The Effect of Changes in Risk Attitude on Strategic Behavior

We study families of normal-form games with fixed preferences over pure action profiles but varied preferences over lotteries. That is, we subject players’ utilities to monotone but non-linear transformations and examine changes in the rationalizable set and set of equilibria. Among our results: The rationalizable set always grows under concave transformations (risk aversion) and shrinks under convex transformations (risk love). The rationalizable set reaches an upper bound under extreme risk aversion, and lower bound under risk love, and both of these bounds are characterized by elimination processes. For generic two-player games, under extreme risk love or aversion, all Nash equilibria are close to pure and the limiting set of equilibria can be described using preferences over pure action profiles. ∗I am grateful for conversations and correspondence with Pierpaolo Battigalli, Tilman Borgers, Amanda Friedenberg and Muhamet Yildiz, anonymous referees, and seminar participants at University of Arizona, Arizona State, University of Texas, Iowa State University, the Stony Brook International Game Theory Festival, and the World Congress of the Econometric Society. An earlier version had the working title “The Behavior of Solution Concepts under Changes in Risk Attitude.”