Codetermination,Price Competition and the Network Industry

This research develops a tractable two‐stage non‐cooperative game with complete information describing the behaviour of price‐setting firms that must choose to be profit maximisers or bargainers under codetermination in a network industry with horizontal product differentiation. The existing theoretical literature has already shown that codetermination might arise as the endogenous market outcome in a strategic competitive quantity‐setting duopoly. In sharp contrast with this result, the present article shows that codetermination does never emerge as a Nash equilibrium in a price‐setting non‐network duopoly. Then, it aims at highlighting the role of network externalities in determining changes of paradigm of the game and letting codetermination become a sub‐game perfect Nash equilibrium when prices are strategic substitutes or strategic complements. This equilibrium may be Pareto efficient. Results allow distinguishing between mandatory codetermination and voluntary codetermination. The article also proposes a model of endogenous codetermination according to which every firm may choose to bargain with its own corresponding union bargaining unit only whether the firm's bargaining strength is exactly the profit‐maximising one. The equilibrium outcomes emerging in this case range from a uniform Nash equilibrium, in which both firms are codetermined, to mixed Nash equilibria, in which only one of them chooses to be codetermined. These results are ‘network depending’ and do not hold in a non‐network duopoly.     

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     

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.     

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.     

Price and Quantity Competition in a Differentiated Duopoly With Network Compatibility Effects

We consider the efficiency of price and quantity competition in a network products market, where we observe product compatibility with network externalities (hereafter, network compatibility effects). In particular, if network compatibility effects between firms are sufficiently asymmetric, the Cournot equilibrium is more efficient than the Bertrand equilibrium in terms of larger consumer, producer and total surpluses. Then, we consider an endogenous choice of the strategic variables, price and quantity. If the degree of network compatibility effects of the rival firm is larger (smaller) than the degree of product substitutability, then choosing prices (quantities) is a dominant strategy for the firm. Thus, if the network compatibility effects of both firms are larger (smaller), the Bertrand (Cournot) equilibrium arises. Furthermore, if the network compatibility effects between the firms are sufficiently asymmetric, the firm with a larger (smaller) network compatibility effect than a certain level of product substitutability chooses quantities (prices). In this case, the Cournot–Bertrand equilibrium arises, which is less (more) efficient than the Cournot equilibrium in terms of consumer (producer) surplus.     

Endogenous fluctuations under evolutionary pressure in Cournot competition

An evolutionary game theoretic model of Cournot competition is investigated. Individuals choose from a finite set of different behavioral rules. Each rule specifies the quantity to be produced in the current period as a function of past quantities. Using more sophisticated rules may require extra information costs. Based upon realized payoffs, the fractions of the population choosing a certain behavioral rule are updated according to the replicator equation with noise. The long-run behavior of the evolutionary system consisting of the population dynamics coupled with the quantity dynamics of the Cournot game may be complicated and endogenous fluctuations may arise. We consider a typical example where firms can choose between two rules: the Nash rule and the best-reply rule. We show that a homoclinic tangency between the stable and unstable manifold of the equilibrium occurs as evolutionary pressure increases, implying bifurcation routes to complicated dynamics and strange attractors.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

ENDOGENOUS TIMING IN QUALITY CHOICES AND PRICE COMPETITION

We modify the price‐setting version of the vertically differentiated duopoly model by Aoki (2003) by introducing an extended game in which firms noncooperatively choose the timing of moves at the quality stage. Our results show that there are multiple equilibria in pure strategies, whereby firms always select sequential play at the quality stage. We also investigate the mixed‐strategy equilibrium, revealing that the probability of generating outcomes out of equilibrium is higher than the probability of playing one Nash equilibria in pure strategies. In the alternative case with full market coverage, we show that the quality stage is solved in dominant strategies and therefore the choice of roles becomes irrelevant as the Nash and Stackelberg solutions coincide. With full market coverage and corner solution, the results show that the game has a unique subgame perfect equilibrium in pure strategies, where the high‐quality firm takes the lead in the quality stage.     

Cooperative R&D and Strategic Trade Policy with Bertrand Competition

This paper uses a strategic trade policy model to analyze the welfare effects from allowing cooperation in R&D when firms compete in a price‐setting game in the product market. A policy game between two governments is analyzed, where each government chooses a particular cooperative R&D policy in order to maximize national welfare. At the Nash equilibrium to this game only one government allows cooperation in R&D. This equilibrium is both individually and jointly optimal. International cooperation in R&D is superior to no cooperation in R&D but is inferior to the Nash equilibrium of the government policy game.     

Service Quality,Competition, and Regulatory Policies in the Postal Sector

This paper presents a simple model which illustrates the possible policy- and welfare-implications of endogenous product selection in the postal sector. The cost of a unit of mail depends on its "quality" (e.g., speed of delivery) and on the type and location of the addressee (firms, urban households, and rural households). Senders have inelastic demands and differ in their willingness to pay for quality. Addressees are passive but their utility may affect social welfare. Two operators play a two-stage game, first choosing qualities and then prices. We first show that the equilibrium with two private (profit maximizing) operators results in an inefficient provision of quality. Then, we consider the mixed (Nash) equilibrium with one private and one (welfare maximizing) public operator. If the budget constraint of the public firm is not binding, this equilibrium is shown to be first-best efficient even if social welfare accounts for the utility of addressees. If the budget constraint is binding, the mixed equilibrium is not efficient but yields a higher level of welfare than the private equilibrium. Finally, we study the impact of minimum quality standards within our setting.     

Strategic Delegation and the Shape of Market Competition

What shape can we expect market competition to exhibit? This question is addressed in the present paper. Firms are allowed to choose whether to act as quantity or price setters, whether to move early or delay as long as possible at the market stage, and whether to be entrepreneurial or managerial. Moreover, firms can endogenously determine the sequence of such decisions. It is shown that in correspondence of the (unique) subgame perfect equilibrium of the game, all firms first decide to delay, then to act as Cournot competitors, and finally stockholders decide to delegate control to managers. Hence, sequential play between either managerial or entrepreneurial firms, as well as simultaneous play between entrepreneurial firms, are ruled out.     

Natural monopoly and differential pricing

Under uniform pricing a monopolist cannot make a positive profit in equilibrium. I analyze how differential pricing can be exploited by a natural monopolist to deter entry when entry is costless. In a two-stage game with price competition before quantity competition I show that the incumbent firm can deter entry and make a positive profit in equilibrium. The incumbent sets two different prices, the low price to deter entry and the high price to generate profit. Entry is not possible because of scale effects. If dumping is allowed for all firms no positive profits are realizable, but welfare is reduced. I show that for some parameter values the incumbent is forced to engage in a stunt (i.e., set a negative low price) to keep entrants out.     

Costly Search, Capacity Constraints, and Bertrand Equilibrium Price Dispersion

This article analyzes the impact of transaction (search) costs and capacity constraints in an almost competitive market with homogeneous firms that compete on price. We characterize conditions under which Nash equilibria with price dispersion exist; in equilibrium, firms play pure strategies in prices and consumers adopt a symmetric mixed search strategy. Price dispersion is possible even though consumers all have the same search cost and valuation for the item and prices charged by all firms are common knowledge.     

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.     

Strategic complementarities and search market equilibrium

In this paper, we apply supermodular game theory to the equilibrium search literature with sequential search. We identify necessary and sufficient conditions for the pricing game to exhibit strategic complementarities and prove existence of equilibrium. We then show that price dispersion is inherently incompatible with strategic complementarities in the sense that the Diamond Paradox obtains when firms are identical and is robust within the class of search cost densities that are small near zero and support strategic complementarities. We also show that a major criticism of the literature, that agents act as if they know the distribution of prices, can be justified in the sense of convergent best response dynamics.     

Coordination in Oligopoly

The private and social efficiency of two "behavioral" coordination mechanisms is examined in this paper. In Cournot oligopoly, firms prefer immediate coordination on the Nash equilibrium (interpreted as a preplay communication) over the best-reply dynamics (and fictitous play) which converge to the equilibrium, but with delay (interpreted as a decentralized learning process). In Bertrand oligopoly, firms prefer the learning process. These results indicate that firms have incentives to create institutions, such as trade associations or informal meetings, to facilitate coordination of production capacities, but not prices. Moreover, quantity agreements may even increase social welfare.     

Bertrand price competition with differentiated commodities

This develops a general equilibrium, differentiated commodity version of Bertrand price competition. We study two, related market games in which buyers as well as sellers announce both quantities and prices. In the first game, buyers' strategies are artificially restricted. The Nash allocations of this game will be nearly competitive, provided that the commodities supplied by sellers are sufficiently similar. In the second game, the restriction on buyers' strategies is relaxed and a stronger solution criterion, called local perfection, is invoked. The locally perfect equilibria of the unrestricted game coincide the Nash equilibria of the restricted game.     

Choosing price or quantity? The role of delegation and network externalities

We consider a differentiated duopoly and endogenise the firm choice of the strategy variable (price or quantity) to play on the product market in the presence of network externalities. We model this choice by assuming both competition between entrepreneurial (owner-managed) firms and competition between managerial firms in which market decisions are delegated from owners to revenue-concerned managers. While network externalities are shown not to alter the symmetric equilibrium quantity choice arising in the no-delegation case, sufficiently strong network effects allow us to eliminate the multiplicity of equilibria under delegation and lead to a unique equilibrium in which both firms choose price.     

The price normalization problem in imperfect competition and the objective of the firm

Summary. General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numéraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the resulting set of Nash equilibria when firms are assumed to maximize profits. This is due to the fact that changing the price normalization amounts to altering the objective functions of the firms. Clearly, the objective of a firm must not be based on price normalization rules void of any economic content. In this paper we propose a definition of the objective of a firm, called maximization of shareholders' real wealth, which takes shareholders' demand explicitly into account. This objective depends on relative prices only. Real wealth maxima are shown to exist under certain conditions. Moreover, we consider an oligopolistic market and prove the existence of a Nash equilibrium in which each firm maximizes the real wealth of its shareholders. Received: July 10, 1997; revised version: July 27, 1998     

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.