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Concept: Nash bargaining game


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


Conflicts over water resources can be highly dynamic and complex due to the various factors which can affect such systems, including economic, engineering, social, hydrologic, environmental and even political, as well as the inherent uncertainty involved in many of these factors. Furthermore, the conflicting behavior, preferences and goals of stakeholders can often make such conflicts even more challenging. While many game models, both cooperative and non-cooperative, have been suggested to deal with problems over utilizing and sharing water resources, most of these are based on a static viewpoint of demand points during optimization procedures. Moreover, such models are usually developed for a single reservoir system, and so are not really suitable for application to an integrated decision support system involving more than one reservoir. This paper outlines a coupled simulation-optimization modeling method based on a combination of system dynamics (SD) and game theory (GT). The method harnesses SD to capture the dynamic behavior of the water system, utilizing feedback loops between the system components in the course of the simulation. In addition, it uses GT concepts, including pure-strategy and mixed-strategy games as well as the Nash Bargaining Solution (NBS) method, to find the optimum allocation decisions over available water in the system. To test the capability of the proposed method to resolve multi-reservoir and multi-objective conflicts, two different deterministic simulation-optimization models with increasing levels of complexity were developed for the Langat River basin in Malaysia. The later is a strategic water catchment that has a range of different stakeholders and managerial bodies, which are however willing to cooperate in order to avoid unmet demand. In our first model, all water users play a dynamic pure-strategy game. The second model then adds in dynamic behaviors to reservoirs to factor in inflow uncertainty and adjust the strategies for the reservoirs using the mixed-strategy game and Markov chain methods. The two models were then evaluated against three performance indices: Reliability, Resilience and Vulnerability (R-R-V). The results showed that, while both models were well capable of dealing with conflict resolution over water resources in the Langat River basin, the second model achieved a substantially improved performance through its ability to deal with dynamicity, complexity and uncertainty in the river system.

Concepts: Game theory, Nash bargaining game, Decision support system, Reservoir, Hydrology, Decision theory, Water, Drainage basin


In the present research, we found that endogenous testosterone and cortisol changes were jointly related to bargaining outcomes. In a face-to-face competitive negotiation (Study 1) and a laboratory-based bargaining game (Study 2), testosterone rises were associated with high earnings and high relationship quality, but only if cortisol dropped. If cortisol rose, testosterone rises were associated with low earnings and poor relationship quality. Conflict between financial and social goals was related to the financially costly dual-hormone profile (testosterone increase and cortisol decrease), whereas the absence of such conflict was related to the financially adaptive dual-hormone profile (testosterone increase and cortisol increase). The findings suggest that when cortisol decreases, rising testosterone is implicated in adaptive bargaining behavior that maximizes earnings and relationship quality. But when cortisol increases, rising testosterone is related to conflict between social and financial motives, weak earnings, and poor relationship quality. These results imply that there are both bright and dark sides to rising testosterone in economic social interactions that depend on fluctuations in cortisol.

Concepts: Collective bargaining, Knitting, Nash bargaining game, Negotiation, Behavior, Sociology, Testosterone, Present


As computer science and complex network theory develop, non-cooperative games and their formation and application on complex networks have been important research topics. In the inter-firm innovation network, it is a typical game behavior for firms to invest in their alliance partners. Accounting for the possibility that firms can be resource constrained, this paper analyzes a coordination game using the Nash bargaining solution as allocation rules between firms in an inter-firm innovation network. We build an extended inter-firm n-player game based on nonidealized conditions, describe four investment strategies and simulate the strategies on an inter-firm innovation network in order to compare their performance. By analyzing the results of our experiments, we find that our proposed greedy strategy is the best-performing in most situations. We hope this study provides a theoretical insight into how firms make investment decisions.

Concepts: Science, Nash bargaining game, Network science, Network theory, Social network, Complex network, Nash equilibrium, Game theory


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


In this paper, a joint machine learning and game theory modeling (MLGT) framework is proposed for inter frame coding tree unit (CTU) level bit allocation and rate control (RC) optimization in High Efficiency Video Coding (HEVC). First, a support vector machine (SVM) based multi-classification scheme is proposed to improve the prediction accuracy of CTU-level Rate-Distortion (R-D) model. The legacy “chicken-and-egg” dilemma in video coding is proposed to be overcome by the learning-based R-D model. Second, a mixed R-D model based cooperative bargaining game theory is proposed for bit allocation optimization, where the convexity of the mixed R-D model based utility function is proved, and Nash bargaining solution (NBS) is achieved by the proposed iterative solution search method. The minimum utility is adjusted by the reference coding distortion and frame-level Quantization parameter (QP) change. Lastly, intra frame QP and inter frame adaptive bit ratios are adjusted to make inter frames have more bit resources to maintain smooth quality and bit consumption in the bargaining game optimization. Experimental results demonstrate that the proposed MLGT based RC method can achieve much better R-D performances, quality smoothness, bit rate accuracy, buffer control results and subjective visual quality than the other state-of-the-art one-pass RC methods, and the achieved R-D performances are very close to the performance limits from the FixedQP method.

Concepts: Video compression, Support vector machine, Utility, Scientific method, Artificial intelligence, Game theory, Economics, Nash bargaining game


In a context sensing system in which a sensor-equipped mobile phone runs an unreliable context-aware application, the application can infer the user’s contexts, based on which it provides personalized services. However, the application may sell the user’s contexts to some malicious adversaries to earn extra profits, which will hinder its widespread use. In the real world, the actions of the user, the application and the adversary in the context sensing system affect each other, so that their payoffs are constrained mutually. To figure out under which conditions they behave well (the user releases, the application does not leak and the adversary does not retrieve the context), we take advantage of game theory to analyze the context sensing system. We use the extensive form game and the repeated game, respectively, to analyze two typical scenarios, single interaction and multiple interaction among three players, from which Nash equilibriums and cooperation conditions are obtained. Our results show that the reputation mechanism for the context-sensing system in the former scenario is crucial to privacy preservation, so is the extent to which the participants are concerned about future payoffs in the latter one.

Concepts: Nash bargaining game, Mechanism design, Mobile phone, Prisoner's dilemma, Self-confirming equilibrium, Nash equilibrium, Repeated game, Game theory


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


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


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