The signal-burying game can explain why we obscure positive traits and good deeds

Abstract

People sometimes make their admirable deeds and accomplishments hard to spot, such as by giving anonymously or avoiding bragging. Such ‘buried’ signals are hard to reconcile with standard models of signalling or indirect reciprocity, which motivate costly pro-social behaviour by reputational gains. To explain these phenomena, we design a simple game theory model, which we call the signal-burying game. This game has the feature that senders can bury their signal by deliberately reducing the probability of the signal being observed. If the signal is observed, however, it is identified as having been buried. We show under which conditions buried signals can be maintained, using static equilibrium concepts and calculations of the evolutionary dynamics. We apply our analysis to shed light on a number of otherwise puzzling social phenomena, including modesty, anonymous donations, subtlety in art and fashion, and overeagerness.

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Fig. 1: The signal-burying game.
Fig. 2: Evolutionary simulations are in line with the equilibrium conditions for burying.
Fig. 3: Evolutionary dynamics of buried signals.
Fig. 4: A comparison of burying with classical signalling.
Fig. 5: Burying equilibria in a model with multiple burying devices.

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Acknowledgements

We thank B. Burum, J. Jordan and E. Yoeli for insightful discussions and constructive feedback, and A. Ferdowsian for his help with setting up the simulations. This work was supported by a grant from the John Templeton Foundation and by the Office of Naval Research Grant N00014-16-1-2914 (M.A.N.). C.H. acknowledges generous support from the ISTFELLOW programme and by the Schrödinger scholarship of the Austrian Science Fund (FWF) J3475. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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All authors contributed to all aspects of this research programme. If some authors contributed more to some aspects, they chose to bury this signal.

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Correspondence to Moshe Hoffman or Christian Hilbe or Martin A. Nowak.

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Supplementary Figures 1–4, Supplementary Notes, Supplementary References 1–2

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Hoffman, M., Hilbe, C. & Nowak, M.A. The signal-burying game can explain why we obscure positive traits and good deeds. Nat Hum Behav 2, 397–404 (2018). https://doi.org/10.1038/s41562-018-0354-z

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