A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Olympic Games as showcase

In the 1992 Barcelona Olympic Games, besides the country-versus-country typical showdown in the backdrop of Olympics, and the economic and political impulses for the host city, there was a third factor complicating the celebration: rivalry between the Catalan hosts and the Spanish state. By guiding the development of and eventual Olympic projection of national identity, Catalan and Spanish politicians hoped to create a resounding rallying point around which they could unite disparate individuals. The text is made up of: an introduction, five paragraphs on the different political perspective, conclusions, a commentary on the tallying of score and a note section with bibliographical references.

Dividends and weighted values in games with externalities

We consider cooperative environments with externalities (games in partition function form) and provide a recursive definition of dividends for each coalition and any partition of the players it belongs to. We show that with this definition and equal sharing of these dividends the averaged sum of dividends for each player, over all the coalitions that contain the player, coincides with the corresponding average value of the player. We then construct weighted Shapley values by departing from equal division of dividends and finally, for each such value, provide a bidding mechanism implementing it.

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.

The economy of the Beijing Olympic Games: An analysis of first impacts and prospects

This paper was presented at the International Sport Business Symposium, held by the Capital University of Economics and Business in Beijing, in 2008. The speakers, Ferran Brunet, as a professor at the Autonomous University of Barcelona and Zuo Xinwen, as a member of Beijing Development and Reform Commission, both set out to analyze changes in the economic and social development of the city which were undertaken with the aim to celebrate the 2008 Olympic Games. They discuss aspects as a transformation in the mode of economic growth, resources of the Organizing Committee, investments related to the Games, transport and communications, industries, the balance of urban and rural development, urban construction and management service and operations into a well-off society.

Free Mobility and Taste-Homogeneity of Jurisdiction Structures

We consider a population of agents distributed on the unit interval. Agents form jurisdictions in order to provide a public facility and share its costs equally. This creates an incentive to form large entities. Individuals also incur a transportation cost depending on their location and that of the facility which makes small jurisdictions advantageous. We consider a fairly general class of distributions of agents and generalize previous versions of this model by allowing for non-linear transportation costs. We show that, in general, jurisdictions are not necessarily homogeneous. However, they are if facilities are always intraterritory and transportation costs are superadditive. Superadditivity can be weakened to strictly increasing and strictly concave when agents are uniformly distributed. Keywords: Consecutiveness, stratification, local public goods, coalition formation, country formation. JEL Classification: C71 (Cooperative Games), D71 (Social Choice; Clubs; Committees; Associations), H73 (Interjurisdictional Differentials and Their Effects).

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

International Institutions as Solutions to Underlying Games of Cooperation

This Working Paper was presented at the international workshop "Game Theory in International Relations at 50", organized and coordinated by Professor Jacint Jordana and Dr. Yannis Karagiannis at the Institut Barcelona d'Estudis Internacionals on May 22, 2009. The day-long Workshop was inspired by the desire to honour the ground-breaking work of Professor Thomas Schelling in 1959-1960, and to understand where the discipline International Relations lies today vis-à-vis game theory.

Gains from switching and evolutionary stability in multi-player matrix games.

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Mean-payoff games and propositional proofs

"Vegeu el resum a l'inici del document del fitxer adjunt."

Prevalence and determinants of QT interval prolongation in medical inpatients.

BACKGROUND: QT interval prolongation carries an increased risk of torsade de pointes and death. AIM: We sought to determine the prevalence of QT prolongation in medical inpatients and to identify determinants of this condition. METHODS: We enrolled consecutive patients who were admitted to the internal medicine ward and who had an electrocardiogram performed within 24 h of admission. We collected information on baseline patient characteristics and the use of QT-prolonging drugs. Two blinded readers manually measured the QT intervals. QT intervals were corrected for heart rate using the traditional Bazett formula and the linear regression-based Framingham formula. We used logistic regression to identify patient characteristics and drugs that were independently associated with QTc prolongation. RESULTS: Of 537 inpatients, 22.3% had a prolonged QTc based on the Bazett formula. The adjusted odds for QTc prolongation based on the Bazett correction were significantly higher in patients who had liver disease (OR 2.9, 95% CI: 1.5-5.6), hypokalaemia (OR 3.3, 95% CI: 1.9-5.6) and who were taking ≥1 QT-prolonging drug at admission (OR 1.7, 95% CI: 1.1-2.6). Overall, 50.8% of patients with QTc prolongation received additional QT-prolonging drugs during hospitalisation. CONCLUSIONS: The prevalence of QTc prolongation was high among medical inpatients but depended on the method used to correct for heart rate. The use of QT-prolonging drugs, hypokalaemia and liver disease increased the risk of QTc prolongation. Many patients with QTc prolongation received additional QT-prolonging drugs during hospitalisation, further increasing the risk of torsade de pointes and death.

Birth records from Swiss married couples analyzed over of the past 35 years reveal an aging of first-time mothers by 5.1 years while the interpregnancy interval has shortened

RésuméIntroduction : Le travail de thèse est un article publié dans le journal « Fertility & Sterility » s'intitulant « Birth records from Swiss married couples analyzed over the past 35 years reveal an aging of first-time mothers by 5.1 years while the interpregnancy interval has shortened ».Méthodes : Les données concernant l'âge auquel les femmes mariées donnaient naissance ont été obtenues de l'Office fédéral de la statistique. Nous avons examiné la période allant de 1969 à 2006. Cet intervalle de temps choisi nous a permis de prendre en considération un total de 2'716'370 naissances. L'âge moyen des parturientes à la naissance de leur 1er, 2ème et 3ème enfant a été calculé pour chaque année à l'aide du logiciel Excel. Grâce à ces données on a pu obtenir les intervalles inter-gestationnels théoriques entre le 1er et 2ème enfant, ainsi qu'entre le 2ème et 3ème enfant.Résultats : Nous pouvons constater que l'intervalle inter-gestationnel théorique entre la première et la deuxième grossesse était de 23.2 mois en 1969 et passait à 13.0 mois en 2006. L'intervalle compris entre la deuxième et la troisième grossesse passait de 22.4 mois en 1969 à 7.9 mois en 2006. Notre analyse suggère donc que c'est le facteur social qui exerce un effet plus important que le facteur biologique sur les intervalles inter-gestationnels, car ces intervalles diminuaient malgré l'augmentation de l'âge des mères à la naissance.