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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.
We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities when unions are present. For the case of a unionised mixed duopoly, there exists a dominant strategy only for the public firm that chooses Bertrand competition irrespective of whether the goods are substitutes or complements; there is no dominant strategy for a private firm. Thus, we show that regardless of the nature of goods, social welfare under Bertrand competition is always determined in equilibrium, wherein Bertrand competition entails higher social welfare than Cournot competition. Moreover, our main results hold irrespective of the nature of goods, with the exception that when a sufficiently large parameter of complements is employed, the ranking of a private firm's profit is not reversed, which is in contrast to the standard findings.
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.
In this paper, we compare Bertrand and Cournot equilibria in a differentiated duopoly with linear demand and cost functions. We extend the Singh and Vives (1984) model by allowing for a wider range of cost and demand (product quality) asymmetry between firms. Focusing on the case of substitute goods, we show that both the efficient firm's profits and industry profits are higher under Bertrand competition when asymmetry is strong and/or products are weakly differentiated. Therefore, Singh and Vives's ranking of profits between the two modes of competition is reversed in a sizeable portion of the relevant parameter space. Contrary to the standard result with symmetric firms, we also show that product differentiation can reduce both the efficient firm's and industry profits, implying that a local incentive towards less differentiation may arise.
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.
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.