When Can Rivals Share Information Truthfully?

The problem with asking rivals to share

A firm might benefit from knowing more about its competitors before setting a price. Yet it might also benefit from giving an intermediary a misleading picture of its own business if that changes the recommendations its competitors receive.

In a preprint, economists Yifan Dai and Anna Merotto study when an intermediary can overcome this tension. Their question is not whether people can send messages, but whether communication can change the outcome when everyone acts in their own interest.

The authors examine a mathematical model of players with independently drawn private information, such as firm-specific demand or costs. The players are symmetric: they face the same rules and their private characteristics come from the same distribution. Their actions are strategic complements, meaning that a player’s preferred action rises when others take higher actions. In the pricing example, a firm tends to prefer a higher price when its competitors raise theirs.

Recommendations must be credible

Before players learn their private characteristics, an initially uninformed mediator commits to a communication rule. After learning their characteristics, players report to the mediator, receive private recommendations and choose their actions. Recommendations can involve randomization.

For the arrangement to work, truth-telling and following the recommendation must be an equilibrium: no player can gain by reporting a different characteristic and then choosing whatever action is best after seeing the resulting recommendation. The researchers compare these outcomes with the model’s unique equilibrium without communication. They call communication informative when it produces a different outcome.

The model separates two consequences of a report. It can influence the actions expected from other players, and it can affect how much a player learns from the recommendation. A mediator can sometimes use the second effect to offset an incentive to manipulate the first. But the mediator cannot promise arbitrary information: recommendations must also be actions that recipients are willing to follow.

Aligned and misaligned incentives

The authors find a sharp distinction based on how private characteristics change players’ preferences. Consider the case in which a higher type prefers a higher action. If higher types benefit less from higher actions by others, the relevant preferences are misaligned. In the model, informative mediated communication is then impossible for any of the type distributions considered.

The reason is a conflict between truth-telling and obedience. Truthful reporting calls for the prospect of higher opponent actions to be directed toward the types that value them more. But the actions players are willing to take in response to recommendations pull the relationship in the opposite direction.

When the preferences are aligned—including the boundary case where types value higher opponent actions equally—the conflict need not rule communication out. Even then, informative communication is possible only if a relevant extreme type is sufficiently far from the average type. Which extreme matters depends on the direction of incentives. This separation determines whether the mediator can provide enough useful information to compensate for the temptation to induce more favorable behavior by others.

One construction uses a cutoff: in a particular case, low reports can sometimes reveal that every report was low, while high reports receive no such additional information. The information available after a low report helps make truthful reporting worthwhile despite the lower expected actions it induces from opponents.

What the pricing example shows

The paper applies the results to firms selling differentiated products and competing on price. With private production costs, higher-cost firms prefer higher prices but benefit less from competitors raising theirs. This is the misaligned case, so the model rules out informative mediation.

With private demand instead, higher-demand firms prefer higher prices and benefit more from competitors’ price increases. Informative communication may then be possible. Under the paper’s nonnegative-markup condition, it requires the lowest demand type to be sufficiently far below the mean.

In the baseline model, every type of every player is at least as well off under a communication equilibrium as without communication. When informative communication is possible, an equilibrium can be constructed that makes every type strictly better off. That is a statement about the players, not a general claim that customers benefit: in the private-demand example, the paper finds lower expected consumer surplus under informative communication.

The authors also compare communication with a benchmark in which recommendations can depend directly on players’ information without eliciting truthful reports. Whenever such information sharing can raise the players’ aggregate payoff above the no-communication level, the best truthful mediated outcome falls strictly short of that benchmark.

These are theoretical results, not evidence that a particular pricing platform succeeds or fails at sharing information. The baseline assumes independent private characteristics, symmetric players and a specific payoff structure. Real intermediaries may also have their own information, verify reports or control decisions—possibilities the model sets aside.