13:30 - 14:15 Stefan Schrott: Filtered Processes
Abstract: Researchers from different areas have independently defined extensions of the usual weak topology between laws of stochastic processes. This includes Aldous' extended weak convergence, Hellwig's information topology and convergence in adapted distribution in the sense of Hoover-Keisler. We show that on the set of continuous processes with canonical filtration these topologies coincide and are metrized by a suitable \emph{adapted Wasserstein distance} $\mathcal{AW}$. Moreover, we show that the resulting topology is the weakest topology that guarantees continuity of optimal stopping. While the set of processes with canonical filtration is not complete, we establish that its completion consists precisely in the space ${\rm FP}$ of stochastic processes with a general filtration. We also observe that $({\rm FP}, \mathcal{AW})$ exhibits several desirable properties. Specifically, it is Polish, martingales form a closed subset and approximation results like Donsker's theorem extend to $\mathcal{AW}$.
Based on joint work with D. Bartl, M. Beiglböck, G. Pammer, X. Zhang.
14:15 - 15:00 Daniel Toneian: Statistical Agreeing
Abstract: Aumann's first formulation of the notion of common knowledge in a set-theoretical framework led to the development of an active field of study. This talk introduces a version of knowledge and common knowledge which naturally extends the original definitions and allows for and quantifies uncertainty in knowledge. Some of the most important theorems on common knowledge are reformulated for this new framework and implications and applications are discussed
15:00 - 15:30 break
15:30 - 16:15 Christina Pawlowitsch: Belief-based refinements, index of equilibria and invariance in signaling games
Abstract: Signaling games typically have multiple Bayes-Nash sequential equilibria. For the game theorist this raises the question of how to refine the equilibrium notion in order to select among equilibria. In this talk, I confront three approaches to equilibrium refinement in signaling games: 1) placing restrictions on beliefs about states of Nature at nodes of the game tree that are not reached along the path played in the equilibrium under study; 2) Index Theory (topological properties of the associated fixed point); 3) "Invariance" - the requirement that an equilibrium should induce a sequential Bayes-Nash equilibrium in every game tree that is mapped to the same game in normal form (=game matrix).
Based partly on joint work with J. Hofbauer.
16:15 - 17:00 Michael Greinecker: Sequential Equilibria in a Class of Infinite Extensive Form Games
Abstract: Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form but is only defined for finite extensive-form games and is inapplicable whenever a player can choose among a continuum of actions. We define a class of infinite extensive form games in which information behaves continuously as a function of past actions and define a natural notion of sequential equilibrium for this class. Sequential equilibria exist in this class and refine Nash equilibria. In standard finite extensive-form games, our definition selects the same strategy profiles as the traditional notion of a sequential equilibrium.
Based on joint work with M. Meier and K. Podczeck.