Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities

The concept of a non-extreme-outcome-additive capacity (neo-additive capacity ) is introduced. Neo-additive capacities model optimistic and pessimistic attitudes towards uncertainty as observed in many experimental studies. Moreover, neo-additive capacities can be applied easily in economic problems, as we demonstrate by examples. This paper provides an axiomatisation of Choquet expected utility with neo-capacities in a framework of purely subjective uncertainty.

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

On the Informational Comparison of Qualitative Fuzzy Measures

International audienceFuzzy measures or capacities are the most general representation of uncertainty functions. However, this general class has been little explored from the point of view of its information content, when degrees of uncertainty are not supposed to be numerical, and belong to a finite qualitative scale, except in the case of possibility or necessity measures. The thrust of the paper is to define an ordering relation on the set of qualitative capacities expressing the idea that one is more informative than another, in agreement with the possibilistic notion of relative specificity. To this aim, we show that the class of qualitative capacities can be partitioned into equivalence classes of functions containing the same amount of information. They only differ by the underlying epistemic attitude such as pessimism or optimism. A meaningful information ordering between capacities can be defined on the basis of the most pessimistic (resp. optimistic) representatives of their equivalence classes. It is shown that, while qualitative capacities bear strong similarities to belief functions, such an analogy can be misleading when it comes to information content

Elicitation of Preferences under Ambiguity

This paper is about behaviour under ambiguity ‒ that is, a situation in which probabilities either do not exist or are not known. Our objective is to find the most empirically valid of the increasingly large number of theories attempting to explain such behaviour. We use experimentally-generated data to compare and contrast the theories. The incentivised experimental task we employed was that of allocation: in a series of problems we gave the subjects an amount of money and asked them to allocate the money over three accounts, the payoffs to them being contingent on a ‘state of the world’ with the occurrence of the states being ambiguous. We reproduced ambiguity in the laboratory using a Bingo Blower. We fitted the most popular and apparently empirically valid preference functionals [Subjective Expected Utility (SEU), MaxMin Expected Utility (MEU) and α­-MEU], as well as Mean-Variance (MV) and a heuristic rule, Safety First (SF). We found that SEU fits better than MV and SF and only slightly worse than MEU and α­-MEU

Information and ambiguity: herd and contrarian behaviour in financial markets

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11238-012-9334-3”The paper studies the impact of informational ambiguity on behalf of informed traders on history-dependent price behaviour in a model of sequential trading in nancial markets. Following Chateauneuf, Eichberger and Grant (2006), we use neo-additive capacities to model ambiguity. Such ambiguity and attitudes to it can engender herd and contrarian behaviour, and also cause the market to break down. The latter, herd and contrarian behaviour, can be reduced by the existence of a bid-ask spread.Research in part funded by ESRC grant RES-000-22-0650

Photochemistry Of Monochloro Complexes Of Copper(ii) In Methanol Probed By Ultrafast Transient Absorption Spectroscopy

Ultrafast transient absorption spectra in the deep to near UV range (212-384 nm) were measured for the [Cu-II(MeOH)(5)Cl](+) complexes in methanol following 255-nm excitation of the complex into the ligand-to-metal charge-transfer excited state. The electronically excited complex undergoes sub-200 fs radiationless decay, predominantly via back electron transfer, to the hot electronic ground state followed by fast vibrational relaxation on a 0.4-4 Ps time scale. A minor photochemical channel is Cu-Cl bond dissociation, leading to the reduction of copper(H) to copper(I) and the formation of MeOH center dot Cl charge-transfer complexes. The depletion of ground-state [Cu-II(MeOH)(5)Cl](+) perturbs the equilibrium between several forms of copper(II) complexes present in solution. Complete re-equilibration between [Cu-II(MeOH)(5)Cl](+) and [Cu-II(MeOH)(4)Cl-2] is established on a 10-500 ps time scale, slower than methanol diffusion, suggesting that the involved ligand exchange mechanism is dissociative

A Revealed Reference Point for Prospect Theory

Without an instrument to identify the reference point, prospect theory includes a degree of freedom that makes the model difficult to falsify. To address this issue, we propose a foundation for prospect theory that advances existing approaches with three innovations. First, the reference point is not known a priori; if preferences are reference-dependent, the reference point is revealed from behavior. Second, the key preference axiom is formulated as a consistency property for attitudes towards probabilities; it entails both a revealed preference test for reference-dependence and a tool suitable for empirical measurement. Third, minimal assumptions are imposed for outcomes, thereby extending the model to general settings. By incorporating these three features we deliver general foundations for prospect theory that show how reference points can be identified and how the model can be falsified