Flávio Ferreira

Fine structures of hyperbolic diffeomorphisms

HR structures.- Solenoid functions.- Self-renormalizable structures.- Rigidity.- Gibbs measures.- Measure scaling functions.- Measure solenoid functions.- Cocycle-gap pairs.- Hausdorff realizations.- Extended Livsic-Sinai eigenvalue formula.- Arc exchange systems and renormalization.- Golden tilings (in collaboration with J.P. Almeida and A. Portela).- Pseudo-Anosov diffeomorphisms in pseudo-surfaces.

Unknown costs in a duopoly with differentiated products

We consider a duopoly model with unknown costs. The firms’ aims are to maximize their profits by choosing the levels of their outputs. The chooses are made simultaneously by both firms.

Bayesian price leadership

In this paper, we consider a linear price setting duopoly competition with differentiated goods and with unknown costs. The firms’ aims are to choose the prices of their products according to the well-known concept of perfect Bayesian Nash equilibrium. There is a firm (F 1) that chooses first the price p 1 of its good; the other firm (F 2) observes p 1 and then chooses the price p 2 of its good.

Quantity Competition in a Differentiated Duopoly

In this paper, we consider a Stackelberg duopoly competition with differentiated goods, linear and symmetric demand and with unknown costs. In our model, the two firms play a non-cooperative game with two stages: in a first stage, firm F 1 chooses the quantity, q 1, that is going to produce; in the second stage, firm F 2 observes the quantity q 1 produced by firm F 1 and chooses its own quantity q 2. Firms choose their output levels in order to maximise their profits. We suppose that each firm has two different technologies, and uses one of them following a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the variations of the expected profits with the parameters of the model, namely with the parameters of the probability distributions, and with the parameters of the demand and differentiation.

Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For difieomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is difierentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria, and ours for one-dimensional expanding dynamics. 1991 AMS Mathematics Subject Classiflcation: 58F15.

Flexibility in Stackelberg Leadership

We consider a Stackelberg model with demand uncertainty, only for the first mover. We study the advantages of leadership and flexibility with the variation of the demand uncertainty. Liu proved for demand uncertainty parameter greater than three that the follower firm can have an advantage with respect to the leading firm for some realizations of the demand intercept. Here, we prove that for demand uncertainty parameter less than three the leading firm is always in advantage.

Privatization and government preferences in a mixed duopoly: Stackelberg versus Cournot

We analyse the relationship between the privatization of a public firm and government preferences for tax revenue, by considering a (sequential) Stackelberg duopoly with the public firm as the leader. We assume that the government payoff is given by a weighted sum of tax revenue and the sum of consumer and producer surplus. We get that if the government puts a sufficiently larger weight on tax revenue than on the sum of both surpluses, it will not privatize the public firm. In contrast, if the government puts a moderately larger weight on tax revenue than on the sum of both surpluses, it will privatize the public firm. Furthermore, we compare our results with the ones previously published by an other author obtained in a (simultaneous) Cournot duopoly.

Price-Setting Dynamical Duopoly with Incomplete Information

We consider a price competition in a duopoly with substitutable goods, linear and symmetric demand. There is a firm (F 1) that chooses first the price p 1 of its good; the other firm (F 2) observes p 1 and then chooses the price p 2 of its good. The conclusions of this price-setting dynamical duopoly are substantially altered by the presence of either differentiated goods or asymmetric information about rival’s production costs.

Stochasticity Favoring the Effects of the R&D Strategies of the Firms

We present stochastic dynamics on the production costs of Cournot competitions, based on perfect Nash equilibria of nonlinear R&D investment strategies to reduce the production costs of the firms at every period of the game. We analyse the effects that the R&D investment strategies can have in the profits of the firms along the time. We observe that, in certain cases, the uncertainty can improve the effects of the R&D strategies in the profits of the firms due to the non-linearity of the profit functions and also of the R&D parameters.

Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Cantor sets. We also present similar statements for (uaa) and Cr Markov families. These results generalize the similar ones of Sullivan and de Faria for Cr expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.