Paper ID: 2310.00179

Network Preference Dynamics using Lattice Theory

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

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.

Submitted: Sep 29, 2023