On the axiomatic theory of bargaining: a survey of recent results

Thomson, William

doi:10.1007/s10058-022-00319-1

Cited by 3 publications

(5 citation statements)

References 180 publications

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“…More broadly, Nash's approach has been deeply influential in demonstrating the power of the cooperative game model in the search for wellbehaved solutions, and beyond that, it has been an important source of inspiration in the development of different cooperative game solutions. Until the present day, a number of game theory researchers have enriched the Nash's original idea through the introduction of a salient point [7]- [8].…”

Section: Technical Concepts and Main Contributionsmentioning

confidence: 99%

“…The BGV solution is the intersection between a ray connecting the disagreement point with the aspiration point, and the bargaining set's boundary. This is equivalent to saying that the BGV solution chooses the maximum individually rational utility profile at which each negotiator's utility gain from his disagreement point has the same proportion to the utility difference between his aspiration point and his disagreement point [8]- [9].…”

Section: Technical Concepts and Main Contributionsmentioning

confidence: 99%

“…We assume that 𝑑, 𝑟 ∈ 𝑆 ⊂ ℝ 𝑛 , and ∃𝑥 ∈ 𝑆 with 𝑥 > 𝑑 and 𝑟 ≥ 𝑑 . The assumption 𝑑 ∈ 𝑆 means that players are able to agree to disagree, the assumption 𝑟 ∈ 𝑆 means that the reference point is feasible, and the assumption 𝑟 ≥ 𝑑 means that the reference point is individually rational [8]- [9].…”

Section: B Fundamental Ideas Of Bgv Solution and Marl Modelmentioning

confidence: 99%

“…Given 𝑆 ⊂ ℝ 𝑛 , let 𝜋(𝑆) ≡ {𝑦 ∈ ℝ 𝑛 |∃𝑥 ∈ 𝑆, 𝑦 = 𝜋(𝑥)} . And, we define a solution function is any function 𝑓: ∑ 𝑛 → ℝ 𝑛 satisfying 𝑓(𝑆, 𝑑, 𝑟) ∈ 𝑆 for every (𝑆, 𝑑, 𝑟) ∈ ∑ 𝑛 , and the 𝑓(𝑆, 𝑑, 𝑟) is a solution point of the bargaining process [8]- [9].…”

Section: B Fundamental Ideas Of Bgv Solution and Marl Modelmentioning

confidence: 99%

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Learning and Game Based Spectrum Allocation Model for Internet of Medical Things (IoMT) Platform

Kim

2023

IEEE Access

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The Internet of Medical Things (IoMT) paradigm provides pervasive healthcare services inhome monitoring networks. Nowadays, these services play an imperative part in the life of human beings. However, excessive requirements of health services result in insufficient spectrum resources and service delays. In this study, a novel spectrum allocation scheme is proposed for the IoMT system platform. The main challenge of our scheme is to effectively share the limited spectrum resource while dynamically handling different service requests. To achieve a mutually desirable solution for multiple IoMT devices, our proposed scheme is designed as a bi-level control algorithm using the ideas of multi-agent reinforcement learning (MARL) and the Balakrishnan-G𝑜́mez-Vohra (BGV) solution. At the first level, each IoMT device selects its salient point according to the MARL model. At the second level, the spectrum resource is distributed through the BGV solution, which is implemented by considering the selected salient point of each device. Through the sequential interactions of intelligent devices, our bi-level control approach can effectively guide individual IoMT devices to choose cooperation strategies while optimizing the spectrum allocation process. Finally, numerical results show the effectiveness of our proposed scheme through the comparisons with benchmark protocols. We demonstrate the performance improvement of our method in terms of the normalized device payoff, IoMT system throughput and device fairness.

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Section: Technical Concepts and Main Contributionsmentioning

confidence: 99%

Section: Technical Concepts and Main Contributionsmentioning

confidence: 99%

Section: B Fundamental Ideas Of Bgv Solution and Marl Modelmentioning

confidence: 99%

Section: B Fundamental Ideas Of Bgv Solution and Marl Modelmentioning

confidence: 99%

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Learning and Game Based Spectrum Allocation Model for Internet of Medical Things (IoMT) Platform

Kim

2023

IEEE Access

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“…Vartiainen (2007) discussed the limited significance of weak Pareto optimality in bargaining problems without disagreement points. For a survey of the literature about efficiency-free characterizations, see Thomson (2022).…”

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confidence: 99%

Collective or individual rationality in the Nash bargaining solution: efficiency-free characterizations

Nakamura

2024

Soc Choice Welf

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In the classical bargaining problem, we propose a very mild axiom of individual rationality, which we call possibility of utility gain. This requires that for at least one bargaining problem, there exists at least one player who reaches a higher utility level than their disagreement utility. This paper shows that the Nash solution (Nash in Econometrica 18(2):155–162, 1950) is characterized by possibility of utility gain and continuity with respect to feasible sets together with Nash’s axioms except weak Pareto optimality. We also show that in Nash’s theorem, weak Pareto optimality can be replaced by conflict-freeness (introduced by Rachmilevitch in Math Soc Sci 76(C):107–109, 2015). This demands that when the agreement most preferred by all players is feasible, this should be chosen. Furthermore, we provide alternative and unified proofs for other efficiency-free characterizations of the Nash solution. This clarifies the role of each axiom in the related results.

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