Network Preference Dynamics using Lattice Theory

Hans Riess, Gregory Henselman-Petrusek, Michael C. Munger, Robert Ghrist, Zachary I. Bell +1 more
9/29/2023
cs.MA

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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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Cite this paper

@article{riess2023network,
  title  = {Network Preference Dynamics using Lattice Theory},
  author = {Hans Riess and Gregory Henselman-Petrusek and Michael C. Munger and Robert Ghrist and Zachary I. Bell and Michael M. Zavlanos},
  year   = {2023},
  eprint = {2310.00179},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2310.00179v2}
}

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