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Self-Organized Criticality in a Dynamic Game

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  • John Duffy
  • Andreas Blume
  • Ted Temzelides

Abstract

We investigate conditions under which self-organized criticality (SOC) arises in a version of a dynamic entry game. In the simplest version of the game, there is a single location -- a pool -- and one agent is exogenously dropped into the pool every period. Payoffs to entrants are positive as long as the number of agents in the pool is below a critical level. Exiting results in a permanent payoff of zero. Agents in the pool decide simultaneously each period whether to stay in or not. We characterize the symmetric mixed strategy equilibrium of the resulting dynamic game. We then introduce local interactions between agents that occupy neighboring pools and demonstrate that, under our payoff structure, local interaction effects are necessary and sufficient for SOC and for an associated power law to emerge. Thus, we provide an explicit game-theoretic model of the mechanism through which SOC can arise in a social context with forward looking agents.

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Bibliographic Info

Paper provided by University of Pittsburgh, Department of Economics in its series Working Papers with number 276.

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Date of creation: Oct 2006
Date of revision: Aug 2008
Handle: RePEc:pit:wpaper:276

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  1. A. Arenas & A. Díaz-Guilera & X. Guardiola & M. Llas & G. Oron & C. J. Pérez & F. Vega-Redondo, 2001. "New Results In A Self-Organized Model Of Technological Evolution," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 89-100.
  2. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
  3. Peter Bak & Kan Chen & Jose Scheinkman & Michael Woodford, 1992. "Aggregate Fluctuations from Independent Sectoral Shocks: Self-Organized Criticality in a Model of Production and Inventory Dynamics," NBER Working Papers 4241, National Bureau of Economic Research, Inc.
  4. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
  5. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  6. Rainer Andergassen & Franco Nardini & Massimo Ricottilli, . "Innovation Waves, Self-organised Criticality and Technological Convergence," Modeling, Computing, and Mastering Complexity 2003 19, Society for Computational Economics.
  7. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
  8. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233 Elsevier.
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