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We consider two versions of a Bertrand duopoly with asymmetric costs and homogeneous goods. They differ in whether predatory pricing is allowed. For each version, we derive the Myopic Stable Set in pure strategies as introduced by Demuynck, Herings, Saulle, and Seel (2017). We contrast our prediction to the prediction of Nash Equilibrium in mixed strategies.
This article tests the prediction of three discrete asymmetric duopoly price competition games in the laboratory. The games differ from each other in terms of the size of the cost asymmetry that induces a systematic variation in the difference between the firms' marginal costs. While the standard theory requires the low-cost firm to set a price just equal to the high-cost firm's marginal cost, which is identical across all three games, and win the entire market, intuition suggests that market price may increase with a decrease in the absolute difference between the two marginal costs. We develop a quantal response equilibrium model to test our competing conjecture.
The static Nash equilibrium solution for a discretized Bertrand-duopoly market with asymmetric constant marginal costs recommends that the low-cost firm should charge a price equal to the high-cost firm's marginal cost, and thus steal the entire market. This sharp prediction holds true for any size of the cost asymmetry. We develop three stylized asymmetric duopoly price competition models, steadily vary the size of the cost asymmetry across these models, and experimentally investigate the impact of this variation on competition. We find that the predictive power of the Bertrand solution crucially depends on the size of the cost asymmetry; the deviation of the observed average market price from the static Nash price systematically increases as the degree of the asymmetry narrows. Thus, behaviorally a smaller cost asymmetry may lead to higher prices in a Bertrand-duopoly - a key insight valuable from an antitrust standpoint.
By permitting firms to have different entry costs, I generalize two previously studied models of two-stage entry and pricing amongst Bertrand competitors. I find that the existing results depend critically on the symmetry assumption. For example, if firms' entry decisions are observed before price-setting occurs, then total welfare can increase following the introduction of a potential entrant, in contrast to the unambiguous welfare reduction found in the symmetric setting. If firms' entry decisions are unobserved before pricing-setting occurs, then the expected price typically decreases or remains unchanged following the introduction of a potential entrant, in contrast to the unambiguous price increase found in the symmetric setting. In both price-setting environments, competition increases following the introduction of potential entrants with sufficiently low entry costs, a finding that is obscured by focusing on the symmetric models.
We consider a mixed duopoly in which private and public firms can choose to strategically set prices or quantities when the public firm is less efficient than the private firm. Thus, even with cost asymmetry, we obtain exactly the same result (i.e., Bertrand competition) of Matsumura and Ogawa (2012) if Singh and Vives' (1984) assumption of positive primary outputs holds. However, compared to endogenous determination of the type of contract without cost asymmetry, our main finding is that in the wider range of cost asymmetry, different type(s) of equilibrium related to or not related to the limit-pricing strategy of the private firm can be sustained. Thus, when considering an implication on privatization, we may overestimate the welfare gain of privatization because Cournot competition takes place after privatization even though cost asymmetry exists between firms. While the result of Matsumura and Ogawa (2012) holds true if the goods are complements, we find the novel results in the case of substitutes.
By permitting firms to have different entry costs, I generalize two previously studied models of two-stage entry and pricing amongst Bertrand competitors. I find that the existing results depend critically on the symmetry assumption. For example, if firms' entry decisions are observed before price-setting occurs, then total welfare can increase following the introduction of a potential entrant, in contrast to the unambiguous welfare reduction found in the symmetric setting. If firms' entry decisions are unobserved before pricing-setting occurs, then the expected price typically decreases or remains unchanged following the introduction of a potential entrant, in contrast to the unambiguous price increase found in the symmetric setting. In both price-setting environments, competition increases following the introduction of potential entrants with sufficiently low entry costs, a finding that is obscured by focusing on the symmetric models.