Games with Linear Conjectures About System Parameters

We study a finite game in which the players’ payoffs are functions not only of their strategy profiles but also of certain (parameter) vector related to the whole system state. Relationships between the strategy profiles and the state vector are defined with mappings of rather general forms. Each player makes a decision on her best response to the system’s state and the other players’ strategies under an additional conjecture about the influence of a variation of her strategy upon the variation of the system’s parameters. We consider two versions: (i) constant conjectures, and (ii) a less restrictive variant, when the players’ conjectures satisfy certain constraints related to strategy profiles and the system’s parameters. We propose a concept of equilibrium in such a game and prove its existence. A couple of illustrative examples complete the manuscript.