Level-k theories are agnostic over whether individuals stop the iterated reasoning because of their own cognitive constraints, or because of their beliefs over the cognitive constraints of their opponents. In practice, individual level of play may be a function both of their own constraints and their beliefs over their opponents' reasoning process. Moreover, the rounds of introspection that players perform may depend on their incentives to think more deeply. We develop a theory which explicitly models players' reasoning procedure. The rounds of introspection that individuals perform and their actual level of play both follow endogenously. This model delivers testable implications as payoffs and opponents change, and it allows for comparisons across games. It also disentangles the cognitive bound of players for a given game from their beliefs about the play of their opponents. In conjunction with the framework, we present an experiment designed to test its predictions. We modify the Arad and Rubinstein (2012) '11-20' game to serve this precise purpose, and administer different treatments which vary beliefs over payoffs and opponents. The results of this experiment are consistent with the model, and appear to lend support to our theory. This experiment also confirms the central premise that individuals change their level of play as incentives to think more and beliefs over opponents vary.

In this paper, a novel rotor speed estimation method using model reference adaptive system (MRAS) is proposed to improve the performance of a sensorless vector control in the very low and zero speed regions. In the classical MRAS method, the rotor flux of the adaptive model is compared with that of the reference model. The rotor speed is estimated from the fluxes difference of the two models using adequate adaptive mechanism. However, the performance of this technique at low speed remains uncertain and the MRAS loses its efficiency, but in the new MRAS method, two differences are used at the same time. The first is between rotor fluxes and the second between electromagnetic torques. The adaptive mechanism used in this new structure contains two parallel loops having Proportional-integral controller and low-pass filter. The first and the second loops are used to adjust the rotor flux and electromagnetic torque. To ensure good performance, a robust vector control using sliding mode control is proposed. The controllers are designed using the Lyapunov approach. Simulation and experimental results show the effectiveness of the proposed speed estimation method at low and zero speed regions, and good robustness with respect to parameter variations, measurement errors, and noise is obtained. terests include linear and nonlinear control theory, including sliding mode control, adaptive control, and robust control, with applications to electric drive and mechatronics systems.Mohammed Ouriagli received the Ph.D. degree in electrical engineering from the Institut National Polytechnique de Lorraine, Lorraine, France, in 1995.Since 2003, he has held a teaching position in automatic control in the Polydisciplinary Faculty of Taza, Université Sidi Mohamed Ben-Abdellah (USMBA), Taza, Morroco. His research interests mainly include linear and nonlinear control theory, including sliding mode control, adaptive control, robust control, electric drive applications, and mechatronics systems.

No abstract