Nash bargaining in ordinal environments

We analyze the implications of Nash’s (1950) axioms in ordinal bargaining environments; there, the scale invariance axiom needs to be strenghtened to take into account all order-preserving transformations of the agents’ utilities. This axiom, called ordinal invariance, is a very demanding one. For two-agents, it is violated by every strongly individually rational bargaining rule. In general, no ordinally invariant bargaining rule satisfies the other three axioms of Nash. Parallel to Roth (1977), we introduce a weaker independence of irrelevant alternatives axiom that we argue is better suited for ordinally invariant bargaining rules. We show that the three-agent Shapley-Shubik bargaining rule uniquely satisfies ordinal invariance, Pareto optimality, symmetry, and this weaker independence of irrelevant alternatives axiom. We also analyze the implications of other independence axioms

How brains make decisions

This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum Decision Theory (QDT) that we have developed in a series of publications since 2008. We formulate a general mathematical scheme of how decisions are taken, using the point of view of psychological and cognitive sciences, without touching physiological aspects. The basic principles of how intelligence acts are discussed. The human brain processes involved in decisions are argued to be principally different from straightforward computer operations. The difference lies in the conscious-subconscious duality of the decision making process and the role of emotions that compete with utility optimization. The most general approach for characterizing the process of decision making, taking into account the conscious-subconscious duality, uses the framework of functional analysis in Hilbert spaces, similarly to that used in the quantum theory of measurements. This does not imply that the brain is a quantum system, but just allows for the simplest and most general extension of classical decision theory. The resulting theory of quantum decision making, based on the rules of quantum measurements, solves all paradoxes of classical decision making, allowing for quantitative predictions that are in excellent agreement with experiments. Finally, we provide a novel application by comparing the predictions of QDT with experiments on the prisoner dilemma game. The developed theory can serve as a guide for creating artificial intelligence acting by quantum rules.Comment: Latex file, 20 pages, 3 figure

European option pricing with constant relative sensitivity probability weighting function

We evaluate European financial options under continuous cumulative prospect theory. Within this framework, it is possible to model investors’ attitude toward risk, which may be one of the possible causes of mispricing. We focus on probability risk attitudes and consider alternative probability weighting functions. In particular, curvature of the weighting function models optimism and pessimism when one moves from extreme probabilities, whereas elevation can be interpreted as a measure of relative optimism. The constant relative sensitivity weighting function is the only one, amongst those in the literature, which is able to model separately curvature and elevation. We are interested in studying the effects of both these features on options prices

Coastal natural and nature-based features: international guidelines for flood risk management

Natural and nature-based features (NNBF) have been used for more than 100 years as coastal protection infrastructure (e.g., beach nourishment projects). The application of NNBF has grown steadily in recent years with the goal of realizing both coastal engineering and environment and social co-benefits through projects that have the potential to adapt to the changing climate. Technical advancements in support of NNBF are increasingly the subject of peer-reviewed literature, and guidance has been published by numerous organizations to inform technical practice for specific types of nature-based solutions. The International Guidelines on Natural and Nature-Based Features for Flood Risk Management was recently published to provide a comprehensive guide that draws directly on the growing body of knowledge and practitioner experience from around the world to inform the process of conceptualizing, planning, designing, engineering, and operating NNBF. These Guidelines focus on the role of nature-based solutions and natural infrastructure (beaches, dunes, wetlands and plant systems, islands, reefs) as a part of coastal and riverine flood risk management. In addition to describing each of the NNBF types, their use, design, implementation, and maintenance, the guidelines describe general principles for employing NNBF, stakeholder engagement, monitoring, costs and benefits, and adaptive management. An overall systems approach is taken to planning and implementation of NNBF. The guidelines were developed to support decision-makers, project managers, and practitioners in conceptualizing, planning, designing, engineering, implementing, and maintaining sustainable systems for nature-based flood risk management. This paper summarizes key concepts and highlights challenges and areas of future research