Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium

In this article we combine Debreu’s (Proc Natl Acad Sci 38(10):886–893, 1952) social system with Hurwicz’s (Econ Design 1(1):1–14, 1994; Am Econ Rev 98(3):577–585, 2008) ideas of embedding a “desired” game form into a “natural” game form that includes all feasible behavior, even if it is “illegal” according to the desired form. For the resulting socio-legal system we extend Debreu’s concepts of a social system and its social equilibria to a socio-legal system with its Debreu–Hurwicz equilibria. We build on a more general version of social equilibrium due to Shafer and Sonnenschein (J Math Econ 2(3):345–348, 1975) that also generalizes the dc-mechanism of Koray and Yildiz (J Econ Theory 176:479–502, 2018) which relates implementation via mechanisms with implementation via rights structures as introduced by Sertel (Designing rights: invisible hand theorems, covering and membership. Tech. rep. Mimeo, Bogazici University, 2001). In the second part we apply and illustrate these new concepts via an application in the narrow welfarist framework of two person cooperative bargaining. There we provide in a socio-legal system based on Nash’s demand game an implementation of the Nash bargaining solution in Debreu–Hurwicz equilibrium.

Risk aversion for losses and the Nash bargaining solution

We call a decision maker risk averse for losses if that decision maker is risk averse with respect to lotteries having alternatives below a given reference alternative in their support. A two-person bargaining solution is called invariant under risk aversion for losses if the assigned outcome does not change after correcting for risk aversion for losses with this outcome as pair of reference levels, provided that the disagreement point only changes proportionally. We present an axiomatic characterization of the Nash bargaining solution based on this condition, and we also provide a decision-theoretic characterization of the concept of risk aversion for losses.

Optimal User Association of LTE/Wi-Fi/Wi-Gig Bands in 5G Cellular Networks

One hypothesis of 5G cellular networks architecture is using three tiers: Macro BS, Wi-Fi Pico BS, and Wi-Gig Femtocell. The challenge addressed in this paper is to associate the user requirement (UE) to the best BS/tier to achieve the optimal operation for the network and maximum data rate for all UE. There are two proposed types of association in this paper; the first one is to find the best BS in the three tiers and then associate the UE to one of them based on the association algorithm, and the second proposed type is to decide the best tier for the UE and then associate the UE to one of the BS of this tier based on the association algorithm. The opportunistic user association problem is worked out as an optimization problem which is solved by the Nash bargaining solution (NBS). The proposed algorithms presented in this paper achieve optimality, 7% and 2% increase in total system data rate (SDR) for the first and second proposed algorithms respectively. They also achieved 6% and 2% increase in total Jain's fairness index (JFI) for the first and second proposed algorithms respectively.

Finding Multiple Equilibria for Raiffa–Kalai–Smorodinsky and Nash Bargaining Equilibria in Electricity Markets: A Bilateral Contract Model

In a deregulated market, energy can be exchanged like a commodity and the market agents including generators, distributors, and the end consumers can trade energy independently settling the price, volume, and the supply terms. Bilateral contracts (BCs) have been applied to hedge against price volatility in the electricity spot market. This work introduces a model to find all solutions for the equilibria implementing the Raiffa–Kalai–Smorodinski (RKS) and the Nash Bargaining Solution (NBS) approaches in an electricity market based on BCs. It is based on creating “holes” around an existing equilibrium within the feasibility set, yielding a new (smaller) feasibility set at each iteration. This research has two players: a generation company (GC) and an electricity supplier company (ESC), aiming to achieve the highest profit for each of them. The results present all possible RKS and NBS, in addition to showing all assigned energies for a case study at different time frames. The multiple equilibria solutions allow the ESC and the GC to apply different strategies knowing that they can still achieve an optimal solution.

Nash Bargaining Solution as Negotiation Concept for Resource Allocation Problem with Groves-Ledyard Mechanism

Motivated by research works on Zeuthen-Hicks bargaining, which leads to the Nash bargaining solution, we analyze experimental data of resource allocation gaming with Groves-Ledyard mechanism. The games were designed in the form of negotiation to allow players to reach consensus. Behavior models based on best response, constant behavior, and Nash bargaining solution are defined. Analysis conducted over decisions made by participants shows that a significant share of all decisions leads to an increase of the Nash bargaining value. It is even higher than the share of decisions that are in agreement with the best-response concept. Consensusended games show light attraction to the Nash bargaining solution, it's less than we obtained in games with the mechanism of Yang-Hajek from another class of so-called proportional allocation mechanisms. We discuss differences of consensus-ended games from timeout-ended games, what decisions lead to the situations with the Nash bargaining value increasing and differences between balanced mechanism Groves-Ledyard and unbalanced mechanism Yang-Hajek.