Context-Dependent Forward Induction Reasoning

This paper studies the case where a game is played in a particular context. The context influences what beliefs players hold. As such, it may affect forward induction reasoning: If players rule out specific beliefs, they may not be able to rationalize observed behavior. The effects are not obvious. Context-laden forward induction may allow outcomes precluded by context-free forward induction. At the formal level, contextual reasoning is defined within an epistemic structure. In particular, we represent contextual forward induction reasoning as “rationality and common strong belief of rationality” (RCSBR) within an arbitrary type structure. (The concept is due to Battigalli-Siniscalchi [6, 2002].) We ask: What strategies are consistent with RCSBR (across all type structures)? We show that the RCSBR is characterized by a solution concept we call Extensive Form Best Response Sets (EFBRS’s). We go on to study the EFBRS concept in games of interest. Forward induction is a basic concept in game theory. It reflects the idea that players rationalize their opponents’ behavior, whenever possible. In particular, players form an assessment about the future play of the game, given the information about the past play and the presumption that their opponents are strategic. This has implications for the play of the game. Here, we study the implications of forward induction reasoning when there is a context to the game. Because there is such a context, a certain event may be “transparent” to the players. That is, the context may rule out certain beliefs. This may limit the ability of players to rationalize past behavior, and so may affect forward induction reasoning. Take the following illustrative example: Consider the case where it is transparent that players all drive on the right side of the road, irrespective of whether they are driving north or south. Suppose, further, that it is transparent that players don’t like automobile accidents. Then, if Ann actually sees Bob drive on the left side of the road, she cannot justify his past behavior. In particular, she We are indebted to Adam Brandenburger, John Nachbar, and Marciano Siniscalchi for many helpful conversations. We also thank Ethan Bueno de Mesquita, Alfredo Di Tillio, Alejandro Manelli, Adam Szeidl, and seminar participants at Bocconi University, Boston University, New York University, Northwestern University, and UC Berkeley for important input. Battigalli thanks MIUR and Bocconi University. Friedenberg thanks the W.P. Carey School of Business and the Olin Business School. c d fi 0 1 3 0 0 9 . r a p Department of Economics and IGIER, Bocconi University, 1 Via Roentgen, 20136 Milan (Italy), [email protected]. Department of Economics, Arizona State University, W.P. Carey School of Business, P.O. Box 873806, Tempe, AZ 85287-3806, [email protected], http://www.public.asu.edu/~afrieden/.