Computer Tips and Tricks Newsletter, March, 2007

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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.

The Microbe browser for comparative genomics.

The Microbe browser is a web server providing comparative microbial genomics data. It offers comprehensive, integrated data from GenBank, RefSeq, UniProt, InterPro, Gene Ontology and the Orthologs Matrix Project (OMA) database, displayed along with gene predictions from five software packages. The Microbe browser is daily updated from the source databases and includes all completely sequenced bacterial and archaeal genomes. The data are displayed in an easy-to-use, interactive website based on Ensembl software. The Microbe browser is available at http://microbe.vital-it.ch/. Programmatic access is available through the OMA application programming interface (API) at http://microbe.vital-it.ch/api.

On the throughput-WIP trade-off in queueing systems, diminishing returns and the threshold property: A linear programming approach

We present a new unifying framework for investigating throughput-WIP(Work-in-Process) optimal control problems in queueing systems,based on reformulating them as linear programming (LP) problems withspecial structure: We show that if a throughput-WIP performance pairin a stochastic system satisfies the Threshold Property we introducein this paper, then we can reformulate the problem of optimizing alinear objective of throughput-WIP performance as a (semi-infinite)LP problem over a polygon with special structure (a thresholdpolygon). The strong structural properties of such polygones explainthe optimality of threshold policies for optimizing linearperformance objectives: their vertices correspond to the performancepairs of threshold policies. We analyze in this framework theversatile input-output queueing intensity control model introduced byChen and Yao (1990), obtaining a variety of new results, including (a)an exact reformulation of the control problem as an LP problem over athreshold polygon; (b) an analytical characterization of the Min WIPfunction (giving the minimum WIP level required to attain a targetthroughput level); (c) an LP Value Decomposition Theorem that relatesthe objective value under an arbitrary policy with that of a giventhreshold policy (thus revealing the LP interpretation of Chen andYao's optimality conditions); (d) diminishing returns and invarianceproperties of throughput-WIP performance, which underlie thresholdoptimality; (e) a unified treatment of the time-discounted andtime-average cases.

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.

Implementing TURF analysis through binary linear programming

This paper introduces the approach of using Total Unduplicated Reach and Frequency analysis (TURF) to design a product line through a binary linear programming model. This improves the efficiency of the search for the solution to the problem compared to the algorithms that have been used to date. The results obtained through our exact algorithm are presented, and this method shows to be extremely efficient both in obtaining optimal solutions and in computing time for very large instances of the problem at hand. Furthermore, the proposed technique enables the model to be improved in order to overcome the main drawbacks presented by TURF analysis in practice.

Impact of a board-game approach on current smokers: a randomized controlled trial.

ABSTRACT: BACKGROUND: The main objective of our study was to assess the impact of a board game on smoking status and smoking-related variables in current smokers. To accomplish this objective, we conducted a randomized controlled trial comparing the game group with a psychoeducation group and a waiting-list control group. METHODS: The following measures were performed at participant inclusion, as well as after a 2-week and a 3-month follow-up period: "Attitudes Towards Smoking Scale" (ATS-18), "Smoking Self-Efficacy Questionnaire" (SEQ-12), "Attitudes Towards Nicotine Replacement Therapy" scale (ANRT-12), number of cigarettes smoked per day, stages of change, quit attempts, and smoking status. Furthermore, participants were assessed for concurrent psychiatric disorders and for the severity of nicotine dependence with the Fagerström Test for Nicotine Dependence (FTND). RESULTS: A time × group effect was observed for subscales of the ANRT-12, ATS-18 and SEQ-12, as well as for the number of cigarettes smoked per day. At three months follow-up, compared to the participants allocated to the waiting list group, those on Pick-Klop group were less likely to remain smoker.Outcomes at 3 months were not predicted by gender, age, FTND, stage of change, or psychiatric disorders at inclusion. CONCLUSIONS: The board game seems to be a good option for smokers. The game led to improvements in variables known to predict quitting in smokers. Furthermore, it increased smoking-cessation rates at 3-months follow-up. The game is also an interesting alternative for smokers in the precontemplation stage.

Restless bandits, linear programming relaxations and a primal-dual index heuristic

We develop a mathematical programming approach for the classicalPSPACE - hard restless bandit problem in stochastic optimization.We introduce a hierarchy of n (where n is the number of bandits)increasingly stronger linear programming relaxations, the lastof which is exact and corresponds to the (exponential size)formulation of the problem as a Markov decision chain, while theother relaxations provide bounds and are efficiently computed. Wealso propose a priority-index heuristic scheduling policy fromthe solution to the first-order relaxation, where the indices aredefined in terms of optimal dual variables. In this way wepropose a policy and a suboptimality guarantee. We report resultsof computational experiments that suggest that the proposedheuristic policy is nearly optimal. Moreover, the second-orderrelaxation is found to provide strong bounds on the optimalvalue.

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.

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.

Synapses on motoneuron dendrites in the brachial section of the frog spinal cord: a computer-aided electron microscopic study of cobalt-filled cells.

Cobalt-labelled motoneuron dendrites of the frog spinal cord at the level of the second spinal nerve were photographed in the electron microscope from long series of ultrathin sections. Three-dimensional computer reconstructions of 120 dendrite segments were analysed. The samples were taken from two locations: proximal to cell body and distal, as defined in a transverse plane of the spinal cord. The dendrites showed highly irregular outlines with many 1-2 microns-long 'thorns' (on average 8.5 thorns per 100 microns 2 of dendritic area). Taken together, the reconstructed dendrite segments from the proximal sites had a total length of about 250 microns; those from the distal locations, 180 microns. On all segments together there were 699 synapses. Nine percent of the synapses were on thorns, and many more close to their base on the dendritic shaft. The synapses were classified in four groups. One third of the synapses were asymmetric with spherical vesicles; one half were symmetric with spherical vesicles; and one tenth were symmetric with flattened vesicles. A fourth, small class of asymmetric synapses had dense-core vesicles. The area of the active zones was large for the asymmetric synapses (median value 0.20 microns 2), and small for the symmetric ones (median value 0.10 microns 2), and the difference was significant. On average, the areas of the active zones of the synapses on thin dendrites were larger than those of synapses on large calibre dendrites. About every 4 microns 2 of dendritic area received one contact. There was a significant difference between the areas of the active zones of the synapses at the two locations. Moreover, the number per unit dendritic length was correlated with dendrite calibre. On average, the active zones covered more than 4% of the dendritic area; this value for thin dendrites was about twice as large as that of large calibre dendrites. We suggest that the larger active zones and the larger synaptic coverage of the thin dendrites compensate for the longer electrotonic distance of these synapses from the soma.