Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
Two firms produce substitute goods with unknown quality. At each stage the firms set prices and a consumer with private information and unit demand buys from one of the fi rms. Both firms and consumers see the entire history of prices and purchases. Will such markets aggregate information? Will the superior rm necessarily prevail? We adapt the classical social learning model by introducing strategic dynamic pricing. We provide necessary and sufficient conditions for learning. In contrast to previous results, learning can occur when signals are bounded.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We study a discounted repeated inspection game with two agents and one principal. Both agents may profit by violating certain rules, while the principal can inspect on at most one agent in each period, inflicting a punishment on an agent who is caught violating the rules. The goal of the principal is to minimize the discounted number of violations, and he has a Stackelberg leader advantage. We characterize the principal's optimal inspection strategy.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We prove that every multiplayer quitting game admits a sunspot epsilon-equilibrium for every epsilon > 0, that is, an epsilon-equilibrium in an extended game in which the players observe a public signal at every stage. We also prove that if a certain matrix that is derived from the payoff s in the game is a Q-matrix in the sense of linear complementarity problems, then the game admits a Nash epsilon-equilibrium for every epsilon > 0.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
The talk will consider evolutionary games on graphs, which is a generalization of matrix games to graphs, using the solution concept of evolutionary stable strategies. In evolutionary games on graphs, there is a graph and a 2x2 matrix. Each node of the graph has a strategy of the matrix game - r or b - and initially all nodes are r. Then, a uniformly random node is made to follow b and the following is repeated until the graph is all one strategy again:1. Find the average payoff of each node when playing against their neighbors in the graph (depending on their current strategies).2.
Elath Hall, 2nd floor, Feldman Building, Edmond J. Safra Campus
We show that a simple decentralized dynamic, where players update theirbids proportionally to how useful the investments were, leads to growth ofthe economy in the long term (whenever growth is possible) but also createsunbounded inequality, i.e. very rich and very poor players emerge. Weanalyze several other phenomena, such as how the relation of a player withothers influences its development and the Gini index of the system.Joint work with Ruta Mehta and Noam Nisan.
Manchester Building (Hall 2), Hebrew University Jerusalem
The Crossing Lemma of Ajtai, Chvátal, Newborn, Szemerédi (1982) and Leighton (1983 )states that if a graph of n vertices and e>4n edges is drawn in the plane, then the number of crossings between its edges must be at least constant times e^3/n^2. This statement, which is asymptotically tight, has found many applications in combinatorial geometry and in additive combinatorics. However, most results that were obtained using the Crossing Lemma do not appear to be optimal, and there is a quest for improved versions of the lemma for graphs satisfying certain special properties.
Abstract:
Hamiltonian impact systems are dynamical systems in which there are two main mechanisms which dictate the system’s behavior - Hamilton’s equations which govern the motion inside the impact system domain, and the billiard reflection rule which governs the motion upon reaching the domain boundary. As the dynamics in impact systems are piecewise smooth by nature due to the
collisions with the boundary, many of the traditional tools used in the analysis of Hamiltonian
systems cannot be applied to impact systems in a straightforward manner. This talk will present a
Abstract: We will discuss connections between Gromov's work on isoperimetry of waists and Milman's work on the M-ellipsoid of a convex body. It is proven that any convex body K in an n-dimensional Euclidean space has a linear image K_1 of volume one satisfying the following waist inequality: Any continuous map f from K_1 to R^d has a fiber f^{-1}(t) whose (n-d)-dimensional volume is at least c^{n-d}, where c > 0 is a universal constant. Already in the case where f is linear, this constitutes a slight improvement over known results.
