Bringing game theory to hypothesis testing: Establishing finite sample bounds on inference

Small sample properties are of fundamental interest when only limited data is avail-able. Exact inference is limited by constraints imposed by speci.c nonrandomizedtests and of course also by lack of more data. These e¤ects can be separated as we propose to evaluate a test by comparing its type II error to the minimal type II error among all tests for the given sample. Game theory is used to establish this minimal type II error, the associated randomized test is characterized as part of a Nash equilibrium of a .ctitious game against nature.We use this method to investigate sequential tests for the di¤erence between twomeans when outcomes are constrained to belong to a given bounded set. Tests ofinequality and of noninferiority are included. We .nd that inference in terms oftype II error based on a balanced sample cannot be improved by sequential sampling or even by observing counter factual evidence providing there is a reasonable gap between the hypotheses.

On equilibria in duopolies with finite strategy spaces

We will call a game a reachable (pure strategy) equilibria game if startingfrom any strategy by any player, by a sequence of best-response moves weare able to reach a (pure strategy) equilibrium. We give a characterizationof all finite strategy space duopolies with reachable equilibria. Wedescribe some applications of the sufficient conditions of the characterization.

Finite horizon bargaining and the consistent field

This paper explores the relationships between noncooperative bargaining games and the consistent value for non-transferable utility (NTU) cooperative games. A dynamic approach to the consistent value for NTU games is introduced: the consistent vector field. The main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. The solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games. We show that for transferable utility, hyperplane and pure bargaining games, the dynamics of the consistent fields converge globally to the unique consistent value. However, in the general NTU case, the dynamics of the consistent field can be complex. An example is constructed where the consistent field has cyclic solutions; moreover, the finite horizon subgame perfect equilibria do not approach the consistent value.

How wide is the gap? An investigation of gender wage differences using quantile regression

In this paper we examine the determinants of wages and decompose theobserved differences across genders into the "explained by differentcharacteristics" and "explained by different returns components"using a sample of Spanish workers. Apart from the conditionalexpectation of wages, we estimate the conditional quantile functionsfor men and women and find that both the absolute wage gap and thepart attributed to different returns at each of the quantiles, farfrom being well represented by their counterparts at the mean, aregreater as we move up in the wage range.

Why do differences in the degree of fiscal decentralization endure?

A notable difference between the U.S. and many countries in Europe is in the degree of fiscal decentralization. Regional (and local) governments in the U.S. have significant autonomy in setting their own taxes and determining how to spend their revenues. This is not true of their counterparts in Spain, France, the United Kingdom, Czech Republic and many other European countries. In recent years, many countries formerly subject to dictatorshipsor communism have been considering decentralizing fiscal responsibility to sub-national governments as part of the process of democratization (see Bird and Ebel, forthcoming). Yet, much of Europe remains immune to adopting effective decentralization in which sub-national units have true taxing authority.

Causal assessment in finite extensive-form games

Two finite extensive-form games are empirically equivalent when theempirical distribution on action profiles generated by every behaviorstrategy in one can also be generated by an appropriately chosen behaviorstrategy in the other. This paper provides a characterization ofempirical equivalence. The central idea is to relate a game's informationstructure to the conditional independencies in the empirical distributionsit generates. We present a new analytical device, the influence opportunitydiagram of a game, describe how such a diagram is constructed for a givenextensive-form game, and demonstrate that it provides a complete summaryof the information needed to test empirical equivalence between two games.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Regional differences in socio-economic health inequalities in Spain

This paper reports an analysis of income related health inequalities at the AutonomousCommunity level in Spain using the self assessed health measure in the 2001 edition of theEncuesta Nacional de Salud. We use recently developed methods in order to cardinalise andmodel self assessed health within a regression framework, decompose the sources ofinequality and explain the observed differences across regions. We find that the regions with the highest levels of mean health tend to enjoy the lowest degrees of income related health inequality and vice-versa. The main feature characterizing regions where income related health inequality is low is the absence of a positive gradient between income and health. In turn, the regions where income related health inequality is greater are characterized by a strong and significant positive gradient between health and income. These results suggest that policies aimed at eliminating the gradient between health and income can potentially lead to greate r reductions in socio-economic health inequalities than policies aimed at redistributing income.

Cultural differences on seeking information: an eye tracking study

The main goal of this research is to investigate how people with different cultural background differ in their interaction style and visual behavior on search engine results pages (SERP), more specifically between groups from the Middle Eastern region vs. Western Europe. We conducted a controlled eye-tracking experiment to explore and evaluate the visual behavior of Arabs and Spaniardusers when scanning through the first page of the search results in Google. Big differences can be observed in the 4 aspects studied: U.A.E. participants stayed on the SERPs for longer, they read more results and they read each snippet in a more complete way than Spaniards. In Spain, people tended to scan the SERP, reading less text on each snippet, and choose a result among the first top rankedones without hardly seeing those in bottom positions.

Differences in diet between the two largest breeding colonies of Audouin's gulls: the effects of fishery activities

We analysed and compared the diet of Audouin´s gulls Larus audouinii between their two largest breeding sites in the world: the Ebro Delta and the Chafarinas Islands (western Mediterranean). These two localities showed marked differences in the features of the commercial fishing fleet: in the Ebro Delta area a large fishing fleet produced large amounts of discards, while in the Chafarinas the fleet discarded smaller amounts of fish and marine invertebrates, due to the smaller number of vessels. It is also likely that the percentage of discards from total catches is also lower around the Chafarinas than at the Ebro Delta. We distinguished two types of fishing to compare diet compositions: diurnal (only trawling activity) and diurnal and nocturnal (trawling and purse-seine activity, respectively). We also differentiated regurgitates from young nestlings (up to 20 days old) and from older nestlings or adult birds. At the two localities, fish was the main food of Audouin´s gulls, with epipelagic prey (mainly clupeoids) being more important when both diurnal and nocturnal fisheries were operating. This confirms that epipelagic prey either caught actively by the gulls or linked to fisheries was particularly important in the feeding habits of Audouin´s gulls. Nevertheless, differences between the two colonies appear mainly when only trawlers operated: while at the Ebro Delta gulls showed higher consumption of benthic-mesopelagic prey (probably linked to a higher trawler discard availability), gulls from the Chafarinas Islands consumed higher biomass of epipelagic prey probably caught actively at night. When both fleets operated around the two colonies, the average biomass of prey in a regurgitate of younger chicks was significantly higher at the Ebro Delta than at Chafarinas, and the opposite trend was recorded for older nestlings and adults. Niche width was broader in Chafarinas than in the Ebro Delta for both age classes and for any fishing fleet schedule, suggesting again that the exploitation of discards was higher at the Ebro Delta than at the Chafarinas, where gulls showed a more varied diet. Despite the fact that availability of discards was probably higher at the Ebro Delta than at Chafarinas, the per capita availability was not so different at both localities due to the increasing seabird community population at the Ebro Delta, which ca. doubled that at Chafarinas in the last decade.

Childhood adversity and psychosis: examinig whether the association is due to genetic confounding using a monozygotic twin differences approach

Purpose: To test whether the association between childhood adversity and positive and negative psychotic experiences is due to genetic confounding. Method: Childhood adversity and psychotic experiences were assessed in a sample of 226 twins from the general population. A monozygotic (MZ) twin differences approach was used to assess possible genetic confounding. Results: In the whole sample, childhood adversity was significantly associated with positive (β =.45; SE=.16; p=.008) and negative psychotic experiences (β=.77; SE=.18; p<.01). Within-pair MZ twin differences in exposure to childhood adversity were significantly associated with differences in positive (β =.71; SE=.29; p=.016) and negative psychotic experiences (β =.98; SE=.38; p=.014) in a subsample of 86 MZ twin pairs. Conclusions: Individuals exposed to childhood adversity are more likely to report psychotic experiences. Furthermore, our findings indicate that unique environmental effects of childhood adversity contribute to the development of psychotic experiences.

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Continuum bound states as surface states of a finite periodic system

We discuss the relation between continuum bound states (CBSs) localized on a defect, and surface states of a finite periodic system. We model an experiment of Capasso et al. [F. Capasso, C. Sirtori, J. Faist, D. L. Sivco, S-N. G. Chu, and A. Y. Cho, Nature (London) 358, 565 (1992)] using the transfer-matrix method. We compute the rate for intrasubband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed.

Generic finite-size enhancement of pairing in mesoscopic Fermi systems

The finite-size-dependent enhancement of pairing in mesoscopic Fermi systems is studied under the assumption that the BCS approach is valid and that the two-body force is size independent. Different systems are investigated such as superconducting metallic grains and films as well as atomic nuclei. It is shown that the finite size enhancement of pairing in these systems is in part due to the presence of a surface which accounts quite well for the data of nuclei and explains a good fraction of the enhancement in Al grains.