The Gaussian CEO competitive pricing game

In this paper, we formulate a non cooperative pricing game over the quadratic Gaussian CEO problem with two agents. The agents observe independently corrupted versions of a source process X which the CEO is interested in estimating within an average distortion D. The agents quote a price per unit rate to generate revenue. They also incur a cost for communicating at the required rate. Given the agent prices, the CEO chooses a rate pair which minimizes its total cost. For a class of CEO problems, we show that when agent costs are convex in their respective rates, the aforementioned pricing game has a unique pure strategy Nash equilibrium. For a special case when the agents incur no costs, we explicitly determine the unique Nash equilibrium.