Putting Yourself in Someone Else’s Shoes: Mirror-Image Mapping in Strategic Decision Making

Abstract This paper characterizes the behavior of a backward inducting first mover (the decision maker) in a two-stage extensive form game. Having limited knowledge of her fellow player’s preference, the decision maker maps each outcome to its mirror image and infers the second mover’s behavior using her own preference. The axioms can be used to test whether such a decision-making procedure is at work. The decision maker’s preference over the outcomes and the mirror-image mapping she applies are both identified from her preference over actions in the first stage of the game.