One Interaction.
Two Reputations.
More Cooperation.

WATCHING one person help another tells us something obvious about the helper. A research team asks us to notice the quieter message: the recipient was considered worth helping. If observers use the same encounter to update both reputations, individual opinions can converge and cooperation can become more stable.

That is the mechanism reported by Tham Yukari Jessica of Kobe University's Graduate School of Humanities, Christian Hilbe of Interdisciplinary Transformation University, and Yohsuke Murase of RIKEN. Murase directs the Mathematical Social Science Team at the RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences and concurrently serves as a senior research scientist in the Discrete Event Simulation Research Team at the RIKEN Center for Computational Science.

Their paper, “Indirect reciprocity with dual private assessment,” appeared in the Proceedings of the National Academy of Sciences on August 28, 2026. The work combines analytical calculations with computer simulations, including a search of more than one million combinations of social norms on RIKEN's Fugaku supercomputer.

The Old Puzzle: Helping Someone Who Will Not Repay You

Indirect reciprocity explains how cooperation can travel through reputation. Alice bears a cost to help Bob. Carol sees or hears about the action and forms a favorable opinion of Alice. Later, Carol helps Alice. The benefit returns through a third person rather than directly from Bob.

The logic requires social norms: rules specifying whom an individual should help and how an observer should judge a decision. Helping a well-regarded person may improve the donor's reputation. Refusing someone with a bad reputation may be judged differently. The answer depends on the norm being modeled.

Early theories often simplified the problem by assuming that everyone agreed on reputations. Private-assessment models remove that convenience. Each observer holds an individual view. A missed interaction or an assessment error can make two people disagree about the same person. Those different opinions produce different choices, which generate more conflicting observations. Small errors spread.

What the Second Reputation Changes

A model interaction contains three roles. The donor decides whether to cooperate. The recipient experiences that decision. An observer evaluates what happened. Conventional models generally update the donor's reputation after the encounter.

Dual reputation updating changes the recipient's reputation as well. If Alice sees Bob help Charlie, she assesses Bob's conduct while also treating Bob's choice as information about Charlie. Charlie may be someone Bob regards as worthy of assistance. One observed action carries another person's implied judgment without requiring gossip or a public registry.

The paper illustrates the idea with Recipient Image Scoring, or RIS. Under that rule, a recipient who receives cooperation is assessed as good; a recipient denied cooperation is assessed as bad. The rule is intentionally spare. It asks only what the donor did to the recipient, information that can be observed directly.

Synchronization Without a Central Scorekeeper

The model's contribution is not simply that recipients can have reputations. They already do. The new feature is that observers revise those reputations from the treatment recipients receive during ordinary interactions.

That creates a synchronization channel. If many observers see the same recipient helped, their individual assessments move in the same direction. More aligned reputations produce more aligned decisions about whom to help. Those aligned decisions then generate more consistent evidence for evaluating donors and recipients.

Mathematical analysis and simulation showed that the feedback can prevent private assessments from drifting apart. In the study's models, opinion alignment raised both the rate of cooperation and evolutionary stability—the ability of a cooperative norm to resist replacement by an invading behavioral strategy.

Evolutionary stability is a technical result, not a certificate of fairness. A rule may resist competing strategies inside a formal population while being undesirable for real people. The study measures cooperation and stability under defined assumptions; it does not measure rights, well-being or procedural justice.

Fugaku Searches More Than One Million Norms

A mechanism can look successful because researchers selected one unusually favorable rule. To test whether recipient assessment was a narrow exception, the team used Fugaku to examine more than one million combinations of social norms.

Kobe University's official English release reports that 61 norms produced both high cooperation and evolutionary stability. Every one of the 61 included some form of dual reputation update. That does not prove dual assessment is necessary in every possible society, but it shows that the effect repeatedly appeared among the strongest rules in the model space examined.

The scale needs a boundary. “More than one million” refers to formal combinations defined by the researchers. It does not enumerate all cultures, institutions, information systems or power relationships that exist in human life. Computational breadth within a model is not the same as empirical generality outside it.

The Same Feedback Can Spread Exclusion

Reputation synchronization sounds helpful only if the shared judgment is accurate. If observers treat assistance as evidence of worth, people who already attract support may receive still more. Social advantage can compound without independent evidence about the recipient's conduct.

The reverse is more troubling. A person may be denied help for an unfair reason. If observers then mark that recipient as bad because they saw the refusal, the first act of exclusion supplies a reason for the next one. Mistreatment becomes reputational evidence, and reputational evidence produces more mistreatment.

The researchers identify exclusion and bullying as possible harmful outcomes. They do not claim to have demonstrated those behaviors in human subjects. The study reveals a plausible feedback structure; experiments and field evidence must determine when people actually use the treatment of others to form reputations.

Why Gossip and Institutions Still Matter

Previous models have used perspective-taking, gossip and public reputation systems to keep private opinions correlated. Those mechanisms exchange or centralize information. Dual updating is attractive because it extracts an additional signal from conduct already being observed.

But behavior is ambiguous. A donor may refuse because help is unsafe, impossible or already provided elsewhere. An observer may not know the recipient's history. A powerful donor may mistreat someone, and others may mistake power for reliable judgment. Direct observation does not eliminate the need for context.

Dual updating therefore complements rather than replaces other coordination mechanisms. If the concept ever informs real institutional design, it would need ways to explain decisions, challenge false assessments, correct errors and protect people who are already marginalized.

A Model With Two Opposing Lessons

The first lesson is economical. Observers may not need a central authority or constant information exchange to align their reputations. Each interaction reveals how the donor acted and how the recipient was treated. Using both signals can stabilize cooperation.

The second lesson is political. If treatment becomes evidence of worth, the people who determine that treatment gain disproportionate influence over everyone else's judgments. Esteem can reproduce esteem. So can stigma.

The study's next step is not automatic deployment. It is measurement: when do people infer reputation from another person's treatment, when do they resist that inference, and what information interrupts a false cascade? Dual reputation updating gives cooperation theory a clean answer inside a model. Its value outside the model will depend on whether societies can preserve the coordination without reproducing the cruelty.