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 Kazuhiro Ohnishi Modern Economy (ME) , 2011, DOI: 10.4236/me.2011.21007 Abstract: We consider a domestic (resp. international) mixed duopoly model in which a domestic public firm and a domestic (resp. foreign) private firm produce complementary goods. First, the domestic government chooses the level of privatization to maximize domestic social welfare. Second, observing the level of privatization, the firms simultaneously and independently choose prices. We present the equilibrium outcomes of the two mixed duopoly models and shows that our result is in marked contrast to that of the price-setting mixed du-opoly model with substitute goods.
 Microeconomics and Macroeconomics , 2012, DOI: 10.5923/j.m2economics.20120101.03 Abstract: This paper focuses on the role that production subsidies play in a Bertrand mixed duopoly. The paper examines four regimes: mixed and private duopoly, each with and without subsidies. The results of this study are compared with the findings of the existing Cournot mixed market literature. As a result, the paper shows that that the introduction of production subsidies into the analyses of Bertrand and Cournot mixed markets can improve social welfare.
 Modern Economy (ME) , 2013, DOI: 10.4236/me.2013.44031 Abstract: This paper analyzes the capacity choice issue under a price-setting mixed duopoly with differentiated goods, when the objective function of the private firm is its relative profit. In this paper, we show that the public firm chooses over-capacity irrespective of the degree of product differentiation and the degree of importance of the relative performance of the private firm. In contrast, we find that the difference between the output and capacity levels of the private firm strictly depends on both the degree of product differentiation and the degree of importance of its relative performance. More precisely, the private firm chooses over-capacity when the degree of importance of its relative performance is high relative to the degree of product differentiation, whereas it chooses under-capacity otherwise.
 Yasuhiko Nakamura Modern Economy (ME) , 2013, DOI: 10.4236/me.2013.45044 Abstract: This paper explores the capacity choice for a public firm that is a welfare-maximizer and for a private firm that is a pure-profit-maximizer in the context of a price-setting mixed duopoly with a simple mechanism of network effects where the surplus that a firm’s client gets increases with the number of other clients of that firm. In this paper, we show that the public firm chooses over-capacity irrespective of the strength of network effects and the demand parameter, and that the difference between the output level and capacity level of the private firm strictly depends on the values of both the strength of network effects and the demand parameter. More precisely, the private firm chooses over-capacity when the strength of network effects is high relative to the demand parameter, while it chooses under-capacity otherwise.
 Shuichi Ohori Theoretical Economics Letters (TEL) , 2014, DOI: 10.4236/tel.2014.42020 Abstract: This paper compares price and quantity competition in a mixed duopoly with emission tax; in a mixed duopoly, one public firm competes with one private firm in the market. We find that social welfare is the highest when both the firms simultaneously choose price levels. Then, the optimal emission tax is sufficiently lower than the marginal social damage.
 Wiroy Shin Computer Science , 2013, Abstract: This paper studies an environment of simultaneous, separate, first-price auctions for complementary goods. Agents observe private values of each good before making bids, and the complementarity between goods is explicitly incorporated in their utility. For simplicity, a model is presented with two first-price auctions and two bidders. We show that a monotone pure-strategy Bayesian Nash Equilibrium exists in the environment.
 American Journal of Economics , 2012, DOI: 10.5923/j.economics.20120201.07 Abstract: This paper considers a two-stage quantity-setting duopoly model. In the first stage, each firm independently announces its output. Each firm can discount its announced output but cannot raise it. In the second stage, each firm independently chooses its actual output. The paper classifies demand functions into the following four cases in terms of the goods relevance and strategic relevance between both firms: “substitute goods and strategic substitutes”, “substitute goods and strategic complements”, “complementary goods and strategic substitutes” and “complementary goods and strategic complements”. The paper presents the subgame perfect Nash equilibrium in each of four cases.
 Yasuhiko Nakamura Theoretical Economics Letters (TEL) , 2013, DOI: 10.4236/tel.2013.34035 Abstract: In their recent work, Matsumura and Ogawa (2012) showed that in the context of a mixed duopoly, equilibrium social welfare is higher in price-setting competition than in quantity-setting competition. We found that when the strength of network effects is sufficiently high, the above result is totally reversed; thus, in a mixed duopoly, the presence of network effects weakens the superiority of price-setting competition with respect to equilibrium social welfare.
 Quantitative Finance , 2015, DOI: 10.1088/1742-5468/2015/11/P11001 Abstract: Competition is a main tenet of economics, and the reason is that a perfectly competitive equilibrium is Pareto-efficient in the absence of externalities and public goods. Whether a product is selected in a market crucially relates to its competitiveness, but the selection in turn affects the landscape of competition. Such a feedback mechanism has been illustrated in a duopoly model by Lambert et al., in which a buyer's satisfaction is updated depending on the {\em freshness} of a purchased product. The probability for buyer $n$ to select seller $i$ is assumed to be $p_{n,i} \propto e^{ S_{n,i}/T}$, where $S_{n,i}$ is the buyer's satisfaction and $T$ is an effective temperature to introduce stochasticity. If $T$ decreases below a critical point $T_c$, the system undergoes a transition from a symmetric phase to an asymmetric one, in which only one of the two sellers is selected. In this work, we extend the model by incorporating a simple price system. By considering a greed factor $g$ to control how the satisfaction depends on the price, we argue the existence of an oscillatory phase in addition to the symmetric and asymmetric ones in the $(T,g)$ plane, and estimate the phase boundaries through mean-field approximations. The analytic results show that the market preserves the inherent symmetry between the sellers for lower $T$ in the presence of the price system, which is confirmed by our numerical simulations.
 Yasuhiko Nakamura Modern Economy (ME) , 2013, DOI: 10.4236/me.2013.411082 Abstract: This paper conducts a welfare analysis in a duopoly with differentiated and substitutable goods composed of one consumer-friendly firm and one absolute profit maximizing firm. We suppose that the consumer-friendly firm maximizes the weighted sum of its absolute profit and consumer surplus. In such a duopoly, when the degree of product differentiation is sufficiently high and the weight that the consumer-friendly firm puts on consumer surplus in its objective function is sufficiently high, the equilibrium social welfare is larger in the quantity competition than in the price competition, which implies that the result is reverse of that obtained in the standard duopoly with substitutable goods composed of absolute profit maximizing firms.
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