Behavioral Heuristics and Market Patterns in a Bertrand-Edgeworth Game

In this paper we consider a setup of market interactions which may provide a stylized representation of realworld counterparts. We explore complementarities between analytical, agentbased and experimental approaches, as seems to be required by the problem. The BertrandEdgeworth game (priceseeting with capacity constraints) does not admit Nash equilibria in pure strategies; the mixed strategy equilibria have quite complicated characterizations. We consider two families of heuristic rules which may define frameworks for price-setting: one where prices respond to the past volume of sales; the other where prices are conditioned by the observed correspondence between price changes and profits. The markets inhabited by artificial agents following such rules, with fixed behavioral parameters, show convergence to ”dynamic equilibria ”, where average prices are more or less constant average prices, but where individual prices keep changing. These states, in addition, can potentially be disturbed by agents who modify adaptively their behavior parameters in a profitenhancing way. The tendency to reach ”quasi steady states ” in aggregate prices is also observed typically in experimental results. The price-setting choices of players in experiments can be approximated reasonably with a variant of a simple salesbased rule which governs period-by-period behavior, and with parameters which show a dynamics on a longer time-scale, as if incorporating an adaptive search for profit. Various salient features of the experimental results can be reproduced with simulations of artificial agents who apply the postulated behavioral salesbased strategy with parameter values calibrated from the experiments.