# Modeling a case of herding behavior in a multi-player game

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## Abstract

The system mentioned in the title belongs to the family of the so-called massively multi-player online social games. It features a scoring system for the elements of the game that is prone to herding effects. We analyze in detail its stationary regime in the thermodynamic limit, when the number of players tends to infinity. In particular, for some classes of input sequences and selection policies, we provide necessary and sufficient conditions for the existence of a complete meanfield-like measure, showing off an interesting *condensation* phenomenon.

## Keywords

Thermodynamical limit Condensation Ergodicity Transience Non-linear differential system Banach space## Mathematics Subject Classification

60J28 34L30 37C40## Notes

### Acknowledgments

This work was supported by Grant 109-2167/R from the *Région Île-de-France*.

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