Particle Swarm Optimization in Agent‐Based Economic Simulations of the Cournot Market Model

Abstract

Summary The numerous variations of the particle swarm optimization (PSO) algorithm originally proposed by Kennedy and Eberhart (. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks IV. IEEE: Piscataway, NJ; 1942–1948) have proven to be powerful optimization methods that rely on exploiting simple analogues of social interaction. In this study, PSO is adopted in lieu of the social or individual evolutionary learning algorithms as a model of individual adaptation in an agent‐based computational model. In this examination of the simple Cournot market framework, each agent's individual strategy evolves according to the PSO algorithm. The model is one in which agents’ strategies must adapt interdependently. That is, a change in one particle may not only affect its performance but also other particles within the same swarm simultaneously. The dynamics and convergence properties associated with this model are compared with those where evolutionary learning algorithms are employed. Similar to evolutionary learning, convergence to equilibrium is dependent on the scope of learning, social or individual. While convergence is dependent on some of the algorithm parameters, prices resulting from the individual PSO are nearest the Cournot equilibrium and those from social PSO are nearest the Walrasian equilibrium in all cases. For particular parameterizations, certain advantages over evolutionary algorithms exist: in the main, decreasing volatility in market prices does not require an election operator or the addition of free parameters through two‐level learning. Copyright © 2015 John Wiley & Sons, Ltd.

Algorithmic Pricing and Price Gouging. Consequences of High-Impact, Low Probability Events

“…We find that the PSO works quite well in setting prices near the optimal one and that such a behavior is robust to different parameters, as other works have shown [9,10]. Then, we analyze how a HILP event distorts the optimal price predicted by the PSO and how competition with a seller that does not use pricing algorithms and a change in the design of the PSO may mitigate its impact.…”

“…This is a common assumption to avoid "jumping" between corner solutions. Similar parametrizations can be found in works where prices are also set by algorithms, such as [10] or [20]. The comparison between two scenarios with low and high differentiation is not trivial, as shown by [36], when using a Q-learning algorithm to set prices.…”

“…Thus, under this requirement and to the best of our knowledge, two potential candidates are the Q-learning and the Particle Swarm Optimization (PSO) algorithms. Both have been successfully applied to experimental economic problems [9,10,20,28,29]. Additionally, we are also interested in AI solutions that could be applied by companies.…”

Artificial Intelligence, Algorithmic Competition and Market Structures

“…We also limit the range of evolutionary velocity, v i ∈ [−0.3, 0.3] to avoid jumping between corner solutions. Similar parameterization appears in other algorithmic pricing research [16].…”

“…Two candidates that fulfill this requirement are Q-learning and Particle Swarm Optimization (PSO) algorithms. Both algorithms are used in experimental economic problems [6], [7], [14], [15], [16]. The Q-learning algorithm is part of the Reinforcement Learning (RL) literature [17], while the PSO is part of the Evolutionary Algorithms (EA) [18].…”