Boundary effects in the Marschak-machina triangle

Abstract

This paper presents the results of a study that sheds new light on the shape of indifference curves in the Marschak-Machina triangle. The most important observation, obtained non-parametrically, concerns jumps in indifference curves at the triangle legs towards the triangle origin. These jumps, however, do not appear at the hypotenuse. The pattern observed suggests discontinuity in lottery valuation when the range of lottery outcomes changes and is best explained by decision-making models based on the psychological phenomenon of range dependence (Parducci, 1965; Cohen, 1992; Kontek & Lewandowski, 2018). Models founded on other psychological phenomena, e.g., discontinuity in decision weights (Kahneman & Tversky, 1979), cumulative probability weighting (Tversky & Kahneman, 1992), attention shifting (Birnbaum, 2008), overweighting of salient payoffs (Bordallo, Gennaioli & Shefrin, 2012), and treating stated probabilities as imperfect information (Viscusi, 1989), predict indifference curve shapes that differ from the one obtained in this study.