Equilibrium

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Aug 24, 2025 · cs.GTJ/K move · Enter open · S save

The price of uncertainty for social consensus

Yunzhe Bai, Alec Sun

How hard is it to achieve consensus in a social network under uncertainty? In this paper we model this problem as a social graph of agents where each vertex is initially colored red or blue. The goal of the agents is to achieve consensus, which is when the colors of all agents align. Agents attempt to do this locally through steps in which an agent changes their color to the color of the majority of their neighbors. In real life, agents may not know exactly how many of their neighbors are red or blue, which introduces uncertainty into this process. Modeling uncertainty as perturbations of relative magnitude

1+\varepsilon

to these color neighbor counts, we show that even small values of

\varepsilon

greatly hinder the ability to achieve consensus in a social network. We prove theoretically tight upper and lower bounds on the price of uncertainty, a metric defined in previous work by Balcan et al. to quantify the effect of uncertainty in network games.

Consensus Game Theory Complex Networks Prices Social Media

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