Foresight, risk attitude, and utility maximization in naturalistic sequential high-stakes decision making

We explore three research questions related to risky sequential choice: (1) Does adherence to expected utility theory increase or decrease over sequential choices? (2) Does risk attitude vary systematically over sequential choices? and (3) To what extent are sequential choices influenced by future possible choices? We selected the game show, Deal or No Deal (DOND), as a context to study sequential decision making under risk with high stakes. We obtained data from complete game episodes involving 1421 players in three versions of the DOND (UK, US primetime, and US syndicated), aired between October 2005 and May 2010. In all three versions of the game, players make a binary choice between accepting a sure-thing offer that ends the game (“deal”) or continuing to play the game under risk (“no deal”). Separate stochastic choice models are constructed for each round of each of the three versions of the game to assess both risk attitude and adherence to expected utility theory. Players were found to be quite risk averse across all rounds and tended to be less risk averse and less rational over rounds in all three versions of the game. Results also suggest that players tend to consider the expected value for different sets of remaining cases one round ahead, but do not consider different possible sure-thing offers one round ahead.