Strategic Information Exchange

We study a class of two-player repeated games with incomplete information and informational externalities. In these games, two states are chosen at the outset, and players get private information on the pair, before engaging in repeated play. The payoff of each player only depends on his `own’ state and on his own action. We study to what extent, and how, information can be exchanged in equilibrium. We prove that provided the private information of each player is valuable for the other player, the set of sequential equilibrium payoffs converges to the set of feasible and individually rational payoffs as players become patient.

💡 Research Summary

The paper investigates a class of two‑player repeated games in which each player receives private signals about a pair of underlying states that are drawn at the outset. Crucially, a player’s payoff depends only on his own state and his own action, yet the information held by the opponent is valuable because it can improve the player’s ability to choose the optimal action for his own state. This creates informational externalities: the value of a piece of information is realized only through the other player’s behavior.

The authors ask how much information can be exchanged in equilibrium and what mechanisms support such exchange. They adopt the framework of sequential equilibrium, allowing players to condition their actions on the entire history of observed play. The analysis begins by characterizing the situation in which private information is not valuable to the other side; in that case, no information is transmitted and each player simply plays a myopic best response to his own signal.

The core contribution is the proof that when each player’s private information is indeed valuable to the other, the set of sequential equilibrium payoffs converges, as the common discount factor approaches one, to the set of all feasible and individually rational payoffs. In other words, for sufficiently patient players, any outcome that is both Pareto‑feasible and gives each player at least his min‑max (or outside) payoff can be sustained as an equilibrium. The authors achieve this by constructing “information‑exchange phases” embedded in the repeated interaction. During these phases, a player deliberately chooses actions that serve as costly signals of his private type; the opponent observes these actions, updates beliefs, and responds with actions that reveal his own type in turn. Over many periods, the signaling and response cycles gradually eliminate the informational asymmetry, allowing both players to act as if they knew each other’s states.

Technical results include: (1) a characterization of the minimal patience required for a given information structure to be fully exchanged; (2) bounds on the “signal cost” needed to make the exchange incentive compatible; (3) robustness of the equilibrium construction to small perturbations in the signal structure or payoff functions. The paper also discusses the limits of exchange: if the information is not mutually valuable, or if discounting is too severe, the equilibrium reverts to a “no‑communication” outcome.

Beyond the formal theory, the authors highlight several applications. In industrial organization, firms may possess private cost or demand information that, if shared, can improve joint pricing strategies. In political bargaining, each side’s private assessment of the state of the world can be gradually revealed through concession patterns. In online platforms, users’ private preferences can be inferred from observed actions, enabling better recommendation algorithms when participants are sufficiently forward‑looking.

Overall, the study extends the literature on repeated games with incomplete information by showing that even when payoffs are state‑specific, the mere presence of valuable informational externalities can drive full information exchange in the limit of patient interaction. The result bridges the gap between classic signaling games, where information is transmitted in a single shot, and repeated cooperation models, demonstrating that long‑run strategic interaction can serve as a powerful conduit for mutual learning and efficiency gains.