Stochastic Choice and Consideration Sets

We model a boundedly rational agent who suffers from limited attention. The agent considers each feasible alternative with a given (unobservable) probability, the attention parameter, and then chooses the alternative that maximises a preference relation within the set of considered alternatives. We show that this random choice rule is the only one for which the impact of removing an alternative on the choice probability of any other alternative is asymmetric and menu independent. Both the preference relation and the attention parameters are identi fied uniquely by stochastic choice data.

Notes on stochastic choice

A general formalism on stochastic choice is presented. Tje Rationalizability and Recoverability (Identification) problems are discussed. For the identification issue parametric examples are analyzed by means of techniques of mathematical tomography (Random transforms).

Stochastic choice analysis of tourism destinations

The analysis of tourist destination choice, defined by intra-country administrative units and by product types “coastal/inland and village/city”, permits the characterisation of tourist flow behaviour, which is fundamental for public planning and business management. In this study, we analyse the determinant factors of tourist destination choice, proposing various research hypotheses relative to the impact of destination attributes and the personal characteristics of tourists. The methodology applied estimates Nested and Random Coefficients Multinomial Logit Models, which allow control over possible correlations among different destinations. The empirical application is realised in Spain on a sample of 3,781 individuals and allows us to conclude that prices, distance to the destination and personal motivations are determinants in destination choice.

Stochastic Complementarity

Classical definitions of complementarity are based on cross price elasticities, and so they do not apply, for example, when goods are free. This context includes many relevant cases such as online newspapers and public attractions. We look for a complementarity notion that does not rely on price variation and that is: behavioural (based only on observable choice data); and model-free (valid whether the agent is rational or not). We uncover a conflict between properties that complementarity should intuitively possess. We discuss three ways out of the impossibility.

Bayesian inference and model comparison for random choice structures

We complete the development of a testing ground for axioms of discrete stochastic choice. Our contribution here is to develop new posterior simulation methods for Bayesian inference, suitable for a class of prior distributions introduced by McCausland and Marley (2013). These prior distributions are joint distributions over various choice distributions over choice sets of di fferent sizes. Since choice distributions over di fferent choice sets can be mutually dependent, previous methods relying on conjugate prior distributions do not apply. We demonstrate by analyzing data from a previously reported experiment and report evidence for and against various axioms.

Imperfect Attention and Menu Evaluation

We model the choice behaviour of an agent who suffers from imperfect attention. We define inattention axiomatically through preference over menus and endowed alternatives: an agent is inattentive if it is better to be endowed with an alternative a than to be allowed to pick a from a menu in which a is is the best alternative. This property and vNM rationality on the domain of menus and alternatives imply that the agent notices each alternative with a given menu-dependent probability (attention parameter) and maximises a menu independent utility function over the alternatives he notices. Preference for flexibility restricts the model to menu independent attention parameters as in Manzini and Mariotti [19]. Our theory explains anomalies (e.g. the attraction and compromise effect) that the Random Utility Model cannot accommodate.

Competing for Attention: Is the Showiest also the Best?

We introduce attention games. Alternatives ranked by quality (producers, politicians, sexual partners...) desire to be chosen and compete for the imperfect attention of a chooser by investing in their own salience. We prove that if alternatives can control the attention they get, then ”the showiest is the best”: the equilibrium ordering of salience (weakly) reproduces the quality ranking and the best alternative is the one that gets picked most often. This result also holds under more general conditions. However, if those conditions fail, then even the worst alternative can be picked most often.

The experimetrics of public goods: inferring motivations from contributions

In public goods experiments, stochastic choice, censoring and motivational heterogeneity give scope for disagreement over the extent of unselfishness, and whether it is reciprocal or altruistic. We show that these problems can be addressed econometrically, by estimating a finite mixture model to isolate types, incorporating double censoring and a tremble term. Most subjects act selfishly, but a substantial proportion are reciprocal with altruism playing only a marginal role. Isolating reciprocators enables a test of Sugden’s model of voluntary contributions. We estimate that reciprocators display a self-serving bias relative to the model.

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.

A test of a stochastic theory of choice,

Mode of access: Internet.

On the choice of an exchange rate regime: target zones revisited

From the classical gold standard up to the current ERM2 arrangement of the European Union, target zones have been a widely used exchange regime in contemporary history. This paper presents a benchmark model that rationalizes the choice of target zones over the rest of regimes: the fixed rate, the free float and the managed float. It is shown that the monetary authority may gain efficiency by reducing volatility of both the exchange rate and the interest rate at the same time. Furthermore, the model is consistent with some known stylized facts in the empirical literature that previous models were not able to produce, namely, the positive relation between the exchange rate and the interest rate differential, the degree of non-linearity of the function linking the exchage rate to fundamentals and the shape of the exchange rate stochastic distribution.

Adaptive search and information updating in sequential mate choice

Classical treatments of problems of sequential mate choice assume that the distribution of the quality of potential mates is known a priori. This assumption, made for analytical purposes, may seem unrealistic, opposing empirical data as well as evolutionary arguments. Using stochastic dynamic programming, we develop a model that includes the possibility for searching individuals to learn about the distribution and in particular to update mean and variance during the search. In a constant environment, a priori knowledge of the parameter values brings strong benefits in both time needed to make a decision and average value of mate obtained. Knowing the variance yields more benefits than knowing the mean, and benefits increase with variance. However, the costs of learning become progressively lower as more time is available for choice. When parameter values differ between demes and/or searching periods, a strategy relying on fixed a priori information might lead to erroneous decisions, which confers advantages on the learning strategy. However, time for choice plays an important role as well: if a decision must be made rapidly, a fixed strategy may do better even when the fixed image does not coincide with the local parameter values. These results help in delineating the ecological-behavior context in which learning strategies may spread.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Arbitrage-Based Pricing when Volatility is Stochastic.

The paper investigates the pricing of derivative securities with calendar-time maturities.

Stochastic Volatility.

This paper prepared for the Handbook of Statistics (Vol.14: Statistical Methods in Finance), surveys the subject of stochastic volatility. the following subjects are covered: volatility in financial markets (instantaneous volatility of asset returns, implied volatilities in option prices and related stylized facts), statistical modelling in discrete and continuous time and, finally, statistical inference (methods of moments, quasi-maximum likelihood, likelihood-based and bayesian methods and indirect inference).