Nash Bargaining Solution Research Articles

The Walrasian objection mechanism and Mas-Colell’s bargaining set in economies with many commodities

We study the Walrasian objection mechanism in the framework of economies with a measure space of agents and a separable Banach space of commodities whose positive cone has a non-empty interior. We provide several characterizations of Walrasian objections and use them to study the bargaining set of the economy, as defined in Mas-Colell (J Math Econ 18(2):129–139, 1989). Our main result shows that whenever the measure space of agents is saturated, every non-competitive allocation can be blocked with a Walrasian objection. This implies that the bargaining set, the core and the set of competitive allocations are equivalent solution concepts.

Price skimming: Commitment and delay in bargaining with outside option

This paper studies a bargaining problem in which the buyer's valuation and outside option are private information. We show that there exists a non-stationary equilibrium in which the seller can secure full commitment profit (from the optimal sales mechanism that exhibits price skimming) if and only if the buyer's outside option takes a zero value with positive probability (non-negligibly zero outside option). Our innovation is to show that (i) both the Coasean reversion and positive selection are necessary for the seller to secure the full commitment profit and (ii) the Coasean equilibria may coexist with positive selection despite their claimed incompatibility if the non-negligibly zero outside option exists.

A large-scale equilibrium model of energy emergency production: Embedding social choice rules into Nash Q-learning automatically achieving consensus of urgent recovery behaviors

A large-scale energy emergency production plan driven by extreme events in energy supply chain networks is the low-probability/high-consequence event that is difficult to prepare. One of the most prominent challenges is efficiently computing the equilibrium point characterized with more frequently involved in common resource conflicts due to different player behaviors in energy supply chain networks. In this paper, a novel large-scale equilibrium model of energy emergency production: embedding social choice rules into Nash Q-learning automatically achieving consensus of urgent recovery behaviors, is proposed to tackle this challenge. The main contributions of this work are that firstly set up a large-scale equilibrium model of energy emergency production to formulate energy emergency production plans by modifying the large-scale energy equilibrium model, and the computational limitations of Generalized Nash Equilibrium are overcame by combination of Nash Q-learning methods and individuals’ preferences reaching a collective decision which guarantees uniqueness of the large-scale Nash equilibrium to achieve both system-level efficiency and maximum fairness. Simulations results show that the generalized Nash bargaining solution can be implemented by the proposed large-scale equilibrium model of energy emergency production, in which outcome of the game is the emergency production stable equilibria alternative with no chance moves in a given consensus level, and compared with the existing techniques considering non-cooperative behaviors, it has a significantly lower minimisation of time for the energy restoration by twenty-nine percent, and reduces minimisation of cost for the energy restoration by seventeen percent and minimisation of carbon dioxide emissions by twenty-three percent with disaster recovery.

Bargaining approach for efficiency assessment and target setting with fixed-sum variables

There are many Data Envelopment Analysis (DEA) applications in which an input or output variable is such that the total amount for all the units in the sample is fixed. In this paper, such situations are modelled as a bargaining problem in which the players correspond to each of the variables for each of the units. All the players try to improve their utility as much as possible, where utility improvement implies a reduction in the case of an input variable or an undesirable output and an increase in the case of a desirable output. The Feasible Set of the bargaining problem derives from the corresponding fixed-sum DEA technology. A centralized DEA model is formulated for computing the Nash bargaining solution, which determines the efficient targets of all the units. From these targets, a modified Enhanced Russell Graph efficiency measure (ERM) is proposed to compute the corresponding efficiency scores. The proposed approach has been validated on different datasets corresponding to a variety of situations involving fixed-sum variables.

Multi-Stakeholder Service Placement via Iterative Bargaining With Incomplete Information

Mobile edge computing based on cloudlets is an emerging paradigm to improve service quality by bringing computation and storage facilities closer to end users and reducing operating cost for infrastructure providers (IPs) and service providers (SPs). To maximize their individual benefits, IP and SP have to reach an agreement about placing and executing services on particular cloudlets. We show that a Nash Bargaining Solution (NBS) yields the optimal solution with respect to social cost and fairness if IP and SP have complete information about the parameters of their mutual cost functions. However, IP and SP might not be willing or able to share all information due to business secrets or technical limitations. Therefore, we present a novel iterative bargaining approach without complete mutual information to achieve substantial cost reductions for both IP and SP. Furthermore, we investigate how different degrees of information sharing impact social cost and fairness of the different approaches. Our evaluation based on the mobile augmented reality game Ingress shows that our approach achieves up to about 82% of the cost reduction that the NBS achieves and a cost reduction of up to 147% compared to traditional Take-it-or-Leave-it approaches, despite incomplete information.

A general Nash Bargaining solution to the TSO-DSOs coordinated flexibility trading market

The increasing penetration of distributed energy resources (DERs) brings the valuable flexibility to the system as well as challenges, which requires the coordination between transmission system operator (TSO) and distribution system operators (DSOs). This paper quantitatively models the goals and constraints of TSO and DSOs in procuring flexibility resources from DERs and proposes a flexibility market. We resolve the potential conflicts between TSO and DSOs in the flexibility market via mutual economic compensation, specified by Nash Bargaining (NB) theory. Two alternative TSO-DSOs interaction modes, i.e., the DSO-managed mode and the hybrid-managed mode, and two detailed payment schemes are discussed and compared. The hybrid-managed mode guarantees efficiency and fairness, while the DSO-managed mode is less complicated and can protect information privacy. Numerical studies further validate our findings.

Incentive design and profit sharing in multi-modal transportation networks

We consider the situation where multiple transportation service providers cooperate to offer an integrated multi-modal platform to enhance the convenience to the passengers through ease in multi-modal journey planning, payment, and first and last mile connectivity. This market structure allows the multi-modal platform to coordinate profits across modes and also provide incentives to the passengers. Accordingly, in this paper, we use cooperative game theory coupled with the hyperpath-based stochastic user equilibrium framework to study such a market. We assume that the platform sets incentives (price discount or excess charge on passengers) along every edge in the transportation network. We derive the continuity and monotonicity properties of the equilibrium flow with respect to the incentives along every edge. The optimal incentives that maximize the profit of the platform are obtained through a two time-scale stochastic approximation algorithm. We use the asymmetric Nash bargaining solution to design a fair profit sharing scheme among the service providers. We show that the profit for each service provider increases after cooperation on such a platform. Finally, we complement the theoretical results through two numerical simulations.

Nash bargaining in a general equilibrium framework: The case of a shared surface water supply

We extend the axiomatic Nash bargaining approach to the context of interregional water sharing in order to assess the approach’s normative implications in a general equilibrium (GE) framework. The GE model is applied to a water development project proposed for the Wasatch Front and Cache Valley regions of Utah — the Bear River Development Project (BRDP). We demonstrate conceptually how an allocation rule and attendant net regional welfare measures are endogenously determined as equilibrium solutions to the bargaining problem. Numerical analysis, based upon a simulation model calibrated to current data, reveals that Nash bargaining is generally infeasible as a solution mechanism for sharing surplus water supplies generated through the implementation of the BRDP, with or without potential ex post side-payments made between Cache Valley and the Wasatch Front. Only in the special case of (1) larger future regional population sizes, (2) a hypothetical, joint per-capita cost-share arrangement where total project (i.e. fixed) costs are shared equally across the two regions, (3) hypothetically larger water augmentation rates, and (4) the ignoring of potential environmental costs, is the Nash bargaining solution viable. Otherwise, for all other scenarios where the analysis is based upon current or future population sizes, joint- or region-specific cost-share arrangements, lower or higher water augmentation rates, and internalized or externalized environmental costs, the Nash bargaining solution is found to be unattainable as a potential mechanism to share surplus water supplies produced by the BRDP.

General Nash bargaining based direct P2P energy trading among prosumers under multiple uncertainties

This paper presents a transaction scheme for the direct peer-to-peer (P2P) energy trading problem among prosumers under uncertainties. Prosumers, in the distribution network, coordinate with neighbors to share the idle energy and maximize the cooperative benefit. Most of the existing researches focus on mechanism design with the assumption of accurate forecast. Nevertheless, the P2P energy trading problem is challenging due to multiple uncertainties, caused by the market price, intermittent power output and load demand variation. Although stochastic or robust optimization approaches are introduced and investigated to manage uncertainties, there are limitations for their application, such as large scenario sizes in the stochastic programming, coordination of the conservativeness and economy in the robust optimization. To address these challenges, a hybrid stochastic/robust optimization model is adopted to manage uncertainties which makes trade-offs between computational time and conservatism. The uncertain price is modeled via various scenarios based on forecast values while a robust optimization is developed to take into account the uncertainties of renewable generation and load. Based on the above uncertainties description, the direct P2P energy trading among prosumers is formulated as a general Nash bargaining (GNB) problem which is decomposed into two subproblem: operation cost minimization problem (P1) and bargaining problem (P2). As P1 and P2 are nonconvex problem, linearization techniques including KKT conditions and logarithmic transformation are employed to transform them as mixed-integer linear programming problem. A linear distflow model is formulated to address an OPF problem considering voltage limits of an AC network in a radial structure. Furthermore, a graph theoretic method is proposed to construct the incident matrix about buses and branches in the network constraints which considerably enhances the solution efficiency. Numerical case studies demonstrate that the constructed model can effectively incentivize direct P2P energy trading among prosumers, and multiple uncertainties affect the operation costs and energy transaction decisions. Additionally, the efficiency of the graph theory based modeling approach is proved for solving the energy trading model with OPF constraints.

Energy Trading Strategy for Heat and Electricity-Coupled Microgrid Based on Cooperative Game

This paper proposes an energy trading framework for a combined heat and power (CHP) microgrid (MG) integrated with a Photovoltaic (PV) generation system. The parties involved in the CHP-MG energy market are a single MG operator (MGO) and multiple users with electric and thermal demand response (DR). The energy trading process between the MGO and users is formulated as a Nash bargaining game, where the users can bargain with the MGO regarding trading volumes and the prices of electricity and heat. The relationship between the Nash bargaining solution (NBS) and social welfare maximum is studied. A distributed optimization algorithm based on the alternating direction method of multipliers (ADMM) is adopted to achieve NBS. Case studies demonstrate the effectiveness of the proposed trading framework, and show the promotion of economic benefits.

Carbon emission reduction and green marketing decisions in a two-echelon low-carbon supply chain considering fairness concern

PurposeThe purpose of this paper is to investigate the impact of fairness concern on the optimal pricing, carbon emission reduction (CER), green marketing efforts (GME) and utility of supply chain members in a two-echelon low-carbon supply chain composed of one manufacturer and one retailer. First, three basic models that consider the manufacturer’s different attitudes toward the retailer’s fairness concern are constructed. The optimal decisions of these models are obtained. Second, these optimal solutions are compared, and the effects of some key parameters including fairness concern on the optimal decisions and utility are examined for the three models. Furthermore, the manufacturer may misestimate the retailer’s fairness concern; therefore, an extended model is proposed.Design/methodology/approachThe authors adopt the manufacturer-led Stackelberg game theoretic framework, where the manufacturer decides the wholesale price and CER level and, then, the retailer determines the retail price and GME.FindingsThe results show that fairness concern has a negative impact on the wholesale price, the level of CER and GME, and fairness concern are not always beneficial for maximizing utility, although it is related to whether the manufacturer pays attention to the retailer’s fairness concern. The manufacturer will gain more utility when considering the fairness concern of retailers than non-consideration. Overestimating or underestimating the fairness concern of the retailers does not lead to benefits for the manufacturer.Research limitations/implicationsThis study has the following two limitations that need to be addressed in future research. First, the authors only consider the fairness concern of a single retailer but not peer-induced fairness among multiple competing retailers, which can be taken into account in future studies. Second, the demand function is linearly related to price, CER and GME. Because of the uncertainty of market information, the uncertainty demand function can be further considered.Originality/valueThis paper simultaneously considers the factors CER, GME and fairness concern. The utility function of the retailer is established according to taking the Nash bargaining solution as a fairness reference point, and four different models are constructed and compared.

DEA-based Nash bargaining approach to merger target selection

Mergers and Acquisitions (M&As) are important business strategies in any industry, as they allow the parties involved to achieve, for example, higher market share, profits and influence in one or more industries. In any M&A activity, the key challenge for an acquirer company is to select the target company that can most improve its performance through synergy. The goal of this research is thus to help acquirer companies model and optimally solve their merger target selection problems (MTSPs) in both horizontal integration and vertical integration settings. We apply both a data envelopment analysis (DEA) based performance evaluation framework and the Nash bargaining solution concept to mathematically model an acquirer company's MTSPs under the two types of integration settings. To the best of our knowledge, the proposed new models are the first DEA-based Nash bargaining models in the literature to help acquirer companies obtain their most desired target companies. Finally, this research provides numerical examples, including real-life examples, to illustrate various aspects and implementation details of the two types of models.

Two-party Bargaining Processes Based on Subjective Expectations: A Model and a Simulation Study

This work presents a model for a two-party bargaining process in which multiple offers are exchanged as the negotiation goes on, under a risk of breakdown. Typical game theoretical analyses of such settings assume the breakdown risk is known and the parties are able to calculate an initial offer that is immediately accepted by the other party, ending the negotiation. Aiming to develop a model that is closer to real-life situations, in which parties do exchange many offers in a bargaining process, we consider the parties are unable to compute the far-reaching consequences of their offers, and are guided by their subjective expectations of the outcome of the negotiation. This introduces a new perspective to the analysis of two-party bargaining processes: the confidence of the bargainers in terms of what they hope to achieve by bargaining with each other. The resulting model can be seen as an extension of the Zeuthen-Hicks bargaining model. We show analytically that under the assumption of concave utilities of both parties, the bargaining process converges to the nonsymmetric Nash bargaining solution, where the asymmetry is caused by differences in expectations. This result provides a new interpretation of the parameters of the nonsymmetric Nash bargaining solution, linking them to behavior in the bargaining process. As an additional contribution, we perform a simulation study to examine the role of confidence and to analyze the outcomes for non-concave utility functions.

A game theory based demand-side management in a smart microgrid considering price-responsive loads via a twofold sustainable energy justice portfolio

This paper introduces a demand-side integration (DSI) framework that upholds the efficacious electrical energy consumption to attain the aims of smart grid as well as the customers’ requirement. The proposed DSI framework is based on a pre-paid orderly energy consumption strategy for a smart microgrid. The interaction between aggregators and end-use customers is captured as a Nash Bargaining Game. A dynamic electricity pricing scheme is implemented to derive the profitable daily electricity tariffs considering an elasticity-based model of price-responsive load. The resources caused by proper response of small-scale consumers are integrated into day-ahead energy scheduling problem. In order to cope the real-time deviations, the DSI program is accompanied by a supplementary pay-off module. The DSI framework is formulated as a stochastic optimization problem in the form of mixed integer nonlinear programming involving probabilistic representation of uncertainty in generation pattern of renewable energy resources. According to the simulation results, in contrast with the normal consumption paradigm, the load factor improves at least 1.36%, the net profit of unified entity enhances 0.27%, and the total gas emissions are mitigated about 10.9%. The outcomes demonstrate the accuracy and merit of the proposed method.

Bargaining over a jointly produced pie: The effect of the production function on bargaining outcomes

Using experimental data, we show that the characteristics of the joint production process have a notable impact on the distribution of bargaining agreements. The setting in which the jointly produced surplus is expressed to be proportional to individual inputs leads to significantly more proportional bargaining agreements. This is in contrast to the setting in which the surplus is expressed as an additive constant, where bargaining agreements are more in line with the Nash bargaining solution.

Features Selection as a Nash-Bargaining Solution: Applications in Online Advertising and Information Systems

Feature selection is a fundamental problem in online advertising, as features usually need to be purchased from third parties, and they are costly. Although many feature selection techniques can be used in online advertising and the general information systems (IS) domain, their performance is often context specific. Therefore, the literature of IS is suffering from a lack of adequate and generic methods. In this study, we address this issue by proposing a novel approach that employs ideas from the field of cooperative game theory. We derive a (continuous) second-order cone program that any convex programming solver can solve for determining the best subset of features. We show the efficacy of our proposed method on a real-life online advertising case study. We demonstrate that our proposed approach performs better in accuracy, precision, recall, and F-1 score than the best of the other approaches with much fewer features. Also, to illustrate that our method’s benefits are not limited to the context of online advertising, we perform an extensive set of simulations and consider a well-established real-life data set drawn from the UCI Machine Learning Repository at the University of California, Irvine. Summary of Contribution: Selecting the best subset of features is an important problem in the context of online advertising and, more broadly, in the field of information systems because firms usually need to buy costly data to model and forecast economic outcomes. In this study, we propose a novel methodology for addressing this problem. The proposed method employs the concept of the Nash bargaining solution in cooperative game theory to create a good balance between maximizing the fit while minimizing the noise when selecting the best subset of features. We apply the method to a real-life online advertising case study, providing superior performance in predicting and interpreting the features. Moreover, we show that the proposed method applies to a broader range of feature selection problems. We conduct a comprehensive computational study on simulated regression data sets and other real-life classification data sets widely available in the machine learning domain. The result of these efforts indicates that our method is robust in terms of prediction accuracy by outperforming several state-of-the-art techniques.

Direct Sourcing from Renewable Energy under Cost Uncertainty: A Bargaining Approach

Sourcing electricity from renewable energy suppliers becomes critical to improving renewable energy penetration. However, the common problem of bilateral bargaining between an electricity retailer and renewable energy supplier has rarely been studied in the literature. Considering the uncertainty of renewable generation cost, we introduce the incentive contract theory and signalling game to examine how the electricity procurement contract is designed in a Rubinstein bargaining framework. We derive the corresponding equilibrium outcomes depending on the renewable supplier’s generation cost uncertainty. The results show that if the possibility of a high generation cost is large, the retailer provides contracts for the renewable supplier of both high and low generation costs to achieve the simultaneous separating equilibrium; otherwise, he only proposes the contract for supplier with a low generation cost to achieve the sequential separating bargaining. Our work demonstrates that the proposed incentive contracts urge the renewable supplier to reveal the private information of generation cost and prevent the retailer’s profit deviation due to the adverse selection.

Decentralized Game-Based Robustly Planning Scheme for Distribution Network and Microgrids Considering Bilateral Energy Trading

In the emerging electricity market, bilateral transactions can be conducted among the distribution network (DN) and microgrids (MGs). It is essential to consider the effects of bilateral energy trading among multiple stakeholders at the planning level. In this paper, a bi-level robustly game-based planning framework is proposed for DN and MGs. To address the multiple non-convexities of traditional robust planning problems, a linear robust counterpart is developed to model the uncertainty of renewable energy sources. Then, the non- continuous robust planning problem is further transformed into an iterative process by alternating optimization procedure (AOP) for the proof of Nash equilibrium (NE) and convergence of distributed algorithms. In each iteration, the upper level utilizes the Nash bargaining solution (NBS) to clear the bilateral transaction electricity and payments in the convex subset generated by the lower level, while the lower level determines the individual planning problem locally with fixed transaction contracts obtained from the upper level. It is proved that the bi-level planning framework benefits all investors and minimizes social costs. Meanwhile, distributed algorithms are adopted to ensure the synchronization and privacy of stakeholders. Simulations on the IEEE 33-bus system demonstrate the effectiveness of the proposed framework.

The Nash bargaining solution in labor market analysis

AbstractTwo alternative strategic foundations have been identified for applications of the Nash bargaining solution in economic modelling. However, neither interpretation is consistent with treating “threat point” or disagreement payoffs as individual outside options, a salient feature of bargaining relationships in most labor market settings. This paper uses a matching and strategic bargaining model to examine the determination of bargaining power weights and threat points in the asymmetric Nash bargaining solution. The key result establishes a strategic foundation for applying this solution to market settings with endogenously determined outside options, and shows that bargaining weights depend on outside market conditions only when the matching prospects of one side of the market or the other are relatively high.

How fairness and dominance guide young children's bargaining decisions.

Reaching agreements in conflicts is an important developmental challenge. Here, German 5-year-olds (N=284, 49% female, mostly White, mixed socioeconomic backgrounds; data collection: June 2016-November 2017) faced repeated face-to-face bargaining problems in which they chose between fair and unfair reward divisions. Across three studies, children mostly settled on fair divisions. However, dominant children tended to benefit more from bargaining outcomes (in Study 1 and 2 but not Study 3) and children mostly failed to use leverage to enforce fairness. Communication analyses revealed that children giving orders to their partner had a bargaining advantage and that children provided and responded to fairness reasons. These findings indicate that fairness concerns and dominance are both key factors that shape young children's bargaining decisions.