Partial Certifiability and Information Precision in a Cournot Game

This paper examines strategic information revelation in a Cournot duopoly with incomplete information about firm 1’s cost and information precision. Firm 2 relies on certifiable and ex post submissions of firm 1, without necessarily knowing whether firm 1 knows its cost or not. The sequential equilibria of the induced communication game are determined for different certifiability possibilities. A perfectly revealing equilibrium in which information precision is irrelevant is obtained under full certifiability. On the contrary, it is shown that if only payoff-relevant (fundamental) events can be certified, then the equilibrium output and profit of firm 1 decreases with its average information precision if this firm is uninformed or if its cost is high. A consequence of this local effect is that information precision has, on average, no value for a firm.