Abstract: The Gromov non-squeezing theorem in symplectic geometry states that is not possible to embed symplectically a ball into a cylinder of smaller radius, although this can be done with a volume preserving embedding. Hence, the biggest radius of a ball that can be symplectically embedded into a symplectic manifold can be used as a way to measure the "symplectic size'' of the manifold. We call the square of this radius times the number \pi the Gromov width of the symplectic manifold. The Gromov width as a symplectic invariant is extended through the notion of "Symplectic Capacity".
Abstract: In this talk, I will introduce diffeological spaces and some (co)homology theories on these spaces. I will also talk on Thom-Mather spaces and their (co)homology in the diffeological context.
Topic: Weighted Utilitarianism, Edgeworth, and the Market (joint work with Rossella Argenziano)
Place: Elath Hall, 2nd floor, Feldman Building, Edmond Safra Campus
Time: Sunday, March 6, 2016 at 4:00 p.m.
Refreshments available at 3:30 p.m.
YOU ARE CORDIALLY INVITED
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We consider a Hotelling game where a finite number of retailers choose a location, given that their potential customers are distributed on a network. Retailers do not compete on price but only on location. We show that when the number of retailers is large enough, the game admits a pure Nash equilibrium and we construct it. We then compare the equilibrium cost bore by the consumers with the cost that could be achieved if the retailers followed the dictate of a benevolent planner. We look at this efficiency of equilibrium asymptotically in the number of retailers.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
This paper considers a sequential social learning game with a general utility function, state and action space. We establish that the value of private information converges to zero almost surely in every Perfect Bayesian equilibrium of any sequential social learning game.We use this result to show that totally unbounded signals are necessary and sufficient for asymptotic learning to hold in every sequential social learning game. Finally, we assume that the utility function of each agent is a private random draw and establish robustness of our results. (Joint with M. Mueller-Frank).
Read more about Game Theory & Math Economics: Itai Arieli (Technion) - "Social Learning and the Vanishing Value of Private Information"
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We show that feasible elimination procedures (Peleg, 1978) can be used to select k from m alternatives. An important advantage of this method is the core property: no coalition can guarantee an outcome that is preferred by all its members.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We present an axiomatic characterization of the Owen-Shapley spatial power index for the case where issues are elements of two-dimensional space.This characterization employs a version of the transfer condition, which enables us to unravel a spatial game into spatial games connected to unanimity games. The other axioms are spatial versions of anonymity and dummy, and two conditions concerned particularly with the spatial positions of the players. We show that these axioms are logically independent.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We Savage's theory to model large populations. Specifically, the notion of aggregative utility capture sensitivity to aggregate uncertainty in a large population. This utility characterizes planners who evaluate lotteries over population profiles according to their expected utility, and whose preferences over deterministic profiles satisfy the Savage postulates. Idiosyncratic risks are ranked separably across the population.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We consider the question of how to define sequential equilibria for multi-stage games with infinite type sets and infinite action sets. The definition should be a natural extension of Kreps and Wilson's 1982 definition for finite games, should yield intuitively appropriate solutions for various examples, and should exist for a broad class of economically interesting games
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
Classically, risk aversion is equated with concavity of the utility function. In this work we explore the conceptual foundations of this definition. In accordance with neo-classical economics, we seek a definition that is based solely on the decisions maker's preference order, independent of numerical values. We present two such definitions, based on simple, conceptually appealing interpretations of the notion of risk-aversion.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We study the subgame perfect equilibria of two-player stochastic games with perfect monitoring for a fixed discount factor. We develop a novel algorithm that, starting from larger correspondences, spirals inwards towards the state-dependent equilibrium payoff correspondence. At each iteration, starting from a vector of pivot points that are on the boundaries of each state's candidate equilibrium payoff set, we shave off part of each state's set of payoffs in a carefully chosen direction. The pivots are then advanced in this direction.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We study the classical problem of prediction with expert advice in the adversarial setting with a geometric stopping time. Cover (1965) gave the optimal algorithm that minimizes worst-case regret for the case of 2 experts. In this talk, I will describe the optimal algorithm, adversary and regret for the case of 3 experts. We will see that optimal algorithm for 2 and 3 experts is a probability matching algorithm (analogous to Thompson sampling) against a particular randomized adversary.
