Optimism and Pessimism in Games

This paper considers the impact of ambiguity in strategic situations. It extends the existing literature on games with ambiguity-averse players by allowing for optimistic responses to ambiguity. We use the CEU model of ambiguity with a class of capacities introduced by Jaffray and Philippe (1997), which allows us to distinguish ambiguity from ambiguity-attitude, and propose a new solution concept, Equilibrium under Ambiguity (EUA), for players who may be characterized by ambiguity-preference. Applying EUA, we study comparative statics of changes in ambiguity-attitude in games with strategic complements. This extends work in Eichberger and Kelsey (2002) on the e¤ects of increasing ambiguity if players are ambiguity averse. Address for Correspondence David Kelsey, Department of Economics, University of Exeter, Rennes Drive, Exeter, Devon, EX4 4PU, ENGLAND. Keywords Ambiguity in games, support, strategic complementarity, optimism, multiple equilibria. JEL Classi…cation C72, D81. Research supported by ESRC grant no. RES-000-22-0650 and a Leverhulme Research Fellowship. We would like to thank Dieter Balkenborg, Andrew Colman, Jayant Ganguli, Simon Grant, Sushma Murty, Anna Stepanova, Jean-Marc Tallon, Peter Wakker and participants in seminars at the universities of Bielefeld, Birmingham, Exeter, the Institute of Advanced Studies in Vienna, Paris School of Economics, FUR and RUD, the referees and editor of this journal for comments and suggestions.