A Particle Swarm Optimization Algorithm for Agent-Based Artificial Markets
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1 A Particle Swarm Optimization Algorithm for Agent-Based Artificial Marets Tong Zhang Research Institute of Economics & Management Southwestern University of Finance & Economics B. Wade Brorsen Agricultural Economics Department Olahoma State University
2 Initial condition Agent-Based Model: Bottom-up Method Carry out the experiments with programmed agents Interactive agents with simple rules Economy Develops over time Observed Maret Equilibrium 2
3 Motivations Agent-Based Model Potential to study auctions and maret mechanism designs, industrial organization topics. Complex problems Alternative to experiments &Analytical method Algorithm complexity and robustness Genetic Algorithm (Arifovic 1994 ) Reinforcement Learning (Erev and Roth 1998) 3
4 Particle Swarm Optimization (PSO) Algorithm Barnhart and Kennedy (1995) 4
5 for Agent-Based Artificial Marets Objectives Adapt particle swarm optimization (PSO) to dynamic marets Compare PSO & GA in Cournot maret 5
6 Particle Swarm Optimization (PSO) Algorithm Global Best Local Best 1 Local Best K Select New strategy Strategy 1 clone 1 Profit Agent 1 clone K Strategy K Select New strategy Simultaneously Maret 1 Maret K clone 1 Agent 2 clone K Local Best 1 Local Best K Global Best 6
7 for Agent-Based Artificial Marets Algorithms Updated Strategy x, ( t + 1) = xi, ( t) vi, ( t) i + l g vi, ( t + 1) = w( t) vi, ( t) + c1u1 ( pi, ( t) xi, ( t)) + c2u2 ( pi, ( t) xi, ( t)) w is an inertia weight factor c 1 c 2 l p i, g p i self confidence factor swarm confidence factor respectively local best global best 7
8 Genetic Algorithm (GA) Sequentially Agent 1 Agent Maret
9 for Agent-Based Artificial Marets Genetic Algorithm ε χ μ elitism rate crossover rate mutation rate a, 1, a 2,, K a l a { 0,1} d = a i l = 1 2 t q i 9
10 Design & Method Maret Structure Oligopsony: M<<N N Sellers Input Product Transaction M Buyers M = 4 Processed Product Transaction Retailers P = $100 10
11 Results Table I-1. PSO & GA Simulation Results with Changing Algorithm Parameters Capacity Ratio Set Parameters Maret Price Buyer 1 Buyer 2 Buyer 3 Buyer 4 PSO w c1 c2 Machine Time Mean % 20.00% 20.00% 20.04% Mean % 20.00% 20.02% 20.00% Mean % 20.00% 20.00% 20.00% 324 SD % 0.01% 0.03% 0.01% Mean % 19.99% 19.85% 19.87% 241 ε μ GA β χ β β 15 10% 86% 0.33% Mean % 18.55% 25.02% 18.76% 3, % 66% 1.00% Mean % 18.75% 19.53% 21.88% 4,037 SD % 2.28% 2.43% 2.56% 4, % 76% 1.00% Mean % 18.55% 17.06% 25.08% % 66% 0.33% Mean % 20.32% 19.93% 19.48% 4,348 Theoretical Results: Maret Price = $80; Quantity Ratio of each buyer =20% 11
12 Results Table I-2. Results under Different Algorithm Structure for PSO and GA Set P L PSO Maret Price Capacity Ratio Buyer 1 Buyer 2 Buyer 3 Buyer 4 Machine Time % 19.99% 20.03% 19.98% % 19.97% 20.04% 20.02% % 20.22% 19.10% 20.22% 45 GA % 20.32% 18.74% 20.31% 35, % 20.31% 25.00% 12.49% 4, % 12.49% 21.97% 22.20% 1,838 12
13 Results 60% Maret Price of PSO & GA 50% 40% Capacity Ratio 30% 20% 10% 0% iteration Buyer 1 Buyer 2 Buyer 3 Buyer 4 (a) GA (b) PSO Quantity Strategy of GA & PSO 13
14 Conclusions Agent-Based Artificial Maret New method in AgEcon industrial organization problems Adapt PSO to dynamic marets PSO>GA 14
15 Than You! 15
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