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On learning and the stability of cycles

  • James Bullard
  • John Duffy

We study a general equilibrium model where the multiplicity of stationary periodic perfect foresight equilibria is pervasive. We investigate the extent of which agents can learn to coordinate on stationary perfect foresight cycles. The example economy, taken from Grandmont (1985), is an endowment overlapping generations model with fiat money, where consumption in the first and second periods of life are not necessarily gross substitutes. Depending on the value of a preference parameter, the limiting backward (direction of time reversed) perfect foresight dynamics are characterized by steady state, periodic, or chaotic trajectories for real money balances. We relax the perfect foresight assumption and examine how a population of artificial, heterogeneous adaptive agents might learn in such an environment. These artificial agents optimize given their forecasts of future prices, and they use forecast rules that are consistent with steady state or periodic trajectories for prices. The agents' forecast rules are updated by a genetic algorithm. We find that the population of artificial adaptive agents is able to eventually coordinate on steady state and low-order cycles, but not on the higher-order periodic equilibria that exist under the perfect foresight assumption.

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Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 1995-006.

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Date of creation: 1995
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Publication status: Published in Macroeconomic Dynamics, v. 2, no. 1 (March 1998) pp. 22-48
Handle: RePEc:fip:fedlwp:1995-006
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  1. Arifovic, Jasmina, 1996. "The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 510-41, June.
  2. Arifovic, Jasmina, 1995. "Genetic algorithms and inflationary economies," Journal of Monetary Economics, Elsevier, vol. 36(1), pages 219-243, August.
  3. Arifovic, Jasmina, 1994. "Genetic algorithm learning and the cobweb model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(1), pages 3-28, January.
  4. Andreoni James & Miller John H., 1995. "Auctions with Artificial Adaptive Agents," Games and Economic Behavior, Elsevier, vol. 10(1), pages 39-64, July.
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