Browsing by Author "Ferreira, Miguel"
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- 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.
- Flexibility in a Stackelberg leadership with differentiated goodsPublication . Ferreira, Fernanda A.; Ferreira, Flávio; Ferreira, Miguel; Pinto, Alberto A.We study the effects of product differentiation in a Stackelberg model with demand uncertainty for the first mover. We do an ex-ante and ex-post analysis of the profits of the leader and of the follower firms in terms of product differentiation and of the demand uncertainty. We show that even with small uncertainty about the demand, the follower firm can achieve greater profits than the leader, if their products are sufficiently differentiated. We also compute the probability of the second firm having higher profit than the leading firm, subsequently showing the advantages and disadvantages of being either the leader or the follower firm.
- 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.
- Towards a de facto nonlinear periodization: extending nonlinearity from programming to periodizingPublication . Afonso, José; Clemente, Filipe Manuel; Ribeiro, João; Ferreira, Miguel; Fernandes, Ricardo J.Planning is paramount in sport. Among different philosophical approaches to planning, periodization is a highly popular concept that refers to structured training periods with ensuing programs encompassing moments of progressively-loaded training, followed by recovery; it is normally deemed paramount to optimize adaptations and performance. While planning provides generic guidelines, periodization refers to the sequencing/ordering of training periods to enforce a given plan, therefore referring to longer temporal scales, and programming refers to more micro-scale aspects. In fact, similar periodization schemes may implement distinct programming strategies. Literature on the topic has used the linear and nonlinear terms to describe the content of periodized programs. However, these concepts have not been clearly defined in the literature, which may lead to inaccurate and misleading interpretations. Moreover, nonlinear periodization is usually using nonlinear programming, but with pre-stipulated sequencing of the training periods. Finally, it can be argued that nonlinearity has been an integral part of periodization since its inception, at least theoretically. In this essay, the literature was critically reviewed to better understand the validity of the linearity and nonlinearity concepts as applied in currently proposed periodization models. In addition, a novel approach for a de facto nonlinear periodization is presented.