Kalai-Smorodinsky Bargaining Solution Research Articles

Heterogeneous Drone Small Cells: Optimal 3D Placement for Downlink Power Efficiency and Rate Satisfaction

In this paper, we delve into the domain of heterogeneous drone-enabled aerial base stations, each equipped with varying transmit powers, serving as downlink wireless providers for ground users. A central challenge lies in strategically selecting and deploying a subset from the available drone base stations (DBSs) to meet the downlink data rate requirements while minimizing the overall power consumption. To tackle this, we formulate an optimization problem to identify the optimal subset of DBSs, ensuring wireless coverage with an acceptable transmission rate in the downlink path. Moreover, we determine their 3D positions for power consumption optimization. Assuming DBSs operate within the same frequency band, we introduce an innovative, computationally efficient beamforming method to mitigate intercell interference in the downlink. We propose a Kalai–Smorodinsky bargaining solution to establish the optimal beamforming strategy, compensating for interference-related impairments. Our simulation results underscore the efficacy of our solution and offer valuable insights into the performance intricacies of heterogeneous drone-based small-cell networks.

Fair Multi-Resource Allocation in Heterogeneous Servers With an External Resource Type

This paper considers the problem of fair allocation of multiple types of resources in heterogeneous servers, along with a resource type external to those servers. Our work is motivated by the need for fair multi-resource allocation in mobile edge computing (MEC), where the users must upload their tasks over a single dedicated wireless communication link that exists outside the computing servers. We propose a fair multi-resource allocation mechanism for this environment, termed Task Share Fairness with External Resource (TSF-ER), which finds the Kalai-Smorodinsky bargaining solution satisfying important fairness properties. We show that TSF-ER is envy-free, Pareto optimal, and strategy-proof, and it satisfies the property of sharing incentive. Large-scale simulation driven by Google and Alibaba cluster trace further shows that TSF-ER significantly outperforms the existing utilitarian, Nash social welfare maximizer, and egalitarian solutions, leading to fairer resource allocation while maintaining a high level of resource utilization.

Kalai-smorodinsky bargaining solution for the logone river basin water allocation

Kalai-smorodinsky bargaining solution for the logone river basin water allocation

A cooperative bargaining framework for decentralized portfolio optimization

Distributing a fixed budget among decentralized intermediaries is a relevant investment problem that has led to a growing research effort in the portfolio optimization literature. While existing contributions have widely focused on the incentive mechanisms driving the actions of the decentralized intermediaries, the idea of a budget partitioning that balances fairness and efficiency has been generally overlooked. In this paper, we consider a cooperative bargaining game for the budget allocation in a class of decentralized investment problems, where financial intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. Focusing on the Nash bargaining solution and the Kalai–Smorodinsky bargaining solution, we propose a reformulation that is valid within a class of risk/disutility measures (that we call quasi-homogeneous measures). This reformulation establishes a form of duality between a complex bilevel optimization model (resulting from the extensive formulation of the equilibrium conditions) and a convex knapsack problem. In the specific case of the Nash bargaining solution, the equilibrium characterization can be established as a convex separable knapsack problem. As empirically shown using stock returns data from U.S. listed enterprises, the notion of quasi-homogeneity not only allows to numerically characterize a budget partitioning that balances fairness and efficiency in decentralized investment, but also gives rise to a computational approach that facilitates its numerical solvability.

MAGIKS: Fair Multi-Resource Allocation Game Induced by Kalai-Smorodinsky Bargaining Solution

We study the problem of fair and efficient mechanism design for allocating multiple resources in multiple servers among a set of users with Leontief utilities. This problem is motivated by a mobile edge computing environment where each mobile user cannot establish a wireless connection simultaneously to multiple edge servers. Each user is a selfish utility maximizing agent that chooses a single server for its job execution. When a server is shared by multiple users, a resource allocation rule decides the utility that each user must receive. Our goal is to design a mechanism that always admits a Nash Equilibrium (NE), i.e., a state where no user has incentive to change its server, that (1) can be reached in polynomial time and (2) provides fair and efficient resource allocation. We propose the Multi-resource Allocation Game Induced by Kalai-Smorodinsky bargaining solution (MAGIKS) and prove that under discrete resource demands it finds an NE in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}({\textrm {poly}(n)})$ </tex-math></inline-formula> moves for any fixed server configuration, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is the number of users. Furthermore, MAGIKS satisfies envy-freeness, sharing incentive, and Pareto optimality on each server. Regarding fairness among users in different servers, we prove that MAGIKS satisfies 2-approximate envy-freeness and maximin share guarantee. Moreover, we show that 2-approximate envy-freeness is the best that any mechanism that satisfies local Pareto optimality can achieve at its NEs.

Wage Bargaining and Minimum Wages in a Search–Matching Model

In this paper, we analyze the introduction of a nonbinding minimum wage in a search–matching model with wage bargaining. Applying the Kalai–Smorodinsky bargaining solution instead of the commonly applied Nash solution, we provide a theoretical explanation for spillover effects of minimum wages on other wages higher up in the wage distribution. The labor market equilibrium in the Kalai–Smorodinsky solution with a minimum wage is characterized by lower market tightness, a higher unemployment rate, and lower vacancy rate than the equilibrium in the Nash solution. Moreover, we show that a nonbinding minimum wage can increase social welfare.

Bargaining solutions in heterogeneous networks: A reinforcement learning‐based approach

To enhance the performance and the coverage area of the next-generation heterogeneous wireless networks (HetNets), smaller cells such as femtocells are deployed. A reasonable resource allocation strategy is crucial for the operation of such systems. In this work, the Nash bargaining solution (NBS), Kalai–Smorodinsky bargaining solution (KSBS), and a proposed bargaining solution, which is the combination of NBS and KSBS, are studied to ensure the efficiency and fairness in the transmission rate allocation among femtocells. The mentioned bargaining solutions are optimised subject to the rate constraints due to the Han–Kobayashi (HK) rate splitting scheme, and a maximum tolerable interference caused by femtocell base stations (FBSs) at the macrocell user equipment. Two methods are used to address the bargaining solutions' optimisations. First, the conventional optimisation-based method is used for the situations where the channel gains are known, then a reinforcement learning-based algorithm for a real environment is proposed without being aware of the channel gains. To accelerate the speed of the learning process and to initialise the values of quality functions, the hotbooting technique is used. The bargaining solutions are compared by fairness and efficiency criteria in both methods. Numerical simulations show that the proposed reinforcement learning-based algorithm achieves the same performance derived from the conventional optimisation method. First, this paper studies the two well-known Nash and Kalai–Smorodinsky bargaining solutions as the good tools to establish fairness in rate allocation problem among femtocells in a HetNet. Then a new bargaining solution is proposed as the combination of the two bargaining solutions. The fairness and the efficiency of the allocated rates to femtocells as the output of optimisation problems of bargaining solutions are compared via Jain index criterion (as the fairness metric) and inverse price of anarchy criterion (as the efficiency metric). Moreover, the femtocell base stations are allowed to use Han–Kobayashi signalling scheme to send their signals in private and common messages which results in the best-known achievable rate region. Two methods are used to solve the optimisation problems: the conventional optimisation method and the reinforcement learning-based method (to formulate a real-world model with the unknown channel gains). It is shown that the proposed bargaining solution (in both methods) results in fairer rates than Nash and Kalai–Smorodinsky bargaining solutions while all of them are efficient.

On the empirical validity of axioms in unstructured bargaining

We report experimental results and test axiomatic models of unstructured bargaining by checking the empirical relevance of the underlying axioms. Our data support strong efficiency, symmetry, independence of irrelevant alternatives and monotonicity, and reject scale invariance. Individual rationality and midpoint domination are violated by a significant fraction of agreements that implement equal division in highly unequal circumstances. Two well-known bargaining solutions that satisfy the confirmed properties explain the observed agreements reasonably well. The most frequent agreements in our sample are the ones suggested by the equal-division solution. In terms of the average Euclidean distance, the theoretical solution that best explains the data is the deal-me-out solution (Sutton, 1986; Binmore et al., 1989, 1991). Popular solutions that satisfy scale invariance, individual rationality, and midpoint domination, as the well-known Nash or Kalai-Smorodinsky bargaining solutions, perform poorly in the laboratory.

On optimal reinsurance treaties in cooperative game under heterogeneous beliefs

In this paper, we study the optimal reinsurance policies as the result of a two-person cooperative game. We assume that both the insurer and the reinsurer are risk averse and expected-utility maximizers. In addition, we assume that they “agree to disagree” on the distribution of the underlying losses in the contract negotiation.In our analysis, we consider two scenarios. In the first one, the reinsurance premium is fully negotiable, whereas in the second one, the premium is determined by the reinsurer using the expected value premium principle. For both scenarios, we first derive the set of Pareto-optimal reinsurance contracts and then identify the reinsurance contract corresponding to the Nash bargaining solution as well as that corresponding to the Kalai–Smorodinsky bargaining solution.

Coordinated Placement and Setting of FACTS in Electrical Network based on Kalai-smorodinsky Bargaining Solution and Voltage Deviation Index

To aid the decision maker, the optimal placement of FACTS in the electrical network is performed through very specific criteria. In this paper, a useful approach is followed; it is based particularly on the use of Kalai-Smorodinsky bargaining solution for choosing the best compromise between the different objectives commonly posed to the network manager such as the cost of production, total transmission losses (Tloss), and voltage stability index (Lindex). In the case of many possible solutions, Voltage Profile Quality is added to select the best one. This approach has offered a balanced solution and has proven its effectiveness in finding the best placement and setting of two types of FACTS namely Static Var Compensator (SVC) and Thyristor Controlled Series Compensator (TCSC) in the power system. The test case under investigation is IEEE-14 bus system which has been simulated in MATLAB Environment.

QoE-Enabled Unlicensed Spectrum Sharing in 5G: A Game-Theoretic Approach

Spectrum sharing is an important aspect of 5G new radio, as it plays a complementary role for fulfilling diversified service requirements. This paper studies unlicensed spectrum sharing, namely, local thermal equilibrium (LTE) over unlicensed bands (LTE-U), for providing a better quality of experience (QoE) in 5G networks. Specifically, unlicensed band selection and resource allocation (time, licensed, and unlicensed) are jointly designed, and an optimization problem is formulated with the objective of maximizing LTE users’ QoE [measured in mean opinion score (MOS)] while protecting incumbent wireless systems such as Wi-Fi in the unlicensed spectrum. To solve the multi-player interaction in this spectrum space fairly, we employ a game-theoretic approach. A virtual coalition formation game (VCFG) is used to solve the unlicensed band selection problem. The outcome of the VCFG defines the optimization problem within each coalition. This optimization problem is then decomposed into two sub-problems: 1) time-sharing problem between the LTE-U and Wi-Fi systems and 2) a resource allocation problem for the LTE-U system. The cooperative Kalai–Smorodinsky bargaining solution is used for solving the first sub-problem, whereas the Q-learning algorithm is used for solving the second. VCFG and Q-learning-based resource allocation algorithms are proposed in this paper. In addition, the stability of VCFG and optimal sharing time are also proved in this paper. Simulation results show the advantages of the proposed approach over other baseline methods in terms of the MOS, percentage of unsatisfied users, and fairness. The results also show that the proposed approach can better protect the performance of Wi-Fi users compared to the conventional listen-before-talk scheme.

Economic Dispatch with Demand Response in Smart Grid: Bargaining Model and Solutions

This paper proposes an economic dispatch strategy for the electricity system with one generation company, multiple utility companies and multiple consumers, which participate in demand response to keep the electricity real-time balance. In the wholesale markets, multiple utility companies will commonly select a reliable agent to negotiate with the generation company on the wholesale price. It is challengeable to find a wholesale price to run the electricity market fairly and effectively. In this study, we use the multiple utility companies’ profits to denote the utility function of the agent and formulate the interaction between the agent and the generation company as a bargaining problem, where the wholesale price was enforced in the bargaining outcome. Then, the Raiffa–Kalai–Smorodinsky bargaining solution (RBS) was utilized to achieve the fair and optimal outcome. In the retail markets, the unfavorable disturbances exist in the power management and price when the consumers participate in the demand response to keep the electricity real-time balance, which motivates us to further consider the dynamic power management algorithm with the additive disturbances, and then obtain the optimal power consumption and optimal retail price. Based on the consumers’ utility maximization, we establish a price regulation model with price feedback in the electricity retail markets, and then use the iterative algorithm to solve the optimal retail price and the consumer’s optimal power consumption. Hence, the input-to-state stability condition with additive electricity measurement disturbance and price disturbance is given. Numerical results demonstrate the effectiveness of the economic dispatch strategy.

Game‐theoretic beamforming techniques for multiuser multi‐cell networks under mixed quality of service constraints

We propose a game-theoretic approach for the downlink beamformer design for a multiuser multi-cell wireless network under a mixed quality of services criterion. The network has real time users that must attain a specific set of signal-to-interference-plus-noise ratios, and non-real time users whose signal-to-interference-plus-noise ratios should be balanced and maximized. We propose a mixed QoS strategic noncooperative game wherein base stations determine their downlink beamformers in a fully distributed manner. In the case of infeasibility, we have proposed a fall back mechanism which converts the problem to a pure max-min optimization. We further propose the mixed QoS bargain game to improve the Nash equilibrium operating point through Egalitarian and Kalai-Smorodinsky bargaining solutions. We have shown that the results of bargaining games are comparable to that of the optimal solutions.

Monotonic Bargaining Solution for Allocating Critically Scarce Transboundary Water

As much as transboundary river basins can be niches for regional cooperation, they could also be causes for interstate water disputes. The risk of water conflict in these river basins is much higher during water scarcity. As a result, establishing a fair and efficient water allocation mechanism is key for the sustainable sharing of these river basins’ water. In this paper, the authors propose a monotonic water allocation mechanism for transboundary river basins under water scarcity by coupling the bankruptcy theory with the Asymmetric Kalai-Smorodinsky bargaining solution concept. The allocation framework takes into account the aspiration water claims of the sharing countries. Additionally, as a case study, the allocation solution was used to allot the contested water of the Nile among the basin countries. For the medium term water demands the framework allocated 61.67%, 89.80%,91.82% and 61.67% of their water claims to Ethiopia, Sudan, Egypt and to the assumed coalition countries on the White Nile referred in this paper as equatorial states (Uganda, Kenya, Tanzania, Burundi, Rwanda, and Democratic Republic of Congo) respectively. On the other hand, for the long term demands, the allocation scheme allocated 63.65%, 69.36%, 71.42% and 60.41% of their water demands to the riparian countries in the same order. In general, the authors hope that the water allocation scheme applied in this article can contribute to the ongoing efforts to design river sharing solutions to river sharing problems in transboundary river basins by understanding the strategic interaction among riparian countries.

COOPERATIVE RESOURCE SHARING OVER SERVICE PROVIDERS POOL IN CLOUD RADIO ACCESS NETWORK

Existing confined wireless network needs a revolutionary change to support diversified data traffic expected in the near future. Cloud Radio Access Network (CRAN) is a new paradigm which will overcome the pitfalls of existing radio access network (RAN) architecture, since its foundation principle is to share resources over multiple service providers. The CRAN architecture needs optimized resource allocation algorithm to achieve the benefits of centralization. This work aims the optimization of resource allocation using CRAN bargaining scheduler (CRAN-BS) framework. In CRAN-BS, resource allocation is formulated as cooperative game between users of multiple service providers, solution of which is obtained using the Kalai-Smorodinsky bargaining solution (KSBS). The CRAN-KSBS approach benefits each user in proportion with user's maximum achievable utility obtained by considering a service provider (SP) acting alone in the network. The proposed CRAN-KSBS proves to improve spectral efficiency of network over non-cooperative traditional RAN for different traffic conditions. The fairness of solution over different service providers is further obtained by considering bargaining power based on instantaneous utility of SP.

Game Theory Framework for MAC Parameter Optimization in Energy-Delay Constrained Sensor Networks

Optimizing energy consumption and end-to-end (e2e) packet delay in energy-constrained, delay-sensitive wireless sensor networks is a conflicting multiobjective optimization problem. We investigate the problem from a game theory perspective, where the two optimization objectives are considered as game players. The cost model of each player is mapped through a generalized optimization framework onto protocol-specific MAC parameters. From the optimization framework, a game is first defined by the Nash bargaining solution (NBS) to assure energy consumption and e2e delay balancing. Secondy, the Kalai-Smorodinsky bargaining solution (KSBS) is used to find an equal proportion of gain between players. Both methods offer a bargaining solution to the duty-cycle MAC protocol under different axioms. As a result, given the two performance requirements (i.e., the maximum latency tolerated by the application and the initial energy budget of nodes), the proposed framework allows to set tunable system parameters to reach a fair equilibrium point that dually minimizes the system latency and energy consumption. For illustration, this formulation is applied to six state-of-the-art wireless sensor network (WSN) MAC protocols: B-MAC, X-MAC, RI-MAC, SMAC, DMAC, and LMAC. The article shows the effectiveness and scalability of such a framework in optimizing protocol parameters that achieve a fair energy-delay performance trade-off under the application requirements.

Resource Optimization-Based Interference Management for Hybrid Self-Organized Small-Cell Network

This paper jointly studies interference management (IM) and self-organization (SO) schemes in a hybrid-SO small-cell network, which is a combination of the centralized and distributed small-cell networks. From the view of downlink transmission, we formulate a resource optimization-based IM (ROIM) problem. In particular, to accommodate to the hybrid architecture, the problem is divided into two subproblems. The first is subchannel allocation, which is investigated with overall network interference alleviation under the assumption of imperfect channel-state information (CSI). The second is power assignment (PA), which aims at constraining the local interference while guaranteeing the network utility. To solve the ROIM problem, we propose a two-step SO-based IM (TSSOIM) scheme. At the first step, the operation and management (O&M) unit adopts an aggressive discrete stochastic approximation (ADSA) algorithm to find the proper channel set for users. At the second step, small cells employ the game-theory-based Kalai–Smorodinsky bargaining solution (KSBS) to assign power to the channels. Simulation results are presented to show the effectiveness of the proposed TSSOIM scheme.

On the Non-Symmetric Nash and Kalai-Smorodinsky Bargaining Solutions

Recently in some negotiation application areas the usual assumption that the negotiators are symmetric has been relaxed. In particular, weights have been introduced to the Nash Bargaining Solution to reflect the different powers of the players. Yet operating with non-symmetric bargaining solutions and their implications is, we feel, not well understood. We analyze the properties and optimization of the non-symmetric Nash Bargaining Solution and of a non-symmetric Kalai-Smorodinsky Bargaining Solution. We provide extensive comparative statics, then comment on the implications of the concepts in supply chain coordination contexts.

Moral hazard and bargaining over incentive contracts

This paper analyses bargaining over an incentive compatible contract in a moral hazard framework. We introduce the Kalai–Smorodinsky bargaining solution and compare the outcome with the commonly applied Nash solution. Whether worker׳s effort is higher in the Nash or the Kalai–Smorodinsky solution depends on the agents׳ bargaining power. The social planner can mitigate inefficiencies arising in both bargaining solutions from the moral hazard problem and even achieve the first-best outcome by allocating the agents׳ bargaining power. If raising the worker׳s bargaining power is necessary to achieve the first-best solution, this increase must be higher in the Nash solution than in the Kalai–Smorodinsky solution.

Efficiency-free characterizations of the Kalai–Smorodinsky bargaining solution

Roth (1977) axiomatized the Nash (1950) bargaining solution without Pareto optimality, replacing it by strong individual rationality in Nash’s axiom list. In a subsequent work (Roth, 1979) he showed that when strong individual rationality is replaced by weak individual rationality, the only solutions that become admissible are the Nash and the disagreement solutions. In this paper I derive analogous results for the Kalai–Smorodinsky (1975) bargaining solution.