Price leadership, spying, and secret price changes: a Stackelberg game with imperfect commitment

We analyze price leadership in a Stackelberg game with incomplete information and imperfect commitment. Sequential play is induced by an information system, represented by a spy, that reports the price of one firm to its rival before the latter chooses its own price. However, the Stackelberg leader may secretly revise its price with some probability. Therefore, the spy’s message is only an imperfect signal. This gives rise to a complex signaling problem where both sender and receiver of messages have private information and the sender has a chance to take another action with some probability. We find partially separating and pooling equilibria that satisfy equilibrium refinements such as the intuitive criterion and support collusive outcomes.