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.

An experimental study of adaptive behavior in an oligopolistic market game

We consider an oligopolistic market game, in which the players are competing firm in the same market of a homogeneous consumption good. The consumer side is represented by a fixed demand function. The firms decide how much to produce of a perishable consumption good, and they decide upon a number of information signals to be sent into the population in order to attract customers. Due to the minimal information provided, the players do not have a well--specified model of their environment. Our main objective is to characterize the adaptive behavior of the players in such a situation.

Setting the rules of the game: The choice of electoral systems in advanced democracies

The origins of electoral systems have received scant attention in the literature. Looking at the history of electoral rules in the advanced world in the last century, this paper shows that the existing wide variation in electoral rules across nations can be traced to the strategic decisions that the current ruling parties, anticipating the coordinating consequences of different electoral regimes, make to maximize their representation according to the following conditions. On the one hand, as long as the electoral arena does not change substantially and the current electoral regime serves the ruling parties well, the latter have no incentives to modify the electoral regime. On the other hand, as soon as the electoral arena changes (due to the entry of new voters or a change in their preferences), the ruling parties will entertain changing the electoral system, depending on two main conditions: the emergence of new parties and the coordinating capacities of the old ruling parties. Accordingly, if the new parties are strong, the old parties shift from plurality/majority rules to proportional representation (PR) only if the latter are locked into a 'non-Duvergerian' equilibrium; i.e. if no old party enjoys a dominant position (the case of most small European states)--conversely, they do not if a Duvergerian equilibrium exists (the case of Great Britain). Similarly, whenever the new entrants are weak, a non-PR system is maintained, regardless of the structure of the old party system (the case of the USA). The paper discusses as well the role of trade and ethnic and religious heterogeneity in the adoption of PR rules.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.

The credit ratings game

The collapse of so many AAA-rated structured finance products in 2007-2008has brought renewed attention to the causes of ratings failures and the conflicts of interestin the Credit Ratings Industry. We provide a model of competition among Credit RatingsAgencies (CRAs) in which there are three possible sources of conflicts: 1) the CRA conflictof interest of understating credit risk to attract more business; 2) the ability of issuersto purchase only the most favorable ratings; and 3) the trusting nature of some investorclienteles who may take ratings at face value. We show that when combined, these give riseto three fundamental equilibrium distortions. First, competition among CRAs can reducemarket efficiency, as competition facilitates ratings shopping by issuers. Second, CRAs aremore prone to inflate ratings in boom times, when there are more trusting investors, andwhen the risks of failure which could damage CRA reputation are lower. Third, the industrypractice of tranching of structured products distorts market efficiency as its role is to deceivetrusting investors. We argue that regulatory intervention requiring: i) upfront paymentsfor rating services (before CRAs propose a rating to the issuer), ii) mandatory disclosure ofany rating produced by CRAs, and iii) oversight of ratings methodology can substantiallymitigate ratings inflation and promote efficiency.

Social value orientation as a moral intuition: Decision-making in the dictator game

We studied the decision making process in the Dictator Game and showed that decisions are the result of a two-step process. In a first step, decision makers generate an automatic, intuitive proposal. Given sufficient motivation and cognitive resources, they adjust this in a second, more deliberated phase. In line with the social intuitionist model, we show that one s Social Value Orientation determines intuitive choice tendencies in the first step, and that this effect is mediated by the dictator s perceived interpersonal closeness with the receiver. Self-interested concerns subsequently leadto a reduction of donation size in step 2. Finally, we show that increasing interpersonal closeness can promote pro-social decision-making.

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

The maximun and the addition of assigment games

[cat] En el context dels mercats a dues bandes, considerem, en primer lloc, que els jugadors poden escollir on dur a terme les seves transaccions. Mostrem que el joc corresponent a aquesta situació, que es representa pel màxim d’un conjunt finit de jocs d’assignació, pot ser un joc no equilibrat. Aleshores proporcionem condicions per a l’equilibri del joc i, per aquest cas, analitzem algunes propietats del core del joc. En segon lloc, considerem que els jugadors poden fer transaccions en diversos mercats simultàniament i, llavors, sumar els guanys obtinguts. El joc corresponent, representat per la suma d’un conjunt finit de jocs d’assignació, és equilibrat. A més a més, sota certes condicions, la suma dels cores dels dos jocs d’assignació coincideix amb el core del joc suma.

Complements and substitutes in multilateral assignment markets

[cat] En aquest treball provo que, en mercats d’assignació amb més de dos costats, agents de diferents sectors poden no ser complementaris mentre que agents del mateix sector poden no ser substituts. Shapley (1962) va provar que això mai pot succeïr quan el mercat d’assignació només té dos costats. No obstant, demostro que existeixen condicions suficients que garanteixen la substitutabilitat i la complementarietat entre agents en aquests tipus de mercats. A més, provo que, quan els béns al mercat son homogenis, el resultat de Shapley (1962) es manté.

A note on the coincidence between Stackelberg and Nash equilibria in a differential game between government and firms

[cat] A Navas i Marín Solano es va demostrar la coincidència entre els equilibris de Nash i de Stackelberg per a una versi´o modificada del joc diferencial proposat por Lancaster (1973). Amb l’objectiu d’obtenir una solució interior, es van imposar restriccions importants sobre el valors dels paràmetres del model. En aquest treball estenem aquest resultat, en el límit en que la taxa de descompte és igual a zero, eliminant les restriccions i considerant totes les solucions possibles.

The maximun and the addition of assigment games

[cat] En el context dels mercats a dues bandes, considerem, en primer lloc, que els jugadors poden escollir on dur a terme les seves transaccions. Mostrem que el joc corresponent a aquesta situació, que es representa pel màxim d’un conjunt finit de jocs d’assignació, pot ser un joc no equilibrat. Aleshores proporcionem condicions per a l’equilibri del joc i, per aquest cas, analitzem algunes propietats del core del joc. En segon lloc, considerem que els jugadors poden fer transaccions en diversos mercats simultàniament i, llavors, sumar els guanys obtinguts. El joc corresponent, representat per la suma d’un conjunt finit de jocs d’assignació, és equilibrat. A més a més, sota certes condicions, la suma dels cores dels dos jocs d’assignació coincideix amb el core del joc suma.

Complements and substitutes in multilateral assignment markets

[cat] En aquest treball provo que, en mercats d’assignació amb més de dos costats, agents de diferents sectors poden no ser complementaris mentre que agents del mateix sector poden no ser substituts. Shapley (1962) va provar que això mai pot succeïr quan el mercat d’assignació només té dos costats. No obstant, demostro que existeixen condicions suficients que garanteixen la substitutabilitat i la complementarietat entre agents en aquests tipus de mercats. A més, provo que, quan els béns al mercat son homogenis, el resultat de Shapley (1962) es manté.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

Observational methodology in football: Development of an instrument to study the offensiva game in football.

The following paper introduces a new approach to the analysis of offensive game in football. Therefore, the main aim of this study was to create an instrument for collecting information for the analysis of offensive action and interactions game. The observation instrument that was used to accomplish the main objective of this work consists of a combination of format fields (FC) and systems of categories (SC). This methodology is a particular strategy of the scientific method that has as an objective to analyse the perceptible behaviour that occurs in habitual contexts, allowing them to be formally recorded and quantified and using an ad hoc instrument in order to obtain a behaviour systematic registration that, since they have been transformed in quantitative data with the necessary reliability and validity determined level, will allow analysis of the relations between these behaviours. The codifications undertaken to date in various games of football have shown that it serves the purposes for which it was developed, allowing more research into the offensive game methods in football.