ESEIG - MAT - Livros, partes de livro ou capítulos de livro
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- Avaliar?... Como?Publication . Soares, Filomena Baptista; Nunes, Maria Paula
- Investing to survive in a duopoly modelPublication . Pinto, Alberto A.; Oliveira, Bruno M. P. M.; Ferreira, Fernanda A.; Ferreira, MiguelWe present deterministic 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 show that small changes in the initial production costs or small changes in the parameters that determine the efficiency of the R&D programs or of the firms can produce strong economic effects in the long run of the profits of the firms.
- Quantity competition in a differentiated duopolyPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Ferreira, Miguel; Pinto, Alberto A.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.
- Flexibility in Stackelberg leadershipPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Pinto, Alberto A.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.
- Stochasticity favoring the effects of the R&D strategies of the firmsPublication . Pinto, Alberto A.; Oliveira, Bruno M. P. M.; Ferreira, Fernanda A.; Ferreira, FlávioWe 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.
- Uncertainty on a Bertrand duopoly with product differentiationPublication . Ferreira, Fernanda A.; Pinto, Alberto A.The conclusions of the Bertrand model of competition are substantially altered by the presence of either differentiated goods or asymmetric information about rival’s production costs. In this paper, we consider a Bertrand competition, with differentiated goods. Furthermore, we suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that this game has exactly one Bayesian Nash equilibrium. We do ex-ante and ex-post analyses of firms’ profits and market prices. We prove that the expected profit of each firm increases with the variance of its production costs. We also show that the expected price of each good increases with both expected production costs, being the effect of the expected production costs of the rival dominated by the effect of the own expected production costs.
- Price-setting dynamical duopoly with incomplete informationPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Pinto, Alberto A.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. In this paper, we consider asymmetric information about rival’s production costs. We do ex-ante and ex-post analyses of firms’ profits and market prices. We compare the ex-ante firms’ expected profits with the ex-post firms’ profits.
- Hausdorff dimension versus smoothnessPublication . Ferreira, Flávio; Pinto, Alberto A.; Rand, David A.There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C1+α Cantor exchange system with bounded geometry that is a C1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.
- Fine structures of hyperbolic diffeomorphismsPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, Flávio
- Cálculo diferencial e integral: exercíciosPublication . Machado, J. A. Tenreiro; Galhano, Alexandra; Ferreira, Flávio; Ferreira, Fernanda A.