Equilibria of quantity setting differentiated duopoly with uncertainty

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.

Quantity-setting competition under uncertain demand

We consider a quantity-setting duopoly model, and we study the decision to move first or second, by assuming that. the firms produce homogeneous goods and that. there is some demand uncertainty. The competitive phase consists of two periods, and in either period, the firms can make a production decision that is irreversible. As far as the firms are allowed to choose (non-cooperatively) the period they make the decision, we study the circumstances that favour sequential rather than simultaneous decisions.

Solid contact PVC membrane electrodes based on neutral or charged carriers for the selective reading of anionic sulfamethoxazole and their application to the analysis of aquaculture water

Sulfamethoxazole (SMX) is among the antibiotics employed in aquaculture for prophylactic and therapeutic reasons. Environmental and food spread may be prevented by controlling its levels in several stages of fish farming. The present work proposes for this purpose new SMX selective electrodes for the potentiometric determination of this sulphonamide in water. The selective membranes were made of polyvinyl chloride (PVC) with tetraphenylporphyrin manganese (III) chloride or cyclodextrin-based acting as ionophores. 2-nitrophenyl octyl ether was employed as plasticizer and tetraoctylammonium, dimethyldioctadecylammonium bromide or potassium tetrakis (4-chlorophenyl) borate was used as anionic or cationic additive. The best analytical performance was reported for ISEs of tetraphenylporphyrin manganese (III) chloride with 50% mol of potassium tetrakis (4-chlorophenyl) borate compared to ionophore. Nersntian behaviour was observed from 4.0 × 10−5 to 1.0 × 10−2 mol/L (10.0 to 2500 µg/mL), and the limit of detection was 1.2 × 10−5 mol/L (3.0 µg/mL). In general, the electrodes displayed steady potentials in the pH range of 6 to 9. Emf equilibrium was reached before 15 s in all concentration levels. The electrodes revealed good discriminating ability in environmental samples. The analytical application to contaminated waters showed recoveries from 96 to 106%.

Functional studies on BolA and related genes: increasing the understanding of a protein with pleiotropic effects

Dissertation presented to obtain a Doctoral degree in Biology by Instituto de Tecnologia Química e Biológica

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

Analysis of Two Arms Working in Cooperation

This paper analyzes the performance of two cooperative robot manipulators. In order to capture the working performancewe formulated several performance indices that measure the manipulability, the effort reduction and the equilibrium between the two robots. In this perspective the proposed indices we determined the optimal values for the system parameters. Furthermore, it is studied the implementation of fractional-order algorithms in the position/force control of two cooperative robotic manipulators holding an object.

Mathematical modelling of shallow flows: closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamics

Canadian Journal of Civil Engineering 36(10) 1605–16

Uncertainty on a Bertrand duopoly with product differentiation

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.

Investing to survive in a duopoly model

We 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.

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.

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.

Strategic trade policy and signaling costs with differentiated goods

We consider a trade policy model, where the costs of the home firm are private information but can be signaled through the output levels of the firm to a foreign competitor and a home policymaker. We compute the separating equilibrium and the Bayesian Nash equilibrium, and we compare the subsidies, firms’ expected profits and home government’s welfare in both equilibria, for different values of the own price effect parameter.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

Measures in Sectorization Problems

Sectorization means dividing a whole into parts (sectors), a procedure that occurs in many contexts and applications, usually to achieve some goal or to facilitate an activity. The objective may be a better organization or simplification of a large problem into smaller sub-problems. Examples of applications are political districting and sales territory division. When designing/comparing sectors some characteristics such as contiguity, equilibrium and compactness are usually considered. This paper presents and describes new generic measures and proposes a new measure, desirability, connected with the idea of preference.

Sectorization: measures and an electromagnetism based approach

Sectorization means dividing a set of basic units into sectors or parts, a procedure that occurs in several contexts, such as political, health and school districting, social networks and sales territory or airspace assignment, to achieve some goal or to facilitate an activity. This presentation will focus on three main issues: Measures, a new approach to sectorization problems and an application in waste collection. When designing or comparing sectors different characteristics are usually taken into account. Some are commonly used, and they are related to the concepts of contiguity, equilibrium and compactness. These fundamental characteristics will be addressed, by defining new generic measures and by proposing a new measure, desirability, connected with the idea of preference. A new approach to sectorization inspired in Coulomb’s Law, which establishes a relation of force between electrically charged points, will be proposed. A charged point represents a small region with specific characteristics/values creating relations of attraction/repulsion with the others (two by two), proportional to the charges and inversely proportional to their distance. Finally, a real case about sectorization and vehicle routing in solid waste collection will be mentioned.