Browsing by Author "Pinto, Alberto A."
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- An economical model for dumping by dumping in a Cournot modelPublication . Banik, Nilanjan; Ferreira, Fernanda A.; Martins, J.; Pinto, Alberto A.We consider an international trade economical model where two firms of different countries compete in quantities and can use three different strategies: (i) repeated collusion, (ii) deviation from the foreigner firm followed by punishment by the home country and then followed by repeated Cournot, or (iii) repeated deviation followed by punishment. In some cases (ii) and (iii) can be interpreted as dumping.We compute the profits of both firms for each strategy and we characterize the economical parameters where each strategy is adopted by the firms.
- Arc exchange systems and renormalizationPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, FlávioWe exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.
- Asymmetric dynamic price competition with uncertaintyPublication . Ferreira, Fernanda A.; Pinto, Alberto A.We consider a dynamic setting-price duopoly model in which a dominant (leader) firm moves first and a subordinate (follower) firm moves second. 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 analyse the effect of the production costs uncertainty on the profits of the firms, for different values of the intercept demand parameters.
- Bertrand model under incomplete informationPublication . Ferreira, Fernanda A.; Pinto, Alberto A.We consider a Bertrand duopoly model with unknown costs. The firms' aim is to choose the price of its product according to the well-known concept of Bayesian Nash equilibrium. The chooses are made simultaneously by both firms. In this paper, 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 analyse the advantages, for firms and for consumers, of using the technology with highest production cost versus the one with cheapest production cost. 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.
- Cantor exchange systems and renormalizationPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, FlávioWe prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.
- Characterizations of power indices based on null player free winning coalitionsPublication . Álvarez-Mozos, M.; Ferreira, Flávio; Alonso-Meijide, J. M.; Pinto, Alberto A.In this paper, we characterize two power indices introduced in [1] using two different modifications of the monotonicity property first stated by [2]. The sets of properties are easily comparable among them and with previous characterizations of other power indices.
- Cournot duopoly with competition in the R&D expendituresPublication . Pinto, Alberto A.; Ferreira, Fernanda A.; Ferreira, Miguel; Oliveira, Bruno M. P. M.We present a new R&D investment in a Cournot Duopoly model and we analyze the different possible types of Nash R&D investments. We observe that the new production costs region can be decomposed in three economical regions, depending on the Nash R&D investment, showing the relevance of the use of patents in new technologies.
- Cournot model with investments to change the market sizePublication . Pinto, Alberto A.; Ferreira, Fernanda A.; Ferreira, Miguel; Oliveira, Bruno M. P. M.We present a new deterministic dynamical model on the market size of Cournot competitions, based on Nash equilibria of R&D investment strategies to increase the size of the market of the firms at every period of the game. We compute the unique Nash equilibrium for the second subgame and the profit functions for both firms. Adding uncertainty to the R&D investment strategies, we get a new stochastic dynamical model and we analyse the importance of the uncertainty to reverse the initial advantage of one firm with respect to the other.
- Equilibria of quantity setting differentiated duopoly with uncertaintyPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Pinto, Alberto A.In this paper, we consider a Stackelberg duopoly competition with differentiated goods and with unknown costs. The firms' aim is to choose the output levels of their products according to the well-known concept of perfect Bayesian equilibrium. There is a firm ( F1 ) that chooses first the quantity 1 q of its good; the other firm ( F2 ) observes 1 q and then chooses the quantity 2 q of its good. We suppose that each firm has two different technologies, and uses one of them following a 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 advantages, for firms and for consumers, of using the technology with the highest production cost versus the one with the cheapest cost.
- Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfacesPublication . Ferreira, Flávio; Pinto, Alberto A.For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable 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.