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Third-party punishment as a costly signal of trustworthiness


Third-party punishment (TPP)1,2,3,4,5,6,7, in which unaffected observers punish selfishness, promotes cooperation by deterring defection. But why should individuals choose to bear the costs of punishing? We present a game theoretic model of TPP as a costly signal8,9,10 of trustworthiness. Our model is based on individual differences in the costs and/or benefits of being trustworthy. We argue that individuals for whom trustworthiness is payoff-maximizing will find TPP to be less net costly (for example, because mechanisms11 that incentivize some individuals to be trustworthy also create benefits for deterring selfishness via TPP). We show that because of this relationship, it can be advantageous for individuals to punish selfishness in order to signal that they are not selfish themselves. We then empirically validate our model using economic game experiments. We show that TPP is indeed a signal of trustworthiness: third-party punishers are trusted more, and actually behave in a more trustworthy way, than non-punishers. Furthermore, as predicted by our model, introducing a more informative signal—the opportunity to help directly—attenuates these signalling effects. When potential punishers have the chance to help, they are less likely to punish, and punishment is perceived as, and actually is, a weaker signal of trustworthiness. Costly helping, in contrast, is a strong and highly used signal even when TPP is also possible. Together, our model and experiments provide a formal reputational account of TPP, and demonstrate how the costs of punishing may be recouped by the long-run benefits of signalling one’s trustworthiness.

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Figure 1: A model of TPP as a costly signal of trustworthiness.
Figure 2: Behavioural experiments confirm key predictions of our model.


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We gratefully acknowledge the John Templeton Foundation for financial support; A. Bear, R. Boyd, M. Crockett, J. Cone, F. Cushman, E. Fehr, M. Krasnow, R. Kurzban, J. Martin, M. Nowak, N. Raihani, L. Santos, and A. Shaw for helpful feedback; and A. Arechar, Z. Epstein, and G. Kraft-Todd for technical assistance.

Author information

Authors and Affiliations



J.J.J., M.H. and D.G.R. designed and analysed the model. J.J.J., P.B. and D.G.R. designed the experiments. J.J.J. conducted the experiments and analysed the results. J.J.J., M.H., P.B. and D.G.R. wrote the paper.

Corresponding authors

Correspondence to Jillian J. Jordan or David G. Rand.

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Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Agent-based simulations from our second microfoundation model in which gaining interaction partners reduces TPP costs.

TPP evolves over time in this modified model, in which a Signaller’s punishment costs are endogenous (decreasing in the number of times she has been accepted as a partner), rather than exogenously fixed as lower for trustworthy types. We use parameters similar to the main text agent-based simulations, where punishment is moderately informative and helping is more informative. Shown is the average over 500 simulations of Signallers’ average probability of helping and punishing (when experiencing the small signalling cost) in each generation, as well as the expected probability of experiencing the small punishing cost for trustworthy and exploitative types (based on the average number of times trustworthy and exploitative types were chosen as partners) at the end of each generation. See Supplementary Information section 1.3.2 for a detailed description of our second microfoundation model.

Extended Data Figure 2 Full agent-based simulation results from the main text model.

Here, we present the Signaller and Chooser strategies for each scenario from our main model agent-based simulations, a summary of which is shown in Fig. 1c. In scenario 1, when only punishment is possible, punishment-signalling evolves, regardless of the informativeness of small helping costs ISH. a, Signallers are likely to punish when the punishment cost is small and b, Choosers are likely to accept Signallers who punish, while they almost always reject those who do not. In scenario 2, when only helping is possible, helping-signalling evolves, and becomes stronger as ISH increases. c, Signallers are increasingly likely to help when the helping cost is small and d, Choosers are increasingly likely to accept Signallers who help, while they almost always reject those who do not. In scenario 3, when both signals are available, agents evolve to use both signals with equal frequency when they are equally informative, but to favour helping as ISH increases. e, As ISH increases, Signallers are increasingly likely to help, both when they have only a small helping cost (light blue dots), and when they have both small costs (dark blue dots); and are decreasingly likely to pay to punish, both when they only have a small punishing cost (light red dots), and when they have both small costs (dark red dots). f, As ISH increases, Choosers are increasingly likely to accept Signallers who help but do not punish (blue dots), and increasingly likely to reject Signallers who punish but do not help (red dots). Furthermore, regardless of ISH, Choosers almost always reject Signallers who neither help nor punish (brown dots). However, Chooser behaviour in response to Signallers who both punish and help (purple dots) stays at chance levels across all values of ISH (because Signallers never send both signals, and thus Choosers do not face selection pressure to respond optimally to such Signallers).

Extended Data Figure 3 Our two-stage experimental design involving Signallers and Choosers.

First, in the signalling stage, the Signaller participates in a third-party punishment game (TPPG). Here a Helper decides whether to share with a Recipient, and then a third-party Punisher decides whether to pay to punish the Helper if the Helper was selfish (chose not to share). In our three experimental conditions, we manipulate the role(s) the Signaller plays in the TPPG. In the punishment-only condition, the Signaller plays once as the Punisher; in the punishment-plus-helping condition, the Signaller plays twice (with two different sets of other people) as the Punisher and the Helper; in the helping-only condition, the Signaller plays once as the Helper. Thus we vary which signal(s) are available. Second, in the partner choice stage, the Chooser plays a trust game with the Signaller. The Chooser decides how much to send the Signaller and any amount sent is tripled by the experimenter. The Signaller then decides how much of the tripled amount to return. Choosers use the strategy method to condition their sending on Signallers’ TPPG decisions.

Extended Data Figure 4 Third-party punishment is perceived as a stronger signal of trustworthiness than retaliation in our additional experiment (study 2).

In our additional experiment, we manipulate whether the second stage of our game is a trust game (TG) or an ultimatum game (UG). In the TG, Choosers maximize their payoffs by sending more money to trustworthy Signallers (who will return a large amount); thus, preferential sending to punishers reflects expectations of punisher trustworthiness. In this game (left bars), punishment has large reputational benefits: replicating study 1, Choosers (n = 405) send 16 percentage points more to punishers than non-punishers, P < 0.001. In the UG, Choosers (n = 421) maximize their payoffs by sending more money to retaliatory Signallers (who are willing to pay the cost required to reject low offers); thus, preferential sending to punishers reflects expectations of punisher retaliation. In this game (right bars), punishment has smaller reputational benefits: Choosers send 3 percentage points more to punishers than non-punishers, P = 0.001. This difference between conditions is significant (P < 0.001) and robust to accounting for the fact that there is less overall variance in UG offers than TG transfers (see Supplementary Information section 6). Thus TPP is perceived as a stronger signal of trustworthiness (in the TG) than willingness to retaliate (in UG). These findings provide further evidence that our TG experiment results (study 1) are not driven by a perception that TPP signals retaliation (although TPP may also signal retaliation in other contexts). Shown is mean sending in each game. Error bars are ± 1 s.e.m.

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Jordan, J., Hoffman, M., Bloom, P. et al. Third-party punishment as a costly signal of trustworthiness. Nature 530, 473–476 (2016).

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