Mixed duopoly, cross-ownership and partial privatization

This paper investigates the effects of cross-ownership on optimal privatization, and vice-versa, in mixed duopoly. It shows that cross-ownership is profitable to the private firm only if the level of privatization of the public firm is sufficiently high. In equilibrium, cross-ownership does not take place even if there is partial privatization. However, the possibility of cross-ownership significantly limits the socially optimal level of privatization in most of the situations. Moreover, it demonstrates that full nationalization is socially optimal, in case of sufficiently convex identical cost functions and homogeneous goods. These results have strong implications to both divestment and competition policies.     

An algorithm of game theory applied to the duopoly problem

In this note, an algorithm of Game Theory — Fictitious Play — is applied to a duopoly model: at each step of the algorithm, each duopolist chooses a quantity which maximizes his expected payoff, given the frequency distribution of his opponent's past choices. The algorithm is interpreted as a dynamic learning process and compared to Cournot's process. The successive pairs of quantities announced by the duopolists are proved to converge to a pair of non-cooperative equilibrium quantities. A more sophisticated version of the algorithm also has the same convergence properties.     

The complexion of dynamic duopoly game with horizontal differentiated products

In this paper, firms are considered on the hypothesis of having incomplete rationality expectation and incomplete information of the market to get the dynamic development of price competition behavior in the Hotelling model (Hotelling, 1929). Under the assumption of the heterogeneous expectations of two firms, we have observed that the Nash equilibrium price can be a dynamic equilibrium to realize when the speed of price adjustment is lower. However, the numerical simulation shows that the system may present a periodic and chaotic status when the speed of price adjustment is higher. The effect of the degree of horizontal differentiation on the stability of Nash equilibrium of the system is also discussed. We have a different conclusion from Lucino Fanti and Luca Gori's (2012); that is the greater the degree of product horizontal differentiation is, the more stable the Nash equilibrium of the system is.     

Mixed ownership in a mixed duopoly with differentiated products

We determine optimal privatization in a symmetric differentiated duopoly when the public firms do not bear the full cost of production and hence their objective functions differ from the government’s objective function. In the social optimum firms will generally have mixed ownership, and it will depend on the type of uncovered cost, the degree of substitutability of the two products and the output decision rule of the partially public firms. Different types of mixed duopoly emerge, ranging from both firms being partially privatized, to one being fully privatized. We also derive an optimal tax-subsidy scheme as a substitute for privatization.      

Mixed duopoly,privatization, and subsidization with excess burden of taxation

We investigate optimal tax‐subsidy policies in mixed and private oligopolies with excess burden of taxation. We compare the optimal subsidies and the resulting welfare levels among four regimes: mixed and private Cournot duopolies and Stackelberg competition with public and private leaderships. We show that, in contrast to the existing works on the privatization neutrality theorem, privatization affects resulting welfare.     

Uncertain spatial demand and price flexibility: A state space approach to duopoly

Sufficient conditions for a unique price equilibrium, in terms of the uncertainty distribution and the state contingent consumer distributions, are given for spatial duopoly. Also considered are efficiency and endogenous locations for the symmetric case and comparative statics on price flexibility.     

Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter

In actual economies, players sometimes would offer an upper limiter to their output due to capacity constraints, financial constraints and cautious response to uncertainty in the world, or offer a lower limiter to their output due to economies of scale or break-even consideration. In this paper, we discuss a dynamic duopoly game with heterogeneous players by assuming that one of them imposes an upper limiter on output, and the other one imposes a lower limiter. We analyze how the limiter affects the dynamics of output and the performance of players, and explore the number of the equilibrium points and the distribution of conditioned equilibrium points of the model. We then discuss the stable region of conditioned equilibrium. The theoretical results and numerical experiments show that adding appropriate limiter can make the system more robust, and even get rid of its chaos. The numerical results show that chaotic output dynamics can be beneficial to one firm but harmful to the other, and can also be harmful to both of them, and also show that adding appropriate limiter can improve the performance of the player.     

Endogenous timing game in a mixed duopoly with partial foreign ownership and asymmetric increasing marginal costs

This study examines a timing game in a mixed duopoly wherein public and private firms compete by taking account of the increasing marginal cost of both firms, as well as partial foreign ownership of the private firm. This study finds that if the private firm has a strong cost advantage over the public firm, public leadership is a risk dominant equilibrium irrespective of foreign ownership ratio. This result means that the cost difference between the public and private firms matters in selecting the risk-dominant equilibrium of the timing game. Additionally, if the private firm has only a weak cost advantage over the public firm, then private leadership (public leadership) is the risk dominant equilibrium if the foreign ownership ratio is (not) small.     

Modelling non-competitive behavior in commodity markets: A game theoretic approach

In this paper, we provide a coalitional alternative to the perfectly competitive and purely non-cooperative assumptions commonly employed in the modelling of commodity markets. These assumptions of perfect competition or pure non-cooperation are usually imposed exogenously without providing an economic basis for assuming why firms that could stand to gain by cooperating would not in fact do so. Three behavioral rules embodied in three different cooperative games are discussed in this paper and a methodology for predicting the coalition structures that would result from each of these is offered. By applying these games to the US copper industry of the 1970's, we show that the theory of games can be profitably employed in conjunction with the traditional institutional approach of industrial organization to yield useful economic predictions.The author is grateful to two anonymous referees whose comments led to a considerably improved version of the paper.     

Choices of organizational structures in religious organizations: a game theoretic approach

This study has extended the work done by Allen [Journal of Economic Behavior and Organization 27 (1995) 97] and others who attempted to show a relationship between a denomination’s doctrine and its organizational structure. While Allen’s work resulted in a one-to-one mapping between doctrinal beliefs and organizational structure, this study has argued that there exists a continuum of structures that are consistent with a particular church’s doctrine. The church’s ultimate organizational structure is a game theoretic outcome resulting when churches attempt to maximize membership subject to the constraints imposed by their doctrines. We examine how churches’ organizational structures depend on the extent to which members are willing to sacrifice their structural preferences to hold on to their doctrines. Consistent with Allen’s outcome, our result indicates the further apart are the doctrines held by two churches, the greater the variation in their structural organization. This paper also examines the relationship between churches’ organizational structures and the degree of the majority church’s majority.     

A market game approach to differential information economies

In this paper we recast a differential information economy as a strategic game in which players propose net trades and prices. Pure strategy Nash equilibria are strong and determine both consumption plans and commodity prices that coincide with the Walrasian Expectations equilibria of the underlying economy. The authors acknowledge support by research grants BEC2003-09067-C04-01 (Ministerio de Educación y Ciencia and FEDER), PGIDT04XIC30001PN (Xunta de Galicia) and SA070A05 (Junta de Castilla y León). JP Torres-Martínez is also grateful to CNPq-Brazil and University of Vigo for financial support. We are indebted to N.C. Yannelis for helpful comments and insights.     

企业采用新技术的时点博弈分析

技术创新可以为企业带来超额利润,具有极大的经济价值,然而新技术的不确定性和风险性又使得企业不会立即采用。本文通过构建双寡头垄断博弈模型对企业采用新技术的时点进行研究,证明企业采用新技术时存在一个最佳时点,在这个最佳时点之前,企业应采取等待策略。     

Peak-load pricing in duopoly

In this paper, we consider peak-load pricing by duopolists that maximize profit (not social welfare). We compare price levels and profits across peak-load versus uniform pricing regimes. Our main result is that the introduction of peak-load pricing can plausibly reduce prices by making price competition more severe and thereby reducing profits. This result suggests that competing firms may engage in collusion by not committing to peak-load pricing. Therefore, from the regulator's perspective, it will be desirable to encourage firms to engage in peak-load pricing to intensify competition.     

Technology choice under duopoly

This paper presents a conjectural variation approach to demonstrate that competing firms will often distort their cost structures away from strict cost minimization for strategic reasons. In particular, it is shown that the nature of the desired distortions of production technology depends critically on the magnitudes of the firms' conjectural variations with respect to outputs as well as the firms' conjectural variations with respect to technology. These results are in sharp contrast to the conventional wisdom based on monopolized or perfectly competitive markets.     

Asymmetric duopoly and the core

It has recently been proposed that an exchange economy with “small” and “large” traders be represented by a measure space whose atoms represent the set of large traders and whose atomless part represents the set of small traders. For such mixed markets, the equivalence of the core and the set of competitive allocations, which holds when the set of atoms is of measure zero, no longer holds necessarily when this set has positive measure. However, if this set consists of identical traders, the equivalence is restored. The asymptotic analogs of these propositions are proved here.     

A game theoretical approach to the international debt overhang

We consider an international financial problem called debt overhang, by which we mean a situation where a sovereign country has borrowed money from foreign banks and has been unable to fulfill the scheduled repayments for some period. The problem is formulated as a noncooperative game withn lender banks as players where each decides either to sell its loan exposure to the debtor country at the present price of debt on the secondary market, or to wait and keep its exposure. This game has many pure and mixed strategy Nash equilibria. We show, however, that in any Nash equilibrium, the resulting secondary market price remains almost the same as the present price for a large number of banks. We also obtain the comparative statics result that in a mixed strategy equilibrium, a bank with a smaller loan exposure has a greater tendency to sell than one with a larger loan exposure. We discuss the implications of these results for the functioning of the secondary market and the resolution of debt overhang.We thank J. Crémer, H. Haller, S. Mendes, and the referees of this Journal for helpful comments on earlier drafts.