This paper studies generic properties of Markov perfect equilibria in dynamic stochastic games. We show that almost all dynamic stochastic games have a finite number of locally isolated Markov perfect equilibria. These equilibria are essential and strongly stable. Moreover, they all admit purification. To establish these results, we introduce a notion of regularity for dynamic stochastic games and exploit a simple connection between normal form and dynamic stochastic games.Keywords dynamic stochastic games, Markov perfect equilibria, regularity, genericity, finiteness, strong stability, essentiality, purifiability, estimation, computation, repeated games This paper studies generic properties of Markov perfect equilibria in dynamic stochastic games. We show that almost all dynamic stochastic games have a finite number of locally isolated Markov perfect equilibria. These equilibria are essential and strongly stable. Moreover, they all admit purification. To establish these results, we introduce a notion of regularity for dynamic stochastic games and exploit a simple connection between normal form and dynamic stochastic games.

Cell membrane is a lipid bilayer that allows the flow of ions through their ionic pumping proteins. The ionic flow can be stimulated with external stimuli to activate specific signaling pathways intracellularly. Although studies have applied electric and magnetic stimuli to modify the cell function, the parameters to stimulate the cell membrane are unknown. Accordingly, a computational model to simulate the effect of electric and magnetic fields on the cell membrane was developed. Cells were stimulated with electric fields from 45 × 103 V/m to 12.6 × 105 V/m and magnetic fields of 2 mT, at frequencies of 60 kHz, 10 MHz, and 1 GHz. Results showed that the electric fields applied to the cell membrane tend to increase according to the frequency used, while magnetic fields do not have any effect on it. It was observed that electric fields generate a high voltage concentrator in the cell membrane of ellipsoidal cells when a frequency window from 1 kHz to 1 GHz was applied. These findings demonstrate that depending on the intensity of the field and frequency, it was possible to stimulate different cell membrane zones. This model is a promising tool to establish the adequate parameters to stimulate cells, and accurately predict if the stimulation modifies the cell membrane potential.

We consider a pool type electricity market in which generators bid prices in a sealed bid form and are dispatched by an independent system operator (ISO). In our model, demand is inelastic and the ISO allocates production to minimize the system costs while considering the transmission constraints. In a departure from received literature, the model incorporates explicit description of the network details. The analysis shows that losses along transmission lines render the market imperfectly competitive. Indeed, it is shown that competition among generators is qualitatively similar to the interaction among firms in a monopolistic competition setting. A lower bound for market prices is derived and it is shown that the costumers' cost of oligopolistic pricing is strictly positive. At a methodological level, we generalize standard oligopoly theory tools. * We would like to thank to Soledad Arellano, Sophie Bade, Ross Baldick, Alex Galetovic, Aldo González, Rodrigo Palma, Robert Wilson, and several seminar participants for useful suggestions. We particularly thank two anonymous referees for their detailed review and suggestions. Anne-Lise Thouroud provided helpful research assistance. This work was partially supported by ICM Complex Engineering Systems.

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Magnetic fields (MFs) have been used as an external stimulus to increase cell proliferation in chondrocytes and extracellular matrix (ECM) synthesis of articular cartilage. However, previously published studies have not shown that MFs are homogeneous through cell culture systems. In addition, variables such as stimulation times and MF intensities have not been standardized to obtain the best cellular proliferative rate or an increase in molecular synthesis of ECM. In this work, a stimulation device, which produces homogeneous MFs to stimulate cell culture surfaces was designed and manufactured using a computational model. Furthermore, an in vitro culture of primary rat chondrocytes was established and stimulated with two MF schemes to measure both proliferation and ECM synthesis. The best proliferation rate was obtained with an MF of 2 mT applied for 3 h, every 6 h for 8 days. In addition, the increase in the synthesis of glycosaminoglycans was statistically significant when cells were stimulated with an MF of 2 mT applied for 5 h, every 6 h for 8 days. These findings suggest that a stimulation with MFs is a promising tool that could be used to improve in vitro treatments such as autologous chondrocyte implantation, either to increase cell proliferation or stimulate molecular synthesis. Bioelectromagnetics. 2020;41:41–51 © 2019 Bioelectromagnetics Society

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