The price of insecurity: Public information transmission in zero-sum games

Alice has information relevant to a zero-sum game that Bob and Eve will be playing and she wants to help Bob. Alice is constrained to communicate publicly. How should she do it? What is the loss in utility to Bob compared to the case where Alice can communicate privately? We define the ratio of payoff achieved by Bob under optimal public signaling and that obtained through optimal private signaling as the `price of insecurity´. This price quantifies the value of secure communication between Alice and Bob. In some situations, some suitably designed public communication has the same value as secure communication. We explore the price of insecurity in different scenarios and show that a concave function on the unit simplex captures the value of public signaling. We derive an algorithm to compute the price of insecurity for a class of scenarios involving two games.