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Phase transition in the Kolkata Paise Restaurant problem
Antika Sinha1, Bikas K Chakrabarti2
1Department of Computer Science, Asutosh College, Kolkata 700026, India.
Chaos (Woodbury, N.Y.)
|September 3, 2020
Summary
Customers in the Kolkata Paise Restaurant problem learn to avoid crowds by making minority choices. This study reveals novel phase transition behaviors and convergence times in agent strategies.
Area of Science:
- Complex Systems
- Agent-Based Modeling
- Statistical Mechanics
Background:
- The Kolkata Paise Restaurant problem models agents seeking unique choices to avoid congestion.
- Agents iteratively learn strategies based on past crowd information to achieve minority status.
Purpose of the Study:
- To investigate novel phase transition behaviors in the Kolkata Paise Restaurant problem.
- To analyze crowd-avoiding strategies and their impact on restaurant utilization and convergence time.
Main Methods:
- Simulating agent behavior with two distinct crowd-avoiding strategies (Strategy I and Strategy II).
- Analyzing steady-state utilization fraction (f) and convergence time (τ) as functions of strategy parameters (α and p) across different dimensions.
Main Results:
- Observed phase transition behavior near critical parameter values (αc=0+ or pc=1-).
- Steady-state wastage fraction (1-f) scales with critical exponents β (≈0.8-1.0).
- Convergence time (τ) exhibits inverse scaling with critical exponents γ (≈1.05-1.18) depending on dimensionality.
Conclusions:
- The study demonstrates a critical phase transition in agent-based restaurant selection.
- Agent strategies significantly influence system dynamics, including efficiency and convergence speed.
- Dimensionality plays a crucial role in the observed scaling laws for convergence time.
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