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Concept: Bargaining


The fair division of a surplus is one of the most widely examined problems. This paper focuses on bargaining problems with fixed disagreement payoffs where risk-neutral agents have reached an agreement that is the Nash-bargaining solution (NBS). We consider a stochastic environment, in which the overall return consists of multiple pies with uncertain sizes and we examine how these pies can be allocated with fairness among agents. Specifically, fairness is based on the Aristotle’s maxim: “equals should be treated equally and unequals unequally, in proportion to the relevant inequality”. In this context, fairness is achieved when all the individual stochastic surplus shares which are allocated to agents are distributed in proportion to the NBS. We introduce a novel algorithm, which can be used to compute the ratio of each pie that should be allocated to each agent, in order to ensure fairness within a symmetric or asymmetric NBS.

Concepts: Game theory, Ratio, Agent, Ratio distribution, Nash bargaining game, Bargaining, Pie, Cooperative games


Women are twice as likely as men to be depressed, a bias that is poorly understood. One evolutionary model proposes that depression is a bargaining strategy to compel reluctant social partners to provide more help in the wake of adversity. An evolutionary model of anger proposes that high upper body strength predisposes individuals to angrily threaten social partners who offer too few benefits or impose too many costs. Here we propose that when social partners provide too few benefits or impose too many costs, the physically strong become overtly angry and the physically weak become depressed. The sexual dimorphism in upper body strength means that men will be more likely to bargain with anger and physical threats and women with depression.

Concepts: Male, Sexual dimorphism, Gender, Sex, Gender differences, Negotiation, Loneliness, Bargaining


One of the best-known and most replicated laboratory results in behavioral economics is that bargainers frequently reject low offers, even when it harms their material self-interest. This finding could have important implications for international negotiations on many problems facing humanity today, because models of international bargaining assume exactly the opposite: that policy makers are rational and self-interested. However, it is unknown whether elites who engage in diplomatic bargaining will similarly reject low offers because past research has been based almost exclusively on convenience samples of undergraduates, members of the general public, or small-scale societies rather than highly experienced elites who design and bargain over policy. Using a unique sample of 102 policy and business elites who have an average of 21 y of practical experience conducting international diplomacy or policy strategy, we show that, compared with undergraduates and the general public, elites are actually more likely to reject low offers when playing a standard “ultimatum game” that assesses how players bargain over a fixed resource. Elites with more experience tend to make even higher demands, suggesting that this tendency only increases as policy makers advance to leadership positions. This result contradicts assumptions of rational self-interested behavior that are standard in models of international bargaining, and it suggests that the adoption of global agreements on international trade, climate change, and other important problems will not depend solely on the interests of individual countries, but also on whether these accords are seen as equitable to all member states.

Concepts: Game theory, Negotiation, Diplomacy, Bargaining, Diplomat


In Wireless Sensor Networks (WSNs), unlicensed users, that is, sensor nodes, have excessively exploited the unlicensed radio spectrum. Through Cognitive Radio (CR), licensed radio spectra, which are owned by licensed users, can be partly or entirely shared with unlicensed users. This paper proposes a strategic bargaining spectrum-sharing scheme, considering a CR-based heterogeneous WSN (HWSN). The sensors of HWSNs are discrepant and exist in different wireless environments, which leads to various signal-to-noise ratios (SNRs) for the same or different licensed users. Unlicensed users bargain with licensed users regarding the spectrum price. In each round of bargaining, licensed users are allowed to adaptively adjust their spectrum price to the best for maximizing their profits. . Then, each unlicensed user makes their best response and informs licensed users of “bargaining” and “warning”. Through finite rounds of bargaining, this scheme can obtain a Nash bargaining solution (NBS), which makes all licensed and unlicensed users reach an agreement. The simulation results demonstrate that the proposed scheme can quickly find a NBS and all players in the game prefer to be honest. The proposed scheme outperforms existing schemes, within a certain range, in terms of fairness and trade success probability.

Concepts: Sensor, Wireless sensor network, Nash bargaining game, Bargaining, Sensor node


In this paper, we assume that a professional pollutant treatment enterprise treats all of the pollutants emitted by multiple small and medium-sized enterprises (SMEs). In order to determine the treatment price, SMEs can bargain with the pollutant treatment enterprise individually, or through forming alliances. We propose a bargaining game model of centralized pollutant treatment to study how the pollutant treatment price is determined through negotiation. Then, we consider that there is a moral hazard from SMEs in centralized pollutant treatment; in other words, they may break their agreement concerning their quantities of production and pollutant emissions with the pollutant treatment enterprise. We study how the pollutant treatment enterprise can prevent this by pricing mechanism design. It is found that the pollutant treatment enterprise can prevent SMEs' moral hazard through tiered pricing. If the marginal treatment cost of the pollutant treatment enterprise is a constant, SMEs could bargain with the pollutant treatment enterprise individually, otherwise, they should form a grand alliance to bargain with it as a whole.

Concepts: Game theory, Price, Negotiation, Nash bargaining game, Bargaining, Mechanism design, Price discrimination


We examine how public sector third-party purchasers and hospitals negotiate quality targets when a fixed proportion of hospital revenue is required to be linked to quality. We develop a bargaining model linking the number of quality targets to purchaser and hospital characteristics. Using data extracted from 153 contracts for acute hospital services in England in 2010/2011, we find that the number of quality targets is associated with the purchaser’s population health and its budget, the hospital type, whether the purchaser delegated negotiation to an agency, and the quality targets imposed by the supervising regional health authority.

Concepts: Health care, Public health, Health insurance, Health, Hospital, Negotiation, Bargaining, Collective bargaining


The alignment of bargaining positions is crucial to a successful negotiation. Prior research has shown that similarity in language use is indicative of the conceptual alignment of interlocutors. We use latent semantic analysis to explore how the similarity of language use between negotiating parties develops over the course of a three-party negotiation. Results show that parties that reach an agreement show a gradual increase in language similarity over the course of the negotiation. Furthermore, reaching the most financially efficient outcome is dependent on similarity in language use between the parties that have the most to gain from such an outcome.

Concepts: Negotiation, Contract, Diplomacy, Bargaining, Collective bargaining


So far many optimization models based on Nash Bargaining Theory associated with reservoir operation have been developed. Most of them have aimed to provide practical and efficient solutions for water allocation in order to alleviate conflicts among water users. These models can be discussed from two viewpoints: (i) having a discrete nature; and (ii) working on an annual basis. Although discrete dynamic game models provide appropriate reservoir operator policies, their discretization of variables increases the run time and causes dimensionality problems. In this study, two monthly based non-discrete optimization models based on the Nash Bargaining Solution are developed for a reservoir system. In the first model, based on constrained state formulation, the first and second moments (mean and variance) of the state variable (water level in the reservoir) is calculated. Using moment equations as the constraint, the long-term utility of the reservoir manager and water users are optimized. The second model is a dynamic approach structured based on continuous state Markov decision models. The corresponding solution based on the collocation method is structured for a reservoir system. In this model, the reward function is defined based on the Nash Bargaining Solution. Indeed, it is used to yield equilibrium in every proper sub-game, thereby satisfying the Markov perfect equilibrium. Both approaches are applicable for water allocation in arid and semi-arid regions. A case study was carried out at the Zayandeh-Rud river basin located in central Iran to identify the effectiveness of the presented methods. The results are compared with the results of an annual form of dynamic game, a classical stochastic dynamic programming model (e.g. Bayesian Stochastic Dynamic Programming model, BSDP), and a discrete stochastic dynamic game model (PSDNG). By comparing the results of alternative methods, it is shown that both models are capable of tackling conflict issues in water allocation in situations of water scarcity properly. Also, comparing the annual dynamic game models, the presented models result in superior results in practice. Furthermore, unlike discrete dynamic game models, the presented models can significantly reduce the runtime thereby avoiding dimensionality problems.

Concepts: Game theory, Mathematics, Physics, Drainage basin, Optimization, Nash equilibrium, Nash bargaining game, Bargaining


Rate control (RC) optimization is indispensable for scalable video coding (SVC) with respect to bitstream storage and video streaming usage. From the perspective of centralized resource allocation optimization, the inner-layer bit allocation problem is similar to the bargaining problem. Therefore, bargaining game theory can be employed to improve the RC performance for spatial SVC. In this paper, we propose a bargaining game based one-pass RC scheme for spatial H.264/SVC. In each spatial layer (SL), the encoding constraints, such as bit rates, buffer size are jointly modeled as resources in the inner-layer bit allocation bargaining game. The modified rate-distortion (R-D) model incorporated with the inter-layer coding information is investigated. Then the generalized Nash bargaining solution (NBS) is employed to achieve an optimal bit allocation solution. The bandwidth is allocated to the frames from the generalized NBS adaptively based on their own bargaining powers. Experimental results demonstrate that the proposed rate control algorithm achieves appealing image quality improvement and buffer smoothness. The average mismatch of our proposed algorithm is within the range of 0:19%2:63%.

Concepts: Game theory, Mathematics, Resource allocation, Nash bargaining game, Bargaining, Algorithmic efficiency, Bit rate, Scalable Video Coding


In this paper, we envisage the architecture of Green Wireless Body Area Nanonetwork (GBAN) as a collection of nanodevices, in which each device is capable of communicating in both the molecular and wireless electromagnetic communication modes. The term green refers to the fact that the nanodevices in such a network can harvest energy from their surrounding environment, so that no nanodevice gets old solely due to the reasons attributed to energy depletion. However, the residual energy of a nanodevice can deplete substantially with the lapse of time, if the rate of energy consumption is not comparable with the rate of energy harvesting. It is observed that the rate of energy harvesting is nonlinear and sporadic in nature. So, the management of energy of the nanodevices is fundamentally important. We specifically address this problem in a ubiquitous healthcare monitoring scenario and formulate it as a cooperative Nash Bargaining game. The optimal strategy obtained from the Nash equilibrium solution provides improved network performance in terms of throughput and delay.

Concepts: Time, Game theory, Nash equilibrium, Equilibrium, Matching pennies, Trembling hand perfect equilibrium, Nash bargaining game, Bargaining