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This paper tackles the issue of choosing roles in differentiated duopoly games. First, it is shown that the leader is not necessarily better off than in the simultaneous equilibrium. Second, it is proved that the sequential equilibria obtain only if both firms are better off under sequential play than under simultaneous play. Finally, a duopoly game under vertical differentiation and Bertrand competition is illustrated, where the price leader can indeed happen to be worse off than in the simultaneous equilibrium.

The behaviour of a multiproduct profit seeking monopolist is evaluated vis à vis that of a social planner, in a model where there is a continuum of consumers characterized by different marginal willingness to pay for quality. When the market is completely covered, the monopolist undersupplies all qualities as long as their number is finite. When quality becomes continuous, the richest consumer is provided with the socially optimal quality. Under the alternative assumption of partial market coverage, the monopolist supplies the same qualities as the social planner, restricting though total output. Finally, it turns out that, for a given number of varieties, under partial market coverage the monopolist can make at least as good as under full market coverage, so that she prefers to distort quantity rather than quality.

The issue of equilibrium selection in a duopoly game between a profit maximizing and a labour managed firm is addressed under either price or quantity competition with product differentiation. If firms can choose the timing of moves before competing in the relevant market variable, the Bertrand game yields multiple equilibria, while the Cournot game has a unique subgame perfect equilibrium with the profit maximizing firm in the leader's role and the labour managed firm in the follower's role. Due to a lower total output, the Cournot-Stackelberg equilibrium yields a lower level of social welfare as compared to the simultaneous equilibrium. This reduces the incentive to transform an LM duopoly into a mixed one.

The stability of collusion in quantities in a differentiated duopoly is analised, and the result is compared to that emerging in the case of price-setting behaviour. It turns out that quantity collusion is generally better sustained than price collusion, unless products are almost perfect substitutes. Under both quantity and price competition, the social damage associated with collusion is increasing in the degree of substitutability.

The paper focuses on trade between two countries where a vertically differentiated commodityis produced by a single firm in each country, operating initially in autarkic conditions. It is assumed that the two countries have overlapping income distributions, giving thus rise, under certain conditions, to two-way trade, i.e., a proper intraindustry trade. It emerges that while consumers always benefit from trade, especially if two-way trade arises, firms may have conflicting preferences on the choice between (i) autarky and trade, as well as (ii) one-way trade and two-way trade.

The incentives to innovate for the incumbent and the entrant in a vertically differentiated market are analised, in the absence of uncertainty. It turns out that if consumers' marginal willingness to pay for quality is sufficiently low, the efficiency effect observationally works so as to favour innovation by the entrant, i.e., competition. Otherwise, it operates to the advantage of the incumbent who acquire the right to innovate, preempting thus the rival.

The effect of delegation on cartel stability is addressed in a duopoly for a homogeneous product, under Cournot competition. The main findings are that if only one firm is managerial, the critical discount factor is increased by the presence of a weight attached to sales, so that cartel stability is decreased, while if both are managerial the opposite holds. As a consequence, the inclusion of sales in both firms' objective function represents an incentive towards collusion.

Extending the analysis carried out in Lambertini (1993), we investigate a horizontally differentiated duopoly in which a public authority can either tax or subsidize firms, in order to induce duopolists to choose the socially optimal locations.

The stability of collusion is analysed for a family of demand functions whose curvature is determined by a parameter varying between zero and infinity. If demand is sufficiently convex, firms may prefer to act as quantity setters in order to increase cartel stability. Otherwise, price-setting behaviour enhances their ability to collude.

The consequences of free trade in an international spatial duopoly are investigated, under different market regimes. The optimal setting for both countries appears to be a private duopoly in which both firms operate under the same fiscal regime and a side payment from the larger to the smaller country occurs.

The choice of the roles by firms in a differentiated duopoly is analysed, under both the assumption of full and non full market coverage. Under the first, it turns out that, due to the endogeneity of product differentiation, both firms would prefer to be price leader, contrarily to the results obtained by previous literature. Under the latter, it is possible to analyse both price and quantity competition. The consequences in terms of social welfare are also outlined.

The endogenous choice between two alternative kinds of product differentiation is addressed in a duopoly model where firms are free to locate along the real axis, while consumers are distributed along a linear city of finite length. It turns out that the nature of differentiation may be heavily affected by the sequence of decisions. If firms simultaneously choose first locations and then prices, product differentiation at equilibrium is horizontal. If instead one firm acts as a Stackelberg leader in both stages, product differentiation at equilibrium is vertical.

This paper proposes a taxonomy of the Stackelberg equilibria emerging from a standard game of horizontal differentiation à la Hotelling in which the strategy set of the sellers in the location stage is the real axis. Repeated leadership appears the most advantageous position. Furthermore, this endogenously yields vertical differentiation between products at equilibrium.

The effects of the delegation of control to managers are investigated in a duopolistic market for differentiated goods. It appears that delegation is profitable to shareholders under Cournot competiton, provided that the rival firm maximizes profit.

In this paper, we show that, contrarily to the conclusions obtained by Cremer and Thisse (1991), the equilibrium emerging from a model of vertical product differentiation does not yield maximum differentiation because of the strtegic complementarity between products in the quality space.