Strategically Valuable Information

We extend the comparison of experiments in Blackwell (1953) to a strategic setting that both simplifies and expands upon ideas in Gossner (2000). We introduce a partial order on correlating signals, called more strategically informative, and prove that it is equivalent to the partial order more strategically valuable — namely, inducing more Bayesian Nash equilibrium payoff vectors. Our conditions are tractable, affording proof of the existence and uniqueness of the maximally informative correlating signal. They are also amenable to applications. For instance, we provide a partial ordering on sunspot equilibria that applies for all environments. In our centerpiece application to repeated games with private monitoring, we show that a more strategically informative monitoring structure weakly expands the set of sequential equilibria. This mirrors an early result of Kandori (1992) for repeated games with imperfect public monitoring