Consensus in Noncooperative Dynamic Games: A Multiretailer Inventory Application

We focus on Nash equilibria and Pareto optimal Nash equilibria for a finite horizon noncooperative dynamic game with a special structure of the stage cost. We study the existence of these solutions by proving that the game is a potential game. For the single-stage version of the game, we characterize the aforementioned solutions and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multistage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately, not necessarily Pareto optimal. The algorithm returns a sequence of joint decisions, each one obtained from the previous one by an unilateral improvement on the part of a single player. We also specialize the game to a multiretailer inventory system.     

Medium access in WiFi networks: strategies of selfish nodes [Applications Corner]

This article provides a game theoretical analysis of the WiFi MAC protocol to understand the risks or the advantages offered by possible modifications of MAC functionalities implemented at the driver level.     

Model quality evaluation in H2 identification

Model quality evaluation in set-membership identification is investigated, In the recent literature, two main approaches have been used to investigate this problem, based on the concepts of n-width and of radius of information. In this paper it is shown that the n-width is related to the asymptotic value of the conditional radius of information of the identification problem with noise free measurements. Upper and lower bounds of the conditional radius of information are derived for the H₂ identification of exponentially stable systems using approximating n-dimensional models linear in the parameters in the presence of power bounded measurement errors. The derived bounds are shown to be convergent to the radius for a large number of data and model dimensions. Moreover, a formula for computing the worst case identification error for any linear algorithm is given. In particular, it is shown that the identification error of the least square algorithm may be increasing with respect to the model dimension (“peaking effect”), An almost-optimal linear algorithm is presented, that is not affected by this peaking effect, and indeed is asymptotically optimal