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This research shows that certain time-dependent congestion reduction schemes involving tolls have the potential for benefiting every driver even if the collected revenues are not returned to the payers. The paper considers a population of commuters who use a single bottleneck during the morning rush hour and try to arrive at work on time. It is assumed that the number of commuters is fixed (independent of the control strategy) and that each commuter wishes to pass through the bottleneck at a given time, which may differ across commuters. Commuters are otherwise identical. Each of them chooses his/her arrival time at the bottleneck so as to minimize a linear combination of monetary cost (tolls), queuing time and deviation from the desired passage time. A time-dependent toll is applied during a time window, but some commuters are exempted from paying it. Every day each commuter is classified as either "free" or "paying." The classification method is such that: (i) in the long-run the fraction of days, f, that a commuter is free is the same for all commuters, and (ii) the fraction of "free" commuters is f every day. "Free" commuters are allowed to use the bottleneck without paying the toll, while "paying" commuters can avoid the toll only if they pass through the bottleneck outside the time window. It is shown that if commuters wish to pass through the bottleneck close together then the toll, the window and the fraction of free commuters can be chosen-1in a way that will benefit everyone by inducing an equilibrium where the "peak is smoothed out" in a particular way. Up to 25% of the total user cost can be eliminated in this way.

In electricity markets, bilateral contracts (BC) are used to hedge against price volatility in the spot market. Pricing these contracts requires scheduling from either the buyer or the seller aiming to achieve the highest profit possible. Since this problem includes different players, a Generation Company (GC) and an Electricity Supplier Company (ESC) are considered. The approaches to solve this problem include the Nash Bargaining Solution (NBS) equilibrium and the Raiffa–Kalai–Smorodinsky (RKS) bargaining solution. The innovation of this work is the implementation of an algorithm based on the RKS equilibrium to find a compromise strategy when determining the concessions to be made by the parties. The results are promising and show that the RKS approach can obtain better results compared to the Nash equilibrium method applied to a case study.