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Stochastische Analysis und Stochastik der Finanzmärkte
HU Berlin, TU Berlin, DFG-FS Matheon
Marco Tolotti (Universita Ca' Foscari Venezia)
Probabilistic Models for Interacting Agents Facing Binary Decisions
Programm / Abstract:
In this talk I present a class of stochastic models useful to represent the dynamics of a system of many interacting agents facing binary decisions. At each time, agents update their choice in order to maximize their payoff, depending on their action, on the state of the system and on a random noise. In particular, I put attention on two different mechanisms for the updating: a “sequential updating” scheme and a “parallel updating” one. The former is more similar in spirit to classical statistical-mechanics, whereas the latter mimics a non-cooperative game played by the agents. I obtain stochastic dynamics for a small number of sufficient statistics that, at the aggregate level, describe the system. In the limit of infinitely many agents, a law of large numbers is derived. Depending on the chosen scheme, different limiting behaviors appear: the attractors can be stable fixed points or periodic orbits. Moreover, the limit dynamics may exhibit the existence of a phase, where a locally stable fixed point coexists with a locally stable cycle. The talk is based on joint works with Emilio Barucci, Paolo Dai Pra and Elena Sartori.
Zeit:
am Donnerstag den 23. Mai 2013 um 17:00
Ort:
Technische Universität Berlin, Institut für Mathematik
Strasse des 17. Juni 136
10623 Berlin
MA 041 Erdgeschoss
eingetragen von Jean Downes(downes@math.tu-berlin.de, )