The Incentive-Targeting Problem in a Reflexive Game with a Point-Type Awareness Structure

Abstract. This paper considers a collective behavior model of agents under strategic uncertainty and incomplete awareness. Decision-making is modeled by a reflexive game in which participants choose their actions based on a hierarchy of beliefs about the game parameters, beliefs about beliefs, and so on. The study is focused on reflexive games with a point-type awareness structure and the linear best response of players. As shown below, the informational equilibrium in such games is analogous to the Nash equilibrium in a game on a network. Explicit expressions for the equilibrium responses of players are derived and conditions for the existence and uniqueness of equilibria are established. An incentive-targeting problem similar to that in a corresponding game on a network is formulated: a relationship is obtained between the equilibria in the game with common knowledge and the game with incomplete awareness in which the Principal individually reports new incentives to the players.

Keywords: reflexive game, informational equilibrium, games on networks, networked control.