In a spatial trust game, a trustor invests and a trustee decides whether to return a share. Cooperation requires trust from the trustor and reciprocity from the trustee. Without any mechanism to promote trustworthy behavior, defection dominates: trustees keep everything, trustors learn not to invest, and the system collapses into mutual distrust.
A natural fix is to reward trustworthy behavior. Zhang, Wang, Liu, del Genio, Boccaletti, and Lu (arXiv:2603.07328, March 2026) introduced an inter-role reward mechanism: a trustor can pay an extra cost to reward a trustee who reciprocates. The expectation is straightforward — rewarding good behavior should promote good behavior.
Moderate rewards do exactly this. They break the dominance of defection, create clusters of cooperating players in the spatial network, and allow trust to spread.
Excessive rewards destroy trust.
When rewards are too large, they create an incentive structure where the reward itself becomes the target. Trustees don't cooperate because trust is valuable — they cooperate because the reward is profitable. And once the reward is large enough, it attracts a different strategy: nonreturn. Players exploit the reward-granting mechanism without sustaining the cooperative relationships that make it worthwhile. The excessive reward converts a trust-building mechanism into an extraction opportunity.
The cost of the reward matters too, and not in the expected direction. Cheap rewards fail to promote trust — they don't create enough advantage for rewarders over non-rewarders to sustain cooperative clusters. More costly rewards (though not excessive ones) work better: the higher cost consolidates the clusters of rewarders by making the investment signal credible. The reward has to be expensive enough to be believable but not so generous that it becomes exploitable.
The optimal regime is moderate reward at moderate cost. Below this, defection dominates. Above this, exploitation dominates. Trust lives in the intermediate region — not because compromise is generically good, but because the incentive landscape has a specific topology where the cooperative equilibrium only survives in a finite band.
Zhang, Wang, Liu, del Genio, Boccaletti, and Lu, "Offer of a reward does not always promote trust in spatial games," arXiv:2603.07328 (March 2026).