# Deterministic multi-player Dynkin games

## Author

Listed:
• Solan, Eilon
• Vieille, Nicolas

## Abstract

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff. We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than one. We prove that a subgame-perfect e-equilibrium in Markovian strategies exists. If the game is not degenerate this e-equilibrium is actually in pure strategies.
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(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

## Suggested Citation

• Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
• Handle: RePEc:eee:mateco:v:39:y:2003:i:8:p:911-929
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File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(03)00021-1

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## References listed on IDEAS

as
1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2001. "On the MaxMin Value of Stochastic Games with Imperfect Monitoring," Discussion Papers 1344, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
4. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
5. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
6. Mertens,Jean-FranÃ§ois & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, May.
• Mertens,Jean-FranÃ§ois & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, April.
7. repec:dau:papers:123456789/6017 is not listed on IDEAS
8. Eilon Solan & Nicolas Vieille, 2001. "Quitting Games," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 265-285, May.
9. Eran Shmaya & Eilon Solan, 2002. "Two Player Non Zero-Sum Stopping Games in Discrete Time," Discussion Papers 1347, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
10. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
11. Brams, Steven J. & Kilgour, D. Mark, 1997. "The Truel," Working Papers 97-05, C.V. Starr Center for Applied Economics, New York University.
12. Fine, Charles H. & Li, Lode, 1989. "Equilibrium exit in stochastically declining industries," Games and Economic Behavior, Elsevier, vol. 1(1), pages 40-59, March.
13. Janos Flesch & Frank Thuijsman & Koos Vrieze, 1997. "Cyclic Markov Equilibria in Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 303-314.
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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Cited by:

1. 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.
2. 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.
3. Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2013. "Subgame-perfection in free transition games," European Journal of Operational Research, Elsevier, vol. 228(1), pages 201-207.
4. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
5. Flesch JÃ¡nos & Kuipers Jeroen & Schoenmakers Gijs & Vrieze Koos, 2008. "Subgame-Perfection in Stochastic Games with Perfect Information and Recursive Payoffs," Research Memorandum 041, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
6. Kuipers, J. & Flesch, J. & Schoenmakers, G. & Vrieze, K., 2009. "Pure subgame-perfect equilibria in free transition games," European Journal of Operational Research, Elsevier, vol. 199(2), pages 442-447, December.
7. Elena Parilina & Georges Zaccour, 2016. "Strategic Support of Node-Consistent Cooperative Outcomes in Dynamic Games Played Over Event Trees," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-16, June.
8. 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).
9. Ayala Mashiah-Yaakovi, 2014. "Subgame perfect equilibria in stopping games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 89-135, February.
10. Ayala Mashiah-Yaakovi, 2009. "Periodic stopping games," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 169-181, June.
11. Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizing existence of equilibrium for large extensive form games: a necessity result," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 407-430, February.
12. Flesch JÃ¡nos & Kuipers Jeroen & Mashiah-Yaakovi Ayala & Schoenmakers Gijs & Solan Eilon & Vrieze Koos, 2010. "Borel Games with Lower-Semi-Continuous Payoffs," Research Memorandum 040, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
13. Kuipers Jeroen & Flesch Janos & Schoenmakers Gijs & Vrieze Koos, 2008. "Pure Subgame-Perfect Equilibria in Free Transition Games," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
14. János Flesch & Arkadi Predtetchinski, 2016. "On refinements of subgame perfect $$\epsilon$$ ϵ -equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 523-542, August.
15. 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.
16. Anna Krasnosielska-Kobos, 2016. "Construction of Nash equilibrium based on multiple stopping problem in multi-person game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 53-70, February.
17. Flesch J. & Kuipers J. & Schoenmakers G. & Vrieze K., 2011. "Subgame-Perfection in Free Transition Games," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
18. Guo, Ivan & Rutkowski, Marek, 2016. "Discrete time stochastic multi-player competitive games with affine payoffs," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 1-32.
19. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.

### JEL classification:

• C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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