IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

Growth of Strategy Sets, Entropy, and Nonstationary Bounded Recall

  • Abraham Neyman
  • Daijiro Okada

One way to express bounded rationality of a player in a game theoretic models is by specifying a set of feasible strategies for that player. In dynamic game models with finite automata and bounded recall strategies, for example, feasibility of strategies is determined via certain complexity measures: the number of states of automata and the length of recall. Typically in these models, a fixed finite bound on the complexity is imposed resulting in finite sets of feasible strategies. As a consequence, the number of distinct feasible strategies in any subgame is finite. Also, the number of distinct strategies induced in the first T stages is bounded by a constant that is independent of T. In this paper, we initiate an investigation into a notion of feasibility that reflects varying degree of bounded rationality over time. Such concept must entail properties of a strategy, or a set of strategies, that depend on time. Specifically, we associate to each subset Ψ i of the full (theoretically possible) strategy set a function y i from the set of positive integers to itself. The value y i(t) represents the number of strategies in Ψ i that are distinguishable in the first t stages. The set Ψ i may contain infinitely many strategies, but it can differ from the fully rational case in the way y i grows reflecting a broad implication of bounded rationality that may be alleviated, or intensified, over time. We examine how the growth rate of y i affects equilibrium outcomes of repeated games. In particular, we derive an upper bound on the individually rational payoff of repeated games where player 1, with a feasible strategy set Ψ 1, plays against a fully rational player 2. We will show that the derived bound is tight in that a specific, and simple, set Ψ 1 exists that achieves the upper bound. As a special case, we study repeated games with non-stationary bounded recall strategies where the length of recall is allowed to vary in the course of the game. We will show that a player w

(This abstract was borrowed from another version of this item.)

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Our checks indicate that this address may not be valid because: 404 Not Found. If this is indeed the case, please notify (David K. Levine)

Download Restriction: no

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000920.

in new window

Date of creation: 30 Dec 2005
Date of revision:
Handle: RePEc:cla:levrem:122247000000000920
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Olivier Gossner & Penélope Hernández & Abraham Neyman, 2006. "Optimal Use of Communication Resources," Econometrica, Econometric Society, vol. 74(6), pages 1603-1636, November.
  2. Robert J. Aumann & Lloyd S. Shapley, 1992. "Long Term Competition-A Game Theoretic Analysis," UCLA Economics Working Papers 676, UCLA Department of Economics.
  3. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
  4. Gossner, O. & Vieille, N., 1999. "How to play with a biased coin?," Papers 99-31, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  5. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  6. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
  7. Abraham Neyman & Daijiro Okada, 2000. "Two-person repeated games with finite automata," International Journal of Game Theory, Springer, vol. 29(3), pages 309-325.
  8. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
  9. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cla:levrem:122247000000000920. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (David K. Levine)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.