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

The system mentioned in the title belongs to the family of the so-called massively multi-player online social games (MMOSG). 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. Key-words: Thermodynamical limit, condensation, ergodicity, non-linear differential system. ∗ This work was supported by grant 109-2167/R from the Région Île-de-France † INRIA Paris–Rocquencourt — Domaine de Voluceau B.P. 105, 78153 Le Chesnay cedex (France) ‡ Revised version accepted for publication in Queueing Systems: Theory and Applications. ha l-0 07 68 32 4, v er si on 2 8 Ju l 2 01 3 Un modèle de comportement grégaire dans un jeu multi-joueurs Résumé : Le système mentionné dans le titre fait partie de la famille des jeux sociaux en ligne dits « massivement multi joueurs ». Il repose sur un système de scores pour les éléments du jeu pouvant générer des comportements grégaires. Nous analysons en détail son régime stationnaire en limite thermodynamique, lorsque le nombre de joueurs tend vers l’infini. Pour certaines classes de paramètres, nous donnons des conditions nécessaires et suffisantes d’existence d’une mesure limite. Des phénomènes de condensation surprenants sont mis en évidence. Mots-clés : Limite thermodynamique, condensation, ergodicité, système différentiel non linéaire. ha l-0 07 68 32 4, v er si on 2 8 Ju l 2 01 3 Modeling a Case of Herding Behavior in a Multi-Player Game 3 The system mentioned in the title belongs to the family of the so-called massively multi-player online social games (MMOSG). 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.