Working Paper: CEPR ID: DP4177
Authors: Robin Mason; Akos Valentinyi
Abstract: This Paper provides a sufficient condition for the existence and uniqueness of equilibrium in monotone pure strategies, in games of incomplete information. First, we show that if each player's incremental ex post pay-off is uniformly increasing in its own action and type, and its type is sufficiently uninformative of the types of its opponents (independence), then its expected pay-off satisfies a strict single crossing property in its own action and type, for any strategy profile played by its opponents. This ensures that a player's best response to any strategy profile is a monotone pure strategy. Secondly, we show that if, in addition, there is sufficient heterogeneity of the conditional density of types, then the best response correspondence is a contraction mapping. This ensures equilibrium existence and uniqueness. Our approach allows us to establish these results in a wide range of applications, including cases where there are no existing existence results.
Keywords: Existence; Heterogeneity; Incomplete Information; Unique Pure Strategy Equilibrium
JEL Codes: C72; D82
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| incremental ex post payoff (G19) | strict single crossing property (C20) |
| independence of types (Y80) | monotonicity in best responses (C73) |
| sufficient heterogeneity in conditional density of types (C46) | best response correspondence becomes a contraction mapping (C45) |
| best response correspondence becomes a contraction mapping (C45) | equilibrium exists and is unique (C62) |