The stability of the equilibrium outcomes in the admission games induced by stable matching rules

A stable matching rule is used as the outcome function for the Admission game where colleges behave straightforwardly and the students` strategies are given by their preferences over the colleges. We show that the college-optimal stable matching rule implements the set of stable matchings via the Nash equilibrium (NE) concept. For any other stable matching rule the strategic behavior of the students may lead to outcomes that are not stable under the true preferences. We then introduce uncertainty about the matching selected and prove that the natural solution concept is that of NE in the strong sense. A general result shows that the random stable matching rule, as well as any stable matching rule, implements the set of stable matchings via NE in the strong sense. Precise answers are given to the strategic questions raised.

A mathematical model for Escherichia coli debris size reduction during high pressure homogenisation based on grinding theory

Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.

Knowledge about a species' conservation status and funding for its preservation: Analysis

Using a species’ population to measure its conservation status, this note explores how an increase in knowledge about this status would change the public’s willingness to donate funds for its conservation. This is done on the basis that the relationship between the level of donations and a species’ conservation status satisfies stated general mathematical properties. This level of donation increases, on average, with greater knowledge of a species’ conservation status if it is endangered, but falls if it is secure. Game theory and other theory is used to show how exaggerating the degree of endangerment of a species can be counterproductive for conservation.

Estratégias de investimento em mercados liberalizados de energia elétrica

Dissertação para obtenção do grau de Mestre em Engenharia Electrotécnica Ramo Energia

Payoff-dependent balancedness and cores (revised version)

We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given.

Altruism, dispersal, and phenotype-matching kin recognition.

We investigate the coevolution between philopatry and altruism in island-model populations when kin recognition occurs through phenotype matching. In saturated environments, a good discrimination ability is a necessary prerequisite for the emergence of sociality. Discrimination decreases not only with the average phenotypic similarity between immigrants and residents (i.e., with environmental homogeneity and past gene flow) but also with the sampling variance of similarity distributions (a negative function of the number of traits sampled). Whether discrimination should rely on genetically or environmentally determined traits depends on the apportionment of phenotypic variance and, in particular, on the relative values of e (the among-group component of environmental variance) and r (the among-group component of genetic variance, which also measures relatedness among group members). If r exceeds e, highly heritable cues do better. Discrimination and altruism, however, remain low unless philopatry is enforced by ecological constraints. If e exceeds r, by contrast, nonheritable traits do better. High e values improve discrimination drastically and thus have the potential to drive sociality, even in the absence of ecological constraints. The emergence of sociality thus can be facilitated by enhancing e, which we argue is the main purpose of cue standardization within groups, as observed in many social insects, birds, and mammals, including humans.

The illusion of control, the structures of prizes and the demand for football pools in Spain

Using data for all the fixtures for the seasons from 1972-73 to 2002-03, we estimate a dynamic model of demand for football pools in Spain paying attention to whether their main economic explanatory variable is the effective price of a ticket or the jackpot. Additionally, we evaluate the importance of the composition of the list of games in terms of whether First Division matches are included or not. Results show that the jackpot model is preferred to the effective price model, having important implications in terms of how the structure of the game should be changed in order to increase demand.

A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

The genetical theory of social behaviour.

We survey the population genetic basis of social evolution, using a logically consistent set of arguments to cover a wide range of biological scenarios. We start by reconsidering Hamilton's (Hamilton 1964 J. Theoret. Biol. 7, 1-16 (doi:10.1016/0022-5193(64)90038-4)) results for selection on a social trait under the assumptions of additive gene action, weak selection and constant environment and demography. This yields a prediction for the direction of allele frequency change in terms of phenotypic costs and benefits and genealogical concepts of relatedness, which holds for any frequency of the trait in the population, and provides the foundation for further developments and extensions. We then allow for any type of gene interaction within and between individuals, strong selection and fluctuating environments and demography, which may depend on the evolving trait itself. We reach three conclusions pertaining to selection on social behaviours under broad conditions. (i) Selection can be understood by focusing on a one-generation change in mean allele frequency, a computation which underpins the utility of reproductive value weights; (ii) in large populations under the assumptions of additive gene action and weak selection, this change is of constant sign for any allele frequency and is predicted by a phenotypic selection gradient; (iii) under the assumptions of trait substitution sequences, such phenotypic selection gradients suffice to characterize long-term multi-dimensional stochastic evolution, with almost no knowledge about the genetic details underlying the coevolving traits. Having such simple results about the effect of selection regardless of population structure and type of social interactions can help to delineate the common features of distinct biological processes. Finally, we clarify some persistent divergences within social evolution theory, with respect to exactness, synergies, maximization, dynamic sufficiency and the role of genetic arguments.

Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

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.

On the impact of fundamentals, liquidity and coordination on market stability

We develop a coordination game to model interactions betweenfundamentals and liquidity during unstable periods in financial markets.We then propose a flexible econometric framework for estimationof the model and analysis of its quantitative implications. The specificempirical application is carry trades in the yen dollar market, includingthe turmoil of 1998. We find a generally very deep market, withlow information disparities amongst agents. We observe occasionallyepisodes of market fragility, or turmoil with up by the escalator, downby the elevator patterns in prices. The key role of strategic behaviorin the econometric model is also confirmed.

The effects of uncertainty avoidance on brand performance: Marketing creativity, product innovation and the brand duration

This paper investigates the link between brand performance and cultural primes in high-risk,innovation-based sectors. In theory section, we propose that the level of cultural uncertaintyavoidance embedded in a firm determine its marketing creativity by increasing the complexityand the broadness of a brand. It determines also the rate of firm product innovations.Marketing creativity and product innovation influence finally the firm marketingperformance. Empirically, we study trademarked promotion in the Software Security Industry(SSI). Our sample consists of 87 firms that are active in SSI from 11 countries in the period1993-2000. We use the data coming from SSI-related trademarks registered by these firms,ending up with 2,911 SSI-related trademarks and a panel of 18,213 observations. We estimatea two stage model in which first we predict the complexity and the broadness of a trademarkas a measure of marketing creativity and the rate of product innovations. Among severalcontrol variables, our variable of theoretical interest is the Hofstede s uncertainty avoidancecultural index. Then, we estimate the trademark duration with a hazard model using thepredicted complexity and broadness as well as the rate of product innovations, along with thesame control variables. Our evidence confirms that the cultural avoidance affects the durationof the trademarks through the firm marketing creativity and product innovation.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Emergence of Cooperation on Static and Dynamic Networks

Game theory is a branch of applied mathematics used to analyze situation where two or more agents are interacting. Originally it was developed as a model for conflicts and collaborations between rational and intelligent individuals. Now it finds applications in social sciences, eco- nomics, biology (particularly evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. Networks are an abstract representation of interactions, dependencies or relationships. Net- works are extensively used in all the fields mentioned above and in many more. Many useful informations about a system can be discovered by analyzing the current state of a network representation of such system. In this work we will apply some of the methods of game theory to populations of agents that are interconnected. A population is in fact represented by a network of players where one can only interact with another if there is a connection between them. In the first part of this work we will show that the structure of the underlying network has a strong influence on the strategies that the players will decide to adopt to maximize their utility. We will then introduce a supplementary degree of freedom by allowing the structure of the population to be modified along the simulations. This modification allows the players to modify the structure of their environment to optimize the utility that they can obtain.