My bibliography  Save this paper

# Perfect Information Games where Each Player Acts Only Once

## Author

Listed:
• Cingiz, Kutay

(General Economics 0 (Onderwijs))

• Flesch, Janos

(QE / Mathematical economics and game the)

• Herings, P. Jean-Jacques

(General Economics 1 (Micro))

(General Economics 1 (Micro))

## Abstract

We study perfect information games played by an infinite sequence of players, each acting only once in the course of the game. We introduce a class of frequency-based minority games and show that these games admit no subgame perfect ϵ-equilibrium for small positive values of ϵ. Furthermore we derive a number of sufficient conditions to guarantee existence of subgame perfect ϵ-equilibrium.

## Suggested Citation

• Cingiz, Kutay & Flesch, Janos & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2016. "Perfect Information Games where Each Player Acts Only Once," Research Memorandum 036, Maastricht University, Graduate School of Business and Economics (GSBE).
• Handle: RePEc:unm:umagsb:2016036
as

File URL: https://cris.maastrichtuniversity.nl/portal/files/5676862/content

## References listed on IDEAS

as
1. Geir B. Asheim, 2010. "Intergenerational Equity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 197-222, September.
2. R. A. Pollak, 1968. "Consistent Planning," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 201-208.
3. Jérôme Renault & Marco Scarsini & Tristan Tomala, 2007. "A Minority Game with Bounded Recall," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 873-889, November.
4. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
5. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 391-401.
6. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
7. Solan, Eilon, 2000. "Absorbing Team Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 245-261, May.
8. János Flesch & Jeroen Kuipers & Ayala Mashiah-Yaakovi & Gijs Schoenmakers & Eran Shmaya & Eilon Solan & Koos Vrieze, 2014. "Non-existence of subgame-perfect $$\varepsilon$$ ε -equilibrium in perfect information games with infinite horizon," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 945-951, November.
9. Renault, Jérôme & Scarlatti, Sergio & Scarsini, Marco, 2008. "Discounted and finitely repeated minority games with public signals," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 44-74, July.
10. Cingiz, Kutay & Flesch, János & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2016. "Doing it now, later, or never," Games and Economic Behavior, Elsevier, vol. 97(C), pages 174-185.
11. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 413-424, May.
12. von Stengel, Bernhard & Zamir, Shmuel, 2010. "Leadership games with convex strategy sets," Games and Economic Behavior, Elsevier, vol. 69(2), pages 446-457, July.
13. János Flesch & Arkadi Predtetchinski, 2016. "Subgame-perfect $$\epsilon$$ ϵ -equilibria in perfect information games with sigma-discrete discontinuities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 479-495, March.
14. Gossner, Olivier & Hörner, Johannes, 2010. "When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 63-84, January.
15. Mertens,Jean-FranÃ§ois & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
• Mertens,Jean-FranÃ§ois & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636.
16. E. S. Phelps & R. A. Pollak, 1968. "On Second-Best National Saving and Game-Equilibrium Growth," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 185-199.
17. Callander, Steven & Hörner, Johannes, 2009. "The wisdom of the minority," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1421-1439.2, July.
18. Hellwig, Martin & Leininger, Wolfgang & Reny, Philip J. & Robson, Arthur J., 1990. "Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 406-422, December.
19. Voorneveld, Mark, 2010. "The possibility of impossible stairways: Tail events and countable player sets," Games and Economic Behavior, Elsevier, vol. 68(1), pages 403-410, January.
20. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
21. von Stengel, Bernhard & Koller, Daphne, 1997. "Team-Maxmin Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 309-321, October.
22. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.
23. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 443-478.
24. Balbus, Łukasz & Jaśkiewicz, Anna & Nowak, Andrzej S., 2015. "Stochastic bequest games," Games and Economic Behavior, Elsevier, vol. 90(C), pages 247-256.
Full references (including those not matched with items on IDEAS)

### JEL classification:

• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
• D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

### NEP fields

This paper has been announced in the following NEP Reports:

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:unm:umagsb:2016036. 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: (Leonne Portz). General contact details of provider: http://edirc.repec.org/data/meteonl.html .

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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.