Static Linear-Quadratic Gaussian Games

Abstract

In this paper a simple static two-player linear-quadratic game where the players have private information is addressed. The players have private information, however each players is able to formulate an expression for his expected payoff, without the need, a la Harsanyi, to provide a prior probability distribution function of the game’s parameter, and without recourse to the player Nature. Hence, the closed-form solution of the game is obtained. It is shown that in this special case of a one-stage linear-quadratic game where the players have private information, the solution is similar in structure to the solution of the game with complete information, namely, the deterministic linear-quadratic game, and the linear-quadratic game with partial information, where the information about the game’s parameter is shared by the players. It is shown that the principle of certainty equivalence holds.