ENDOGENOUS TIMING IN MULTI-STAGE DUOPOLY GAMES*

This paper presents an investigation of the endogenous timing in multi-stage duopoly games in which duopolists choose two variables over two periods. The paper elaborates the two-stage strategic commitment game discussed by Brander and Spencer (1983). Duopolists decide their outputs and cost-reducing investments and they are allowed to choose which action to take first. The paper discusses two types of games; one is a three-stage game in which each duopolist can commit to the order of choices before it chooses its output or cost-reducing investments, and the other is a two-stage game in which it cannot. The paper finds that at least one firm chooses its output first. Furthermore, the three-stage game has the unique equilibrium outcome in which both firms choose their outputs first.     

The control of game form recognition in experiments: understanding dominant strategy failures in a simple two person “guessing” game

This paper focuses on instructions and procedures as the reasons that subjects fail to behave according to the predictions of game theory in two-person “guessing game” (beauty contest game) experiments. In this game, two individuals simultaneously choose a number between 0 and 100. The winner is the person whose chosen number is the closest to 2/3 of the average of the two numbers. The weakly dominant strategy is zero. Because of the simplicity of the game, the widespread failure of subjects to choose the weakly dominant strategy has been interpreted as evidence of some fundamental inability to behave strategically. By contrast, we find that subjects’ behavior reflects a lack of understanding of the game form, which we define as the relationships between possible choices, outcomes and payoffs. To a surprising degree, subjects seem to have little understanding of the experimental environment in which they are participating. If subjects do not understand the game form, the experimental control needed for testing game theory is lost. The experiments reported here demonstrate that the failure to act strategically is related to how the game is presented. We test how well subjects are able to recognize the game under a variety of different presentations of the game. Some subjects fail to recognize the game form when it is presented abstractly. When the game is transformed into a simple isomorphic game and presented in a familiar context, subjects do choose weakly dominant strategies. While our results confirm the ability of subjects to make strategic decisions, they also emphasize the need to understand the limitations of experimental subjects’ ability to grasp the game as the experimenter intends. Given these limitations, we provide suggestions for better experimental control.     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000     

A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

Low-quality leadership in a vertically differentiated duopoly with Cournot competition

We model a vertically differentiated duopoly with quantity-setting firms as an extended game in which firms noncooperatively choose the timing of moves at the quality stage, to show that at the subgame, perfect equilibrium sequential play obtains, with the low-quality firm taking the leader’s role.     

Strategic interactions and airline network morphology under demand uncertainty

In this paper, we examine how strategic interactions affect airline network under demand uncertainty. We develop a three-stage duopoly game: at stage 1 airlines determine their network structure (linear versus hub-and-spoke); at stage 2 they decide on their capacities; at stage 3 firms compete in quantities. The main feature of the model is that firms have to decide on network structure and capacities while facing demand uncertainty. We show that while hubbing is efficient, airlines may choose a linear network for strategic reasons. Furthermore, we show that this structure softens competition by preventing contagion of competition across markets.     

Adoption of Pollution Prevention Techniques: The Role of Management Systems and Regulatory Pressures

This paper investigates the extent to which firm level technological change that reduces unregulated emissions is driven by regulatory pressures, and firms’ technological and organizational capabilities. Using a treatment effects model with panel data for a sample of S&P 500 firms over the period 1994–1996, we find that organizational change in the form of Total Quality Environmental Management leads firms to adopt pollution prevention practices, after controlling for the effects of various regulatory pressures and firm-specific characteristics. We find that the threat of anticipated regulations and the presence of ‘complementary assets’ is important for creating the incentives and an internal capacity to undertake incremental adoption of pollution prevention techniques.     

Similarities and differences when building trust: the role of cultures

We run an experiment in which students of different European nationalities are matched in groups of five and repeatedly choose with whom within their group they want to play a trust game. Participants observe of each other age, gender, nationality and number of siblings. The region of origin, “North” or “South” is a major determinant of success in the experiment. Participants tend to trust those they trusted before and who trusted them. We do not find evidence of regional discrimination per se. It is only the underlying and significant differences in behavior that translate through repeated interactions into differences in payoffs between the two regions.     

Plant location and strategic environmental policy with inter-sectoral linkages

In recent debates on trade liberalisation the concern has often been expressed that with more competitive international trade governments will be worried that by setting tougher environmental policies than their trading rivals they will put domestic producers at a competitive disadvantage, and in the extreme case this could lead to firms relocating production in other countries. The response by governments to such concerns will be to weaken environmental policies (‘eco-dumping’). In competitive markets such concerns are ill founded, but there is a small amount of literature which has analysed whether governments will indeed have incentives for eco-dumping in the more relevant case of markets where there are significant scale economies; even here there is no presumption that the outcome will involve eco-dumping.In this paper we extend the analysis of strategic environmental policy and plant location decisions by analysing the location decision of firms in different sectors which are linked through an input-output structure of intermediate production. The reason why we introduce inter-sectoral linkages between firms is that they introduce an additional factor, relative to those already analysed in the literature, in the plant location decision, which is the incentive for firms in different sectors to agglomerate in a single location. This has a number of important effects. First, there is now the possibility of multiple equilibria in location decisions of firms. Following from this there is the possibility of catastrophic effects where a small increase in an environmental tax can trigger the collapse of an industrial base in a country; however there is also the possibility that a country which raises its environmental tax could attract more firms to locate in that country, because of the way the tax affects incentives for agglomeration. Finally, and again related to the previous effects, there is the possibility of a hysteresis effect where raising an environmental tax in one country can cause firms to relocate to another country, but subsequently lowering that tax will not induce firms to relocate back into the original country.We consider a simple model with two countries, two industries, an upstream and a downstream sector, and two firms per industry. The analysis proceeds through a three-stage game: in the first stage the governments of the two countries set their environmental policies; in the second stage the firms in both industries choose how many plants to locate and where; in the third stage firms choose their output levels, with the demand for the upstream firms being determined endogenously by the production decisions of the downstream firms. We assume that there are no limits to production capacity, so that firms do not build more than one plant in any country. However, firms may build plants in different countries because of positive transport costs. Although the model appears very simple, it cannot be solved analytically, so all the conclusions must be drawn from numerical simulations.     

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.     

Price leadership and firm size asymmetry: an experimental analysis

We use laboratory experiments to examine the effect of firm size asymmetry on the emergence of price leadership in a price-setting duopoly with capacity constraints. Independent of the level of size asymmetry, the unique subgame perfect equilibrium of our timing game predicts that the large firm is the price leader. Experimental data show that price leadership by the large firm is frequent, but simultaneous moves are also often observed. Profit outcomes in the previous period affect the subjects’ decisions to announce or wait in a way that hampers convergence to the equilibrium. Furthermore, while both small and large firms display a strong tendency to wait to announce their price when firm size asymmetry is low, they often set prices early when size asymmetry is high. Prices are higher when price setting is sequential rather than simultaneous and when firm size asymmetry is high. Hence, price leadership by either type of firm has an anti-competitive effect that is more pronounced when the size difference between firms is large.     

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.     

Solving coordination failure with “all-or-none” group-level incentives

Coordinating activity among members is an important problem faced by organizations. When firms, or units within firms, are stuck in bad equilibria, managers may turn to the temporary use of simple incentives—flat punishments or rewards—in an attempt to transition the firm or unit to a more efficient equilibrium. We investigate the use of incentives in the context of the “minimum-effort,” or “weak-link,” coordination game. We allow groups to reach the inefficient equilibrium and then implement temporary, flat, “all-or-none” incentives to encourage coordination on more efficient equilibria. We vary whether incentives are positive (rewards) or negative (penalties), whether they have substantial or nominal monetary value, and whether they are targeted to a specific outcome (the efficient equilibrium) or untargeted (apply to more than one outcome). Overall, incentives of all kinds are effective at improving coordination while they are in place, but there is little long-term persistent benefit of incentives—once incentives are removed, groups tend to return to the inefficient outcome. We find some differences between different kinds of incentives. Finally, we contrast our results to other recent work demonstrating greater long-term effectiveness of temporary incentives.      

The effect of debt capacity on the long-term stock returns of debt-free firms

This article examines the long-term stock market performance of debt-free firms with high and low levels of debt capacity to see whether they are different. We use Fama and French’s (1993) three-factor and Carhart’s (1997) four-factor models to examine the subsequent 1, 2, 3, 4 and 5-year stock returns of firms that stayed debt free for 3- and 5-year periods. We measure debt capacity as the expected asset liquidation value of a firm, which is proxied by the firm-level tangibility measure defined by Berger, Ofek, and Swary (1996). We find that regardless of the level of debt capacity, zero-debt firms generate positive abnormal returns in the long run after controlling for key risk factors. We also find support for the notion that preserving debt capacity in the form of higher tangibility reinforces the positive abnormal returns over and above the effect of a zero-leverage policy.     

Location choice with delegation: Bertrand vs. Cournot competition

The conventional wisdom indicates that firms' optimal locations are sensitive to the modes of product-market competition, leading to a difficulty for firms to make concrete location decisions. This difficulty is especially crucial for the high entry-cost firms. The paper develops an uncovered-market model à la Economides (1984) to explore this sensitivity by taking into account a delegation game. It shows that firms' location configurations remain unchanged regardless of the modes of product-market competition as the owners offer the managers a contract with a relative-performance incentive scheme. Moreover, the paper shows that, by introducing a delegation game, the competition between managers under Bertrand competition is mitigated such that the managers have no incentive to choose price undercutting as they locate themselves far enough away from each other.     

Minimum wages and welfare in a Hotelling duopsony

Two firms choose locations (non-wage job characteristics) on the interval [0, 1] prior to announcing wages at which they employ workers who are uniformly distributed; the (constant) marginal revenue products of workers may differ. Subgame perfect equilibria of the two-stage location-wage game are studied under laissez-faire and under a minimum wage regime. Up to a restriction for the existence of pure strategy equilibria, the imposition of a minimum wage is always welfare-improving because of its effect on non-wage job characteristics.     

Aspects of International Fragmentation

The paper uses a specific‐factors framework to address efficiency and distributional implications of international fragmentation which is driven by a low foreign wage rate. Focusing on the cost‐savings linkage between fragmentation and labor demand in the remaining domestic activities, the author establishes a fragmentation surplus. If capital is an indivisible asset specific to the fragment produced abroad, then fragmentation may cause a domestic welfare loss, because outsourcing takes place in discrete steps where it affords firms “quasi‐market‐power” on the domestic labor market. The regime shift from domestic production to fragmentation is modeled as a two‐stage game. In stage one, firms locate indivisible assets at home or abroad; in stage two they choose optimal employment. The share of fragmented firms is endogenously determined. The paper explores conditions under which outsourcing is beneficial for the domestic economy.     

Multinational Production, Absorptive Capacity, and Endogenous R&D Spillovers

Do R&D spillovers have an impact on whether firms choose to go multinational or not? We present a three‐stage Cournot duopoly model, which identifies under what conditions firms choose to service a foreign market through exports or localized production. The establishment of a foreign subsidiary improves the ability to learn from foreign R&D since spillovers are strongly moderated by geographical distance. We explicitly model the concept of absorptive capacity, where gains from spillovers are determined by own R&D investments. With exogenous R&D investments, the absorptive capacity effect contributes to increase the gains from going multinational when the firm is R&D‐intensive. However, if R&D investments are endogenous, only medium‐sized absorptive capacity effects will result in firms going multinational. Furthermore, higher spillover rates do not necessarily drive down R&D and profits for the multinational firm. This stands in contrast to models that ignore absorptive capacity effects.     

Capacity precommitment and price competition yield the Cournot outcome

We introduce a simple model of oligopolistic competition where firms first build capacity, and then, after observing the capacity decisions, choose a reservation price at which they are willing to supply their capacities. This model describes many markets more realistically than the model of Kreps and Scheinkman [Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell J. Econ. 14, 326–337]. We show that in this new model every pure strategy equilibrium yields the Cournot outcome, and that the Cournot outcome can be sustained by a pure strategy subgame perfect equilibrium.     

Strategic technology choice in regulated markets with demand uncertainty

This paper presents a simple model of a non-competitive market with demand uncertainty in which firms can choose their technology of production. Technology is characterised by two parameters: capacity and flexibility. The first has a strong commitment value while flexibility is needed to face uncertainty. Lack of competition requires active regulation to ensure that the price is not set at excessive level. When choosing their technology, firms take into account not only the effects of this choice on the opponent(s) but also the effect on the regulated price. In this framework, and because of regulation, firms have an incentive to strategically manipulate their cost (cost padding). This causes monopoly regulation aiming at improving allocative efficiency to be ineffective. In fact, by “tying its hand” to a low level of capacity, the monopolistic firm is able to get round the constraint imposed by the regulator. Increasing the number of firms in the market may restore regulation effectiveness. The reason is that if demand is sufficiently volatile, then firms strategically choose flexible techniques and this effect dominates over the incentive to manipulate costs in order to escape regulation. In this case, regulation is effective precisely because cost padding is hampered by firms’ non-cooperative behaviour.