Dear Colleagues,

We would like to invite you to the following SPASS https://sites.google.com/unipi.it/spass seminars, jointly organized by UniPi, SNS, UniFi and UniSi:

- *N-player Games and Mean Field Games of Moderate Interaction* Giulia Livieri (Scuola Normale Superiore di Pisa)

- *Scaling Limits of Multi-Type Markov Branching Trees* Robin Stephenson (University of Sheffield)

The seminars will take place in person on *TUE, 08.11.2022 at 14:00* (the second talk starting at 15:00) in Sala Seminari, Dipartimento di Matematica, University of Pisa and streamed online here https://meet.google.com/gji-phwo-vbg.

The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass

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Abstracts:

*N-player Games and Mean Field Games of Moderate Interaction* *We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player games. This proof depends upon the derivation of a law of large numbers for the empirical processes in the limit as the number of players tends to infinity. Because it is of independent interest, we prove this result in full detail. We characterize the solutions of the limiting game via a verification argument.*

*Scaling Limits of Multi-Type Markov Branching Trees* *Consider a population where individuals have two characteristics: a size, which is a positive integer, and a type, which is a member of a finite set. This population reproduces in a Galton-Watson fashion, with one additional condition: given that an individual has size n, the sum of the sizes of its children is less than or equal to n. We call multi-type Markov branching tree the family tree of such a population.*