Duality, area-considerations, and the Kalai–Smorodinsky solution

We introduce a new solution concept for 2-person bargaining problems, which can be considered as the dual of the Equal-Area solution (EA) (see Anbarcı and Bigelow (1994)). Hence, we call it the Dual Equal-Area solution (DEA). We show that the point selected by the Kalai–Smorodinsky solution (see Kalai and Smorodinsky (1975)) lies in between those that are selected by EA and DEA. We formulate an axiom–area-based fairness–and offer three characterizations of the Kalai–Smorodinsky solution in which this axiom plays a central role. © 2016 Elsevier B.V

Distributed optimisation techniques for wireless networks

Alongside the ever increasing traffic demand, the fifth generation (5G) cellular network architecture is being proposed to provide better quality of service, increased data rate, decreased latency, and increased capacity. Without any doubt, the 5G cellular network will comprise of ultra-dense networks and multiple input multiple output technologies. This will make the current centralised solutions impractical due to increased complexity. Moreover, the amount of coordination information that needs to be transported over the backhaul links will be increased. Distributed or decentralised solutions are promising to provide better alternatives. This thesis proposes new distributed algorithms for wireless networks which aim to reduce the amount of system overheads in the backhaul links and the system complexity. The analysis of conflicts amongst transmitters, and resource allocation are conducted via the use of game theory, convex optimisation, and auction theory. Firstly, game-theoretic model is used to analyse a mixed quality of service (QoS) strategic non-cooperative game (SNG), for a two-user multiple-input single-output (MISO) interference channel. The players are considered to have different objectives. Following this, the mixed QoS SNG is extended to a multicell multiuser network in terms of signal-to-interference-and-noise ratio (SINR) requirement. In the multicell multiuser setting, each transmitter is assumed to be serving real time users (RTUs) and non-real time users (NRTUs), simultaneously. A novel mixed QoS SNG algorithm is proposed, with its operating point identified as the Nash equilibrium-mixed QoS (NE-mixed QoS). Nash, Kalai-Smorodinsky, and Egalitarian bargain solutions are then proposed to improve the performance of the NE-mixed QoS. The performance of the bargain solutions are observed to be comparable to the centralised solutions. Secondly, user offloading and user association problems are addressed for small cells using auction theory. The main base station wishes to offload some of its users to privately owned small cell access points. A novel bid-wait-auction (BWA) algorithm, which allows single-item bidding at each auction round, is designed to decompose the combinatorial mathematical nature of the problem. An analysis on the existence and uniqueness of the dominant strategy equilibrium is conducted. The BWA is then used to form the forward BWA (FBWA) and the backward BWA (BBWA). It is observed that the BBWA allows more users to be admitted as compared to the FBWA. Finally, simultaneous multiple-round ascending auction (SMRA), altered SMRA (ASMRA), sequential combinatorial auction with item bidding (SCAIB), and repetitive combinatorial auction with item bidding (RCAIB) algorithms are proposed to perform user offloading and user association for small cells. These algorithms are able to allow bundle bidding. It is then proven that, truthful bidding is individually rational and leads to Walrasian equilibrium. The performance of the proposed auction based algorithms is evaluated. It is observed that the proposed algorithms match the performance of the centralised solutions when the guest users have low target rates. The SCAIB algorithm is shown to be the most preferred as it provides high admission rate and competitive revenue to the bidders

Some Recent Developments on Pareto-optimal Reinsurance

This thesis focuses on developing Pareto-optimal reinsurance policy which considers the interests of both the insurer and the reinsurer. The optimal insurance/reinsurance design has been extensively studied in actuarial science literature, while in early years most studies were concentrated on optimizing the insurer’s interests. However, as early as 1960s, Borch argued that “an agreement which is quite attractive to one party may not be acceptable to its counterparty” and he pioneered the study on “fair” risk sharing between the insurer and the reinsurer. Quite recently, the question of how to strike a balance in risk sharing between an insurer and a reinsurer has drawn considerable attention. This thesis contributes to the existing study in terms of the following aspects: first, we derive the set of Pareto-optimal reinsurance policies within risk mimization framework; second, we obtain the set of Pareto-optimal reinsurance policies within expected utility maximization framework. In addition, we uniquely identify the policy according to classical bargaining models; third, we blend risk minimization criterion and expected utility maximization criterion and study the so called Pareto-optimal reinsurance policy with maximal synergy. The thesis is structured as follows. Chapter 1 introduces the problem and reviews the most recent advances on related topics. Chapter 2 applies a geometric approach to derive the Pareto-optimal reinsurance policy under Value-at-Risk minimization criterion. The geometric approach visualize the process of seeking the solution which greatly simplifies the mathematical proof. As a natural extention, Chapter 3 studies the design of Pareto-optimal reinsurance policy by assuming that distortion risk measures are employed to measure the risks of the insurer and the reinsurer. The optimal reinsurance policy is derived through three methods: Lagrange dual method, generalized Neyman-Pearson lemma and dynamic control approach. Chapter 4 studies the problem through maximizing the weighted expected utility and applies the results from classical bargaining models to identify the “best” policy on the Pareto efficient frontier. Chapter 5 revisits the problem by considering a mixture of risk minimization and expected utility maximization criteria. Chapter 6 gives potential directions for future research

Discrete Geometry (hybrid meeting)

A number of important recent developments in various branches of discrete geometry were presented at the workshop, which took place in hybrid format due to a pandemic situation. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as topology, combinatorics, algebraic geometry or functional analysis. The open questions abound and many of the results presented were obtained by young researchers, confirming the great vitality of discrete geometry

Wage and employment determination in agricultural labour markets in India

The thesis is concerned with the problem of wage and employment determination in the (casual) agricultural labour markets of India. It is argued that the extant theories of wage determination poorly accord with the stylized facts of the Indian situation. An alternative perspective on agricultural labour markets is developed, where wage determination at the village level is interpreted as the outcome of tacit collective bargaining between village labourers and employers. It is argued that cooperative behaviour, necessary to support such collective bargaining, can often be sustained through the operation of certain informal social sanctions against wage cutting behaviour. With an asymmetric Nash framework, a theoretical model of the village-level market for agricultural labour is developed, which simultaneously determines the agricultural wage rate, the level of employment and the employers' profits. The model is consistent with the existence of involuntary unemployment, while also explaining variability of wages. In the extended version of the model, male and female labourers are introduced as separate bargaining parties. The extended model provides a possible explanation for the existence of gender wage (and employment) disparities. Both the basic and extended models are econometrically estimated for ten villages in central, south and west India, using data collected by the International Crops Research Institute for Semi-Arid Tropics (Hyderabad). Bargaining powers of employers', male and female labourers (interpreted as the coefficients on their net gains from agreement) are estimated. The results show significant inequalities of bargaining power between employers and labourers, and between male and female labourers. Simulations based on the estimated models indicate that the observed inequalities of bargaining power are a quantity decisive influence on wage, employment and profit outcomes in the village labour markets

Fairness in operations.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 131-136).This thesis deals with two basic issues in resource allocation problems. The first issue pertains to how one approaches the problem of designing the "right" objective for a given resource allocation problem. The notion of what is "right" can be fairly nebulous; we consider two issues that we see as key: efficiency and fairness. We approach the problem of designing objectives that account for the natural tension between efficiency and fairness in the context of a framework that captures a number of problems of interest to operations managers. We state a precise version of the design problem, provide a quantitative understanding of the tradeoff between efficiency and fairness inherent to this design problem and demonstrate the approach in a case study that considers air traffic management. Secondly, we deal with the issue of designing implementable policies that serve such objectives, balancing efficiency and fairness in practice. We do so specifically in the context of organ allocation for transplantation. In particular, we propose a scalable, data-driven method for designing national policies for the allocation of deceased donor kidneys to patients on a waiting list, in a fair and efficient way. We focus on policies that have the same form as the one currently used in the U.S., that are policies based on a point system, which ranks patients according to some priority criteria, e.g., waiting time, medical urgency, etc., or a combination thereof. Rather than making specific assumptions about fairness principles or priority criteria, our method offers the designer the flexibility to select his desired criteria and fairness constraints from a broad class of allowable constraints. The method then designs a point system that is based on the selected priority criteria, and approximately maximizes medical efficiency, i.e., life year gains from transplant, while simultaneously enforcing selected fairness constraints. Using our method, we design a point system that has the same form, uses the same criteria and satisfies the same fairness constraints as the point system that was recently proposed by U.S. policymakers. In addition, the point system we design delivers an 8% increase in extra life year gains. We evaluate the performance of all policies under consideration using the same statistical and simulation tools and data as the U.S. policymakers use. We perform a sensitivity analysis which demonstrates that the increase in extra life year gains by relaxing certain fairness constraints can be as high as 30%.by Nikolaos K. Trichakis.Ph.D

User-Oriented Methodology and Techniques of Decision Analysis and Support

This volume contains 26 papers selected from Workshop presentations. The book is divided into two sections; the first is devoted to the methodology of decision analysis and support and related theoretical developments, and the second reports on the development of tools -- algorithms, software packages -- for decision support as well as on their applications. Several major contributions on constructing user interfaces, on organizing intelligent DSS, on modifying theory and tools in response to user needs -- are included in this volume