%0 Book Section %1 statphys23_0571 %A Okubo, T. %A Odagaki, T. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K dynamics phase processes social statphys23 stochastic systems topic-11 transitions %T Novel transition in emergence of social hierarchy %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=571 %X Emergence of hierarchies is found in wide range of the societies or animal clusters. In these phenomena, a little difference of each individual is enhanced by some causes, and the classes are organized spontaneously. We analyze these phenomena by use of a simple agent based model originally proposed by Bonabeau et al.Physica A 217, 373 (1995). In their model each individual is assumed to have power and diffuses on the square lattice. If two individuals meet, they fight and then the winner increases its power, while the power of loser decreases. In competition with this battle effect, the powers of all individuals relax toward zero gradually. This model found to exhibit a transition from the homogeneous equal society to a heterogeneous hierarchical society. We generalize the mean-field analysis of Bonabeau et al. to societies obeying complex diffusion rules where each individual selects a moving direction following their power rankings , and we apply this analysis to the pacifist society model recently investigated by use of Monte Carlo simulation Physica A 367, 435 (2006). In this society, all individuals hope not to fight as much as possible. Therefore it always moves to a vacant site if it exists around them. If all of the nearest neighbor sites are occupied, it moves to a site occupied by an individual whose power is the smallest among the neighbors. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased. There are three phase, one egalitarian and two hierarchical states. A difference between the first and the second hierarchical state is whether winners exist or not; all individuals belong to either middle class or losers in the first hierarchical state. We also highlight that the transition from the egalitarian phase to the first hierarchical is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.

@incollection{statphys23_0571, abstract = {Emergence of hierarchies is found in wide range of the societies or animal clusters. In these phenomena, a little difference of each individual is enhanced by some causes, and the classes are organized spontaneously. We analyze these phenomena by use of a simple agent based model originally proposed by Bonabeau {\it et al.}[Physica A \textbf{217}, 373 (1995)]. In their model each individual is assumed to have {\it power} and diffuses on the square lattice. If two individuals meet, they fight and then the winner increases its power, while the power of loser decreases. In competition with this battle effect, the powers of all individuals relax toward zero gradually. This model found to exhibit a transition from the homogeneous equal society to a heterogeneous hierarchical society. We generalize the mean-field analysis of Bonabeau {\it et al.} to societies obeying complex diffusion rules where each individual selects a moving direction following their {\it power rankings} , and we apply this analysis to the pacifist society model recently investigated by use of Monte Carlo simulation [Physica A \textbf{367}, 435 (2006)]. In this society, all individuals hope not to fight as much as possible. Therefore it always moves to a vacant site if it exists around them. If all of the nearest neighbor sites are occupied, it moves to a site occupied by an individual whose power is the smallest among the neighbors. We show analytically that the self-organization of hierarchies occurs in two steps as the individual density is increased. There are three phase, one egalitarian and two hierarchical states. A difference between the first and the second hierarchical state is whether winners exist or not; all individuals belong to either middle class or losers in the first hierarchical state. We also highlight that the transition from the egalitarian phase to the first hierarchical is a continuous change in the order parameter and the second transition causes a discontinuous jump in the order parameter.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Okubo, T. and Odagaki, T.}, biburl = {https://www.bibsonomy.org/bibtex/217a545c2dd6c6a5b932db107b62f8b00/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {b6e3f0bee444b71ff41b8bce03057971}, intrahash = {17a545c2dd6c6a5b932db107b62f8b00}, keywords = {dynamics phase processes social statphys23 stochastic systems topic-11 transitions}, month = {9-13 July}, timestamp = {2007-06-20T10:16:23.000+0200}, title = {Novel transition in emergence of social hierarchy}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=571}, year = 2007 }