Communication and Coordination : The Case of Boundedly Rational Players

Using the level-k model of boundedly rational interaction, we fully characterize the e¤ects of pre-play communication in symmetric and generic 2 2 games. We …nd that oneway communication weakly increases coordination on Nash equilibrium outcomes in all such games. Although one-way communication entails Nash equilibrium when relatively sophisticated players meet, there are games in which average payo¤s fall when one-way communication is allowed. Two-way communication can yield higher average payo¤s than one-way communication in coordination games such as Stag Hunt, but in other games twoway communication reduces both average payo¤s and the degree of coordination below the no-communication level. Extending our analysis to larger and less symmetric games, we …nd that communication facilitates coordination in all two-player common interest games. However, we also identify games in which communication hampers coordination. Keywords: Pre-play communication, coordination games, Stag Hunt, level-k, bounded rationality. JEL codes: C72. This paper is an extensive revision of Ellingsen and Östling (2006). We have bene…ted greatly from the detailed comments from Vincent Crawford and three anonymous referees. We are also grateful for helpful discussions with Colin Camerer, Drew Fudenberg, Joseph Tao-yi Wang and seminar participants at the Arne Ryde Symposium 2007, California Institute of Technology, and Stockholm School of Economics. Financial support from the Torsten and Ragnar Söderberg Foundation and the Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged. yAddress: Department of Economics, Stockholm School of Economics, Box 6501, SE–113 83 Stockholm, Sweden. E-mail: tore.ellingsen@hhs.se. zAddress: Department of Economics, Stockholm School of Economics, Box 6501, SE–113 83 Stockholm, Sweden. E-mail: robert.ostling@hhs.se