Dynamic duopoly with learning through market experimentation

2003

In this paper we report the results from a series of experiments on Cournot (homogeneous and differentiated products) and Bertrand (differentiated products) duopoly markets with no uncertainty, fixed endpoints and random matching. For each set, the experiments are designed with three alternative information set up: I) no information (participants are only informed on their own payoff for the period), 2) average industrial profit (participants are informed on their own performance, as well as on the average profit in all markets), 3) imitation (players are informed, on request, on their rivals' past successful actions). The effect of different information structures on individual behaviour in market experiments is a long debated issue. Recently, using evolutionary arguments, it has been argued that the imitation of successful strategies induces more competitive equilibria in market games . By the same token, the information on the industry's average profitability might induce more collusive outcomes, if such markets signals are perceived by players as aspiration levels and if they therefore try new strategies anytime their profits fall below such threshold (F. . Our aim is to test such predictions in duopoly price and quantity games. We find that the imitation learning rule prevails when players have full information on their rivals' previous choices, and such learning behaviour induces more competitive outcomes in the Cournot market designs. As for the aspiration learning rule, the evidence is unclear. Whilst in the majority of the cases, players experiment new strategies when their payoff falls below the average profit, as predicted by the aspiration rule, we find no evidence of convergence to collusion, though in the Cournot experiments, the fraction of players choosing cooperative actions in the last stages of the game significantly increase in the second information setting.

Games and Economic Behavior, 2013

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In a symmetric differentiated experimental duopoly we test the ability of Price Guarantees (PGs) to raise prices above the competitive levels. Different types of PGs ('aggressive' and 'soft' price-beating and price-matching) are implemented either as an exogenously imposed market rule or as a business strategy. Our results show that PGs may lead close to the collusive outcome, depending on whether the interaction between duopo-lists is repeated and provided that the guarantee is not of the 'aggressive' price-beating type.

2016

This article analyses price competition in a two-period duopoly model in which only one firm knows the degree of substitutability between products. Using a Hotelling model, we analyse the informed firm ́s incentive to reveal its private information throughout its price set in period 1. In this setting, the price set by the informed firm only reveals the degree of product differentiation in period 1 when the prior probability of closer substitutes is sufficiently high and the discount factor is sufficiently low. Finally, we find that firms differentiate their products as far as possible under asymmetric information.

The RAND Journal of Economics, 2015

We characterize a duopoly buffeted by demand and cost shocks. Firms learn about shocks from common observation, private observation, and noisy price signals. Firms internalize how outputs affect a rival's signal, and hence output. We distinguish how the nature of informationpublic versus private-and of what firms learn about-common versus private values-affect equilibrium outcomes. Firm outputs weigh private information about private values by more than common values. Thus, prices contain more information about private-value shocks. * We thank Marco Ottaviani for helpful comments.

European Economic Review, 2002

This paper considers a duopoly price-choice game in which the unique Nash equilibrium is the Bertrand outcome. Price competition, however, is imperfect in the sense that the market share of the high-price firm is not zero. Economic intuition suggests that price levels should be positively related to the market share of the high-price firm. Although this relationship is not predicted by standard game theory, it is implied by a generalization of the Nash equilibrium that results when players make noisy (logit) best responses to expected payoff differences. This logit equilibrium model was used to design a laboratory experiment with treatments that correspond to changing the market share of the high-price firm. The model predicts the final-period price averages for both treatments with remarkable accuracy. Moreover computer simulations of a naive learning model were used, ex ante, to predict the observed differences in the time paths of average prices.

Mathematical Social Sciences, 2010

In a Hotelling's duopoly with a general transportation cost function, we study competition through catalog: each firm chooses at the same time a price and a location. With simultaneous catalog offers, there is no equilibrium in pure strategies for high valuations of the consumers, while a Stackelberg equilibrium exists under mild conditions. The follower is better off than the leader, whose price is smaller: the location preemption effect is weaker than the price leadership effect. We obtain closed-form solutions for the linear and quadratic cost cases. Using these results, we discuss the nature of competition depending on the relative flexibility of products and prices.

2000

We consider a homogenous good oligoply with identical consumers who learn about prices either by (sequentially) visiting firms or by consulting a price agency who sells information about which firm charges the lowest price. In the sequential equilibrium with maximal trade and minimal search, prices are dispersed and consumers randomize between consulting a price agency and buying at the first

This paper considers a duopoly price-choice game in which the unique Nash equilibrium is the Bertrand outcome. Price competition, however, is imperfect in the sense that the market share of the high-price firm is not zero. Economic intuition suggests that price levels should be positively related to the market share of the high-price firm. Although this relationship is not predicted by standard game theory, it is implied by a generalization of the Nash equilibrium that results when players make noisy (logit) best responses to expected payoff differences. This logit equilibrium model was used to design a laboratory experiment with treatments that correspond to changing the market share of the high-price firm. The model predicts the final-period price averages for both treatments with remarkable accuracy. Moreover computer simulations of a naive learning model were used, ex ante, to predict the observed differences in the time paths of average prices.

This paper aims to investigate the possibility for monopolistically competitive firms to set the price and the quantity of goods through a reinforcement learning approach. The model incorporates a set of firms that produce and sell differentiated goods in monopolistically competitive markets and households that supply different types of labor, purchase goods for consumption and hold money. The households behave optimally, maximizing their utility, while the firms learn their desired markup by a reinforcement learning algorithm in order to set the price.