# The Social Climbing Game

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## Abstract

The structure of societies depends, to some extent, on the incentives of the individuals they are composed of. We study a stylized model of this interplay, that suggests that the more individuals aim at climbing the social hierarchy, the more society’s hierarchy gets strong. Such a dependence is sharp, in the sense that a persistent hierarchical order emerges abruptly when the preference for social status gets larger than a threshold. This phase transition has its origin in the fact that the presence of a well defined hierarchy allows agents to climb it, thus reinforcing it, whereas in a “disordered” society it is harder for agents to find out whom they should connect to in order to become more central. Interestingly, a social order emerges when agents strive harder to climb society and it results in a state of reduced social mobility, as a consequence of ergodicity breaking, where climbing is more difficult.

## Keywords

Social networks Phase transitions Game theory## Notes

### Acknowledgements

We thank Sanjeev Goyal and Giacomo Gori for precious hints and fruitful discussions. C. J. T. acknowledges financial support from Swiss National Science Foundation through grant 100014_126865 and SBF (Swiss Confederation) through research project C09.0055. M. B. heartily thanks M. V. Carlucci for her dedicated support.

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