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The Joint Effect of Social Comparison and Social Distance on Evaluation of Intertemporal Choice Outcomes in Event-related Potential Studies
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Non-equilibrium time-dependent solution to discrete choice with social interactions.

James Holehouse1, Hector Pollitt2

  • 1School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.

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|May 26, 2022
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We present a novel, fast method to solve dynamic binary decision models, revealing that altruistic agents, despite short-term gains, face greater risks of non-optimal states compared to selfish agents. This approach aids in calibrating agent-based models with real-world data.

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Area of Science:

  • Agent-based modeling
  • Computational economics
  • Stochastic processes

Background:

  • The Brock and Durlauf (2001) binary decision model is foundational in social science but challenging to solve dynamically, especially out of equilibrium.
  • Existing methods often rely on computationally intensive simulations or equilibrium assumptions, limiting analysis of path-dependent behaviors.

Purpose of the Study:

  • To develop a computationally efficient, time-dependent solution for the binary decision model.
  • To analyze path-dependent behaviors and metastable effects in both selfish and altruistic agent scenarios.
  • To construct a likelihood function for calibrating agent-based models using non-equilibrium data.

Main Methods:

  • Solution of the binary decision model using the resolvent of the master operator of the stochastic process.
  • Application of first passage time theory to calculate equilibrium attainment timescales.
  • Development of a time-dependent solution applicable to various binary decision models and the mean-field Ising model.

Main Results:

  • A computationally fast and accurate method for solving the binary decision model out of equilibrium.
  • Observation of metastable effects dependent on agent rationality thresholds.
  • Finding that altruistic agents, while initially more cohesive, are more susceptible to non-optimal metastable regimes than selfish agents.
  • Construction of a novel likelihood function for model calibration with non-equilibrium data.

Conclusions:

  • The developed method provides a significant advancement for analyzing dynamic agent-based models, offering insights into agent behavior and model calibration.
  • Altruism introduces unique dynamics, increasing vulnerability to suboptimal outcomes despite short-term coordination benefits.
  • The ability to calibrate models using non-equilibrium data is crucial, though data representativeness remains a key challenge for accurate model fitting.