Biased-Belief Equilibrium

Belief-based equilibrium

We introduce a new solution concept for short-sighted players engaging in a repeated interaction: a Belief-based equilibrium (BBE). In a BBE, players optimize myopically given their beliefs which are not necessarily correct, but are not contradicted by the data. We show that, if the stage game has a unique correlated equilibrium then the play of a BBE resembles a Nash equilibrium play. However,...

Convergence to equilibrium of biased plane Partitions

We study a single-flip dynamics for the monotone surface in (2 + 1) dimensions obtained from a boxed plane partition. The surface is analyzed as a system of non-intersecting simple paths. When the flips have a non-zero bias we prove that there is a positive spectral gap uniformly in the boundary conditions and in the size of the system. Under the same assumptions, for a system of size M , the m...

Counterfactuals, belief changes, and equilibrium refinements

Random belief equilibrium in normal form games

We de ̄ne Random Belief Equilibrium (RBE) in ̄nite, normal form games. We assume that a player's beliefs about the strategy choices of others are randomly drawn from a belief distribution. This distribution is dispersed around a central strategy pro ̄le, the focus. At an RBE: (1) Each player chooses a best response relative to her drawn beliefs. (2) The expected choice of each player coincides wi...

On Equilibrium Computation in Biased Games with Quadratic Penalties

In this paper, we study games with continuous action spaces and non-linear payoff functions. Our key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in these games. We begin by studying Lipschitz games, which encompass, for example, all concave games with Lipschitz continuous payoff functions. We provide an efficient...