Distributed Negotiation with a Class of Quadratic Cost Functions

Abstract

This paper deals with the conflicting situation in which a set of players (or agents) have local objective functions, but depending on both: local decisions and decisions of other players. In particular, the cost functions are quadratic in the local decision variables, but they are linearly coupled with the decisions of neighbors. The players follow a game-based distributed negotiation pursuing to reach an equilibrium that satisfies them. This work derives the conditions for the existence, uniqueness and stability of Nash equilibriums when the decision variables are not constrained. For the case of constrained decision variables, the paper develops sufficient conditions for the convergence to these equilibriums. These results find application in distributed agent-based estimation, when the amount of information to be transmitted is limited.