Bayesian Nash equilibrium and variational inequalities

Takashi Ui

Journal of Mathematical Economics, 2016, vol. 63, issue C, 139-146

Abstract: This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.

Keywords: Bayesian game; Linear quadratic Gaussian game; Network game; Potential game; Variational inequality; Strict monotonicity (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (23)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:63:y:2016:i:c:p:139-146

DOI: 10.1016/j.jmateco.2016.02.004

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