Complexity of Allocation Processes : Chaos and Path Dependence

Allocation processes|the division of some commodity among multiple agents|are fundamental to social interactions in various arenas. Examples include wealth/income distribution in populations, natural resource exploitation, market share for competing corporations, satellite bandwidth division among many users, and CPU time usage by multiple software agents running simultaneously. In the case where each agent prefers more to less of the commodity|as in these examples|preference, or Condorcet, cycles are inevitable. We determine the consequences of this fact on an analytically tractable process of allocation subject to random external perturbations. This is a complex system: under majority rule the process is chaotic, while under weighted majority rule the system self-organizes to produce a path-dependent majority owner/dictator/monopolist. Journal of Economic Literature Classi cation System: D71, D31, C69. 1999 Physics and Astronomy Classi cation Scheme: 05.65.+b, 05.40.Jc, 89.90.+n. American Mathematical Society Subject Classi cation: 90A80, 90A08, 54H20, 60J65.