More on maximum likelihood equilibria for games with random payoffs and participation

Abstract

Maximum likelihood Nash equilibria were introduced by Borm et al. (1995) for games with nitely many players and random payos. In Voorneveld (1999) random participation was added to the model. These existence results were extended by Balder (2000c) to continuum games with random payos and participation. However, in that paper the complicated measurability issue for the central equilibrium likelihood notion was bypassed by using inner probabilities for the central equilibrium likelihood notion. Here those measurability questions are shown to have a quite satisfactory resolution; this makes the maximum likelihood equilibrium notion more natural. Our main results are not only more general than those found in Borm et al. (1995) and Voorneveld (1999), but also improve upon them.