Secondary Spectrum Market: To acquire or not to acquire side information?

In a secondary spectrum market primaries set prices for their unused channels to the secondaries. The payoff of a primary depends on the channel state information (CSI) of its competitors. We consider a model where a primary can acquire its competitors CSI at a cost. We formulate a game between two primaries where each primary decides whether to acquire its competitor's CSI or not and then selects its price based on that. Our result shows that no primary decide to acquire its competitor's CSI with an absolute certainty. When the cost of acquiring the CSI is above a threshold, there is a unique Nash Equilibrium (NE) where both the primaries remain uninformed of their respective competitor's CSI. When the cost is below the threshold, in the unique NE each primary randomizes between its decision to acquire the CSI or not. Our result reveals that irrespective of the cost of acquiring the CSI, the expected payoff of a primary remains the same.