Imperfect-Recall Abstractions with Bounds in Games

Imperfect-recall abstraction has emerged as the leading paradigm for practical large-scale equilibrium computation in incomplete-information games. However, imperfect-recall abstractions are poorly understood, and only weak algorithm-specific guarantees on solution quality are known. In this paper, we show the first general, algorithm-agnostic, solution quality guarantees for Nash equilibria and approximate self-trembling equilibria computed in imperfect-recall abstractions, when implemented in the original (perfect-recall) game. Our results are for a class of games that generalizes the only previously known class of imperfect-recall abstractions where any results had been obtained. Further, our analysis is tighter in two ways, each of which can lead to an exponential reduction in the solution quality error bound. We then show that for extensive-form games that satisfy certain properties, the problem of computing a bound-minimizing abstraction for a single level of the game reduces to a clustering problem, where the increase in our bound is the distance function. This reduction leads to the first imperfect-recall abstraction algorithm with solution quality bounds. We proceed to show a divide in the class of abstraction problems. If payoffs are at the same scale at all information sets considered for abstraction, the input forms a metric space. Conversely, if this condition is not satisfied, we show that the input does not form a metric space. Finally, we use these results to experimentally investigate the quality of our bound for single-level abstraction

On a model of forced axisymmetric flows

In this work, we consider a model of forced axisymmetric flows which is derived from the inviscid Boussinesq equations. What makes these equations unusual is the boundary conditions they are expected to satisfy and the fact that the boundary is part of the unknown. We show that these flows give rise to an unusual Monge-Ampere equations for which we prove the existence and the uniqueness of a variational solution. We take advantage of these Monge-Ampere equations and construct a solution to the model

Atto primo. il bundesverfassungsgericht rinvia alla corte di giustizia su omt e poteri della bce. un’occasione per il futuro dell’unione europea

L’articolo si sofferma sulla recente ordinanza con cui il Bundesverfassungsgericht ha per la prima volta sollevato un rinvio pregiudiziale alla Corte di giustizia dell’Unione europea. Poiché le questioni vertono sulla legittimità del piano OMT (Outright Monetary Transactions) lanciato dalla Bce, la decisione del BVerfG potrebbe segnare uno snodo importante sia per il “cammino europeo” di Karlsruhe sia per le prospettive di sviluppo del processo di integrazione europea.The article focuses on the recent order by which, for the first time, the German Federal Constitutional Court has raised a preliminary ruling to the Court of Justice of the European Union. Since the questions concern the lawfulness of the OMT programme (Outright Monetary Transactions) launched by the ECB, the decision of the BVerfG could be an important turning point for both the “European path” of Karlsruhe and for future developments of the European integration process

Swampland geometry and the gauge couplings

The purpose of this paper is two-fold. First we review in detail the geometric aspects of the swampland program for supersymmetric 4d effective theories using a new and unifying language we dub "domestic geometry", the generalization of special Kahler geometry which does not require the underlying manifold to be Kahler or have a complex structure. All 4d SUGRAs are described by domestic geometry. As special Kahler geometries, domestic geometries carry formal brane amplitudes: when the domestic geometry describes the supersymmetric low-energy limit of a consistent quantum theory of gravity, its formal brane amplitudes have the right properties to be actual branes. The main datum of the domestic geometry of a 4d SUGRA is its gauge coupling, seen as a map from a manifold which satisfies the geometric Ooguri-Vafa conjectures to the Siegel variety; to understand the properties of the quantum-consistent gauge couplings we discuss several novel aspects of such "Ooguri-Vafa" manifolds, including their Liouville properties. Our second goal is to present some novel speculation on the extension of the swampland program to non-supersymmetric effective theories of gravity. The idea is that the domestic geometric description of the quantum-consistent effective theories extends, possibly with some qualifications, also to the non-supersymmetric case

To cruise the Med: Banksy fra turismo e migrazione

none1noQuesto articolo esplora l’opera di Banksy mettendo in luce la tematizzazione costante del rapporto fra crisi migratoria e turismo. Spesso, infatti, nei lavori del più importante street artist, i due temi sono trattati non separatamente, ma come se fossero figure bistabili e reversibili l'una nell'altra, specchio ironico dei paradossi del mondo globalizzato. Dimostreremo che c’è un’escalation, in questo senso, che culmina nella Louise Michel, l'acquisto di uno yacht privato convertito in nave umanitaria. L’operazione di Banksy vale non solo come domanda aperta e provocazione, oggi, sulla funzione sociale dell’arte, ma come indicazione della possibilità, salvifica, di un’uscita dalla disuguaglianza fra chi ha e chi non ha, per migrare tutti verso suoli abitabili in comune.opentiziana miglioreMigliore, TIZIANA MARI