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We consider a secondary spectrum market where primaries set prices for their unused channels. The payoff of a primary then depends on the availability of channels for its competitors, which a primary might not have information about. We study a model where a primary can acquire this competitor’s channel state information (C-CSI) at a cost. We formulate a game between two primaries, where each primary decides whether to acquire the C-CSI or not and then selects its price based on that. We first characterize the Nash equilibrium of this game for a symmetric model where the C-CSI is perfect. We show that the payoff of a primary is independent of the C-CSI acquisition cost. We then generalize our analysis to allow for imperfect estimation and cases, where the two primaries have different C-CSI costs or different channel availabilities. Our results show interestingly that the payoff of a primary increases when there is estimation error. We also show that surprisingly the expected payoff of a primary may decrease when the C-CSI acquisition cost decreases or primaries have different availabilities. [ABSTRACT FROM PUBLISHER]

We study a mean-field approximation of the M/M/ $$\infty $$ queueing system. The problem we deal is quite different from standard games of congestion as we consider the case in which higher congestion results in smaller costs per user. This is motivated by a situation in which some TV show is broadcast so that the same cost is needed no matter how many users follow the show. Using a mean-field approximation, we show that this results in multiple equilibria of threshold type which we explicitly compute. We further derive the social optimal policy and compute the price of anarchy. We then study the game with partial information and show that by appropriate limitation of the queue-state information obtained by the players, we can obtain the same performance as when all the information is available to the players. We show that the mean-field approximation becomes tight as the workload increases, thus the results obtained for the mean-field model well approximate the discrete one. [ABSTRACT FROM AUTHOR]

Traffic congestion in urban environment is one of the most critical issue for drivers and city planners for both environment and efficiency reasons. Traffic lights are one of the main tools used to regulate traffic by diverting the drivers between different paths. Rational drivers, in turn, react to the traffic light duration by evaluating their options and, if necessary, by changing direction in order to reach their destination quicker. In this paper, we introduce a macroscopic traffic model for urban intersections that incorporates this rational behavior of the drivers. Then, we exploit it to show that, by providing additional information about the expected red-time duration to the drivers, one can decrease the amount of congestion in the network and the overall length of the queues at the intersections. Additionally, we develop a control policy for the traffic lights that exploits the reaction of the drivers in order to divert them to a different route to further increase the performances. These claims are supported by extensive numerical simulations. • A traffic-flow macroscopic model of the drivers' rational decision-making. • It considers origin-destination pairs and the ability to show the red time duration. • Numerical simulations illustrate the effectiveness of showing the red time duration. • A novel control policy that exploit the drivers' reaction to the red time duration. • The increased efficiency of the controller is validated with extensive simulations. [ABSTRACT FROM AUTHOR]