent with estimates from other studies and estimates of the discernment parameter suggest contestants have difficulty making choices
