Cops or robbers - a bistable society

Details Cops or robbers - a bistable society Cops or robbers - a bistable society

2008-02-11

arxiv.org/abs/0802.1488v3

Int. J. Mod. Phys. C 19 (2008) 1105

Physics

Physics and Society

8 pages, 2 figures. Some misleading sentences are removed from section 3

Scientific paper

10.1142/S0129183108012753

The norm game described by Axelrod in 1985 was recently treated with the master equation formalism. Here we discuss the equations, where {\it i)} those who break the norm cannot punish and those who punish cannot break the norm, {\it ii)} the tendency to punish is suppressed if the majority breaks the norm. The second mechanism is new. For some values of the parameters the solution shows the saddle-point bifurcation. Then, two stable solutions are possible, where the majority breaks the norm or the majority punishes. This means, that the norm breaking can be discontinuous, when measured in the social scale. The bistable character is reproduced also with new computer simulations on the Erd{\H o}s--R\'enyi directed network.

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