QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

R&D,free entry,and social inefficiency

We employ a three-stage game model with cost-reducing research and development (R&D) that is subject to spillovers to consider the problem of excess entry under free-entry equilibrium relative to the social optimum. Firms choose to enter or exit a market in the first stage, choose R&D in the second stage and output in the final stage. Results show that there is socially inefficient or excessive entry in equilibrium. However, we uniquely demonstrate that research spillovers hold the key to whether established results regarding socially inefficient entry hold. Specifically, excessive entry occurs as long as research spillovers are relatively small, but this is not necessarily the case with large spillovers. Some policy implications are discussed.     

扶持我国出口导向企业实施RRC战略的理论依据

文章探讨本国企业与外国企业在以产量竞争的方式争夺出口市场的情况下,本国政府对本国企业实施提高竞争对手成本(RRC)战略的投资进行补贴的理论依据。通过两次运用两阶段博弈,文章对由补贴政策、企业RRC投资、产量和利润水平决定构成的三阶段博弈进行了因果关系的比较静态分析,认为在一般情况下,对本国企业RRC投资补贴有利于本国企业在国际市场中产量、市场份额和利润的增加,也有利于本国社会总福利水平的增加,对外国企业产量、利润和社会福利则形成负面影响。由于RRC战略较之掠夺性定价温和且更易实施,这一政策对于保持我国出口稳定增长具有一定积极意义。     

Demand fluctuations and capacity utilization under duopoly

Summary.  This paper studies the impact of uncertain demand on firms’ capacity decisions when they operate in an oligopolistic environment. We define a two-stage game where firms choose capacity in the first stage without knowing which state of Nature is going to realize, and output levels in the second, knowing which state is realized. We prove the existence of a symmetric subgame perfect equilibrium at which firms are in excess capacity compared with the capacity they would choose in the Cournot certainty equivalent game. Received: May 17, 1996; revised version July 31, 1996     

Decompositions and potentials for normal form games

A basic model of commitment is to convert a two-player game in strategic form to a “leadership game” with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.     

Observable versus unobservable R&D investments in duopolies

Journal of Economics - We study a quantity-setting duopoly with homogeneous products in which two firms first make their cost-reducing R&D investments, and then compete in quantities. When...     

Environmental Policy with Endogenous Plant Locations

In a game between the governments of two countries, each chooses its own environmental policy. The Nash equilibria of the game are generally not Pareto optimal. On the one hand, each country may want to attract industry, giving it an incentive to choose low environmental taxes or standards. On the other hand, if disutility from pollution is sufficiently high, each country might prefer that a firm locates only in other countries. This effect tends to make the environmental policy under non-cooperation stricter than it would be with cooperation.     

Wage-rise contract and endogenous timing in international mixed duopoly

This paper examines an endogenous-timing mixed model, where a public firm competes against a foreign private firm. Each firm first chooses the timing for adopting a wage-rise contract as a strategic instrument. The following situation is considered. In the first stage, each firm simultaneously and independently chooses the stage in which it adopts a wage-rise contract, namely either stage 2 or stage 3. In the second stage, the firm choosing stage 2 can adopt the wage-rise contract in this stage. In the third stage, the firm choosing stage 3 can adopt the wage-rise contract in this stage. At the end of the game, each firm simultaneously and independently chooses its output. The paper discusses the equilibrium of the endogenous-timing mixed model.     

Individually selecting among conventions - an evolutionary and experimental analysis

Conventions can be narrowly interpreted as coordinated ways of equilibrium play, telling all players which of possibly several equilibria to play or more broadly how to choose in a game without imposing the equilibrium property. Since coordination often takes place before learning about the game, one has to coordinate on a prescribing principle. For the subclass of 2×2-bimatrix games with two strict equilibria, we analyze the evolutionary stability of various such principles. In our experiment, we allow participants to coordinate on principles before playing various games. Based on between-subjects treatments, participants do so being completely (they know neither their role nor the game parameters), partially (they know either their role or the game parameters) ignorant, or with no veil of ignorance (they know their role and the game parameters).     

Sequential,nonzero-sum “Blotto”: Allocating defensive resources prior to attack

The strategic allocation of resources across multiple fronts has long been studied in the context of Blotto games in which two players simultaneously select their allocations. However many allocation problems are sequential. For example, a state trying to defend against a terrorist attack generally allocates some or all of its resources before the attacker decides where to strike. This paper studies the allocation problem confronting a defender who must decide how to distribute limited resources across multiple sites before an attacker chooses where to strike. Unlike many Blotto games which only have very complicated mixed-strategy equilibria, the sequential, nonzero-sum “Blotto” game always has a very simple pure-strategy subgame perfect equilibrium. Further, the defender always plays the same pure strategy in any equilibrium, and the attacker's equilibrium response is generically unique and entails no mixing. The defender minmaxes the attacker in equilibrium even though the game is nonzero-sum, and the attacker strikes the site among its best replies that minimizes the defender's expected losses.     

Sequential, nonzero-sum “Blotto”: Allocating defensive resources prior to attack

The strategic allocation of resources across multiple fronts has long been studied in the context of Blotto games in which two players simultaneously select their allocations. However many allocation problems are sequential. For example, a state trying to defend against a terrorist attack generally allocates some or all of its resources before the attacker decides where to strike. This paper studies the allocation problem confronting a defender who must decide how to distribute limited resources across multiple sites before an attacker chooses where to strike. Unlike many Blotto games which only have very complicated mixed-strategy equilibria, the sequential, nonzero-sum “Blotto” game always has a very simple pure-strategy subgame perfect equilibrium. Further, the defender always plays the same pure strategy in any equilibrium, and the attacker's equilibrium response is generically unique and entails no mixing. The defender minmaxes the attacker in equilibrium even though the game is nonzero-sum, and the attacker strikes the site among its best replies that minimizes the defender's expected losses.     

Equilibrium audit strategies against tax treaty shopping

This paper examines game‐theoretic models of tax treaty shopping. An investor can choose a direct or indirect investment route across countries to minimize tax. A tax agency can audit the investor. The audit is costly but it can give additional revenue to the tax agency. In simultaneous‐move games, regardless of whether incomplete information exists and whether a home country allows foreign tax credits, there are mixed‐strategy equilibria where the investor may choose tax‐minimizing indirect routes and the tax agency may audit the investor. This equilibrium random audit strategy helps the tax agency raise revenue and reduce treaty shopping. Comparative statics yields an implication consistent with empirical evidence. However, if the home country has a foreign tax credit system with a high tax rate, or if the tax agency observes the investor's action in a sequential‐move game, the investor always chooses the direct route, and no treaty shopping occurs in equilibrium.     

Competition and innovation: an experimental investigation

The paper analyzes the effects of more intense competition on firms’ investments in process innovations. More intense competition corresponds to an increase in the number of firms or a switch from Cournot to Bertrand competition. We carry out experiments for two-stage games, where R&D investment choices are followed by product market competition. An increase in the number of firms from two to four reduces investments, whereas a switch from Cournot to Bertrand increases investments, even though theory predicts a negative effect in the four-player case. The results arise both in treatments in which both stages are implemented and in treatments in which only one stage is implemented. However, the positive effect of moving from Cournot to Bertrand competition is more pronounced in the former case.     

Technology Strategy And Product Diversity

This paper considers a three-stage game of a differentiated oligopoly: firms first make their entry decisions, then they choose production technologies and in the third stage of the game they decide product prices. The technology choice can be understood as selecting one from a pool of those recently available as well as developing a new technology through innovative activities. The resulting market equilibrium is then compared with the social optimum. The main conclusions are that a monopolistically competitive market will typically undersupply both product variety and production scale. R&D competition in a free entry differentiated oligopoly will lead to insufficient R&D investment at firm and industry levels.     

Endogenous transfers in the Prisoner's Dilemma game: An experimental test of cooperation and coordination

We test a two-stage compensation mechanism for promoting cooperation in Prisoner's Dilemma games. Players first simultaneously choose binding non-negative amounts to pay their counterparts for cooperating, and then play the induced game knowing these amounts. In our games, all payment pairs consistent with mutual cooperation in subgame-perfect equilibrium transform these games into coordination games, with both mutual cooperation and mutual defection as Nash equilibria in the second stage. When endogenous transfer payments are not permitted, cooperation is much less likely. Mutual cooperation is most likely when the (sufficient) payments are identical, and it is also substantially more likely with payment pairs that bring the mutual-cooperation payoffs closer together. Both the Fehr–Schmidt and Charness–Rabin models predict that transfers that make final payoffs closer are preferred; however, they do not explain why equal transfers are particularly effective. Transfers are also effective in sustaining cooperation even when they are imposed and not chosen.     

Building and rebuilding trust with promises and apologies

Using trust games, we study how promises and messages are used to build new trust where it did not previously exist and to rebuild damaged trust. In these games, trustees made non-binding promises of investment-contingent returns, then investors decided whether to invest, and finally trustees decided how much to return. After an unexpected second game was announced, but before it commenced, trustees could send a one-way message. This design allowed us to observe the endogenous emergence and natural distribution of trust-relevant behaviors and focus on naturally occurring remedial strategies used by promise-breakers and distrusted trustees, their effects on investors, and subsequent outcomes. In the first game 16.6% of trustees were distrusted and 18.8% of trusted trustees broke promises. Trustees distrusted in the first game used long messages and promises closer to equal splits to encourage trust in the second game. To restore damaged trust, promise-breakers used apologies and upgraded promises. On average, investments in each game paid off for investors and trustees, suggesting that effective use of cheap signals fosters profitable trust-based exchange in these economies.     

Competition Policy as Strategic Trade with Differentiated Products

The paper analyzes how countries use competition policy as a tool for strategic trade. In the model, two countries export to a third country. Each exporting country is endowed with a set of differentiated products. Each government chooses the number of exporters for its country and the products that each exporter sells in the first period, and a tax policy in the second period. Firms choose prices or quantities independently in the third period. In the unique subgame‐perfect equilibrium, both countries group all their products within a single firm—the “national champion policy.” We study the implication of different assumptions about the timing of the game.     

Pollution Haven with Technological Externalities Arising from Foreign Direct Investment

This paper presents a two-stage game, in which in the first stage two multinational firms (MNFs) seeking pollution havens choose a location, that is, whether to export to or undertake FDI in the host country, and in the second stage, these two MNFs and a firm in the host country play a Cournot game. The MNFs’ location decisions are influenced by the fixed cost of FDI, the spillover of technologies to a foreign firm, and pollution emission standards in the host and home countries. There exist multiple equilibria in the location pattern because of the technology spillover accompanied by FDI. In addition, the analysis leads to the possibility of an equilibrium based on the Prisoners’ Dilemma. When the host country relaxes emission standards, the MNFs choose FDI, although their profits are higher if both choose to export instead. This provides a rationale for the FDI source country’s intervention to restrict the MNFs’ FDI according to the level of environmental regulation in the host country.     

Sequential Entry in a Vertically Differentiated Market

This paper considers a sequential entry game of homogeneous firms in a vertically differentiated market. A firm can choose any variety of products, with a fixed cost per product. Each product can be withdrawn afterwards without exit costs. Then each firm chooses one product at most in equilibrium because of a commitment problem. The first firm chooses the highest quality if the fixed cost is so large that subsequent entry is blockaded. It chooses middle quality to deter entry of a low–quality firm if the fixed cost decreases. Hence everyone becomes worse off as the entrant becomes more dangerous. JEL Classification Numbers: D43, L13.     

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

In this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.