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A House Divided: Cooperation, Polarization, and the Power of Reputation

Jul 2023 (Written: Jun 2022)

Sebastian Wild, Phillip Keldenich, Jann Spiess, Maximilian Schlund, Jano Costard, Jonas Radbruch, Paul Stursberg, and Sándor Fekete:

Research Square, In Review

| read herePDFDOI GitHub |

We explore mathematical models for the evolution of reputation and polarization, in search for the minimal requirements driving these phenomena.

Our work provides a fundamental explanation for how robust cooperation may break down when faced with eroding universality of globally recognized values and of local, direct reciprocity; it might also help to prevent behavior-based reputation systems from giving way to emergent polarization and, ultimately, purely membership-based tribalism.

Model & Findings

We study agents engaged in a repeated Prisoner’s dilemma equipped with the capacity for using observations of past behavior in future choices. We first present a (to our knowledge) new and highly successful reputation system, “Gandhi”, that achieves the fastest spread among known reputation systems.

However, we demonstrate that Gandhi (and similarly effective reputation systems) are inherently susceptible to polarization: the division of the population into two factions following the same reputation system, but who fight each other.

We finally consider two additional mechanisms for Gandhi: interaction with globally recognized authorities and direct reciprocity. The resulting system, “Gandhi++”, can overcome polarization and sustain collaboration. However, in a direct confrontation, Gandhi++ is taken over by Gandhi or, which in turn slowly gives way to purely membership-based strategy, “Mafia”.


This work started in the Algorithmic Game Theory group as part of scientific program of the German National Academic Foundation: »Natur- und ingenieurwissenschaftliches Kolleg II« der Studienstifung des Deutschen Volkes.