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arXiv · 2310.00179

Network Preference Dynamics using Lattice Theory

Hans Riess·Gregory Henselman-Petrusek·Michael C. Munger·Robert Ghrist·Zachary I. Bell·Michael M. Zavlanos
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Abstract

Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume, revise their preferences as they gain more information about other agents. Exploiting the ordered algebraic structure of preferences, we introduce a message-passing algorithm for heterogeneous agents distributed over a network to update their preferences based on aggregations of the preferences of their neighbors in a graph. We demonstrate the existence of equilibrium points of the resulting global dynamical system of local preference updates and provide a sufficient condition for trajectories to converge to equilibria: stable preferences. Finally, we present numerical simulations demonstrating our preliminary results.

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Hans Riess, Gregory Henselman-Petrusek, Michael C. Munger, Robert Ghrist, Zachary I. Bell, Michael M. Zavlanos. 2023-09-29. Network Preference Dynamics using Lattice Theory. https://arxiv.org/abs/2310.00179

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