Stochastic games with endogenous transitions

Reinoud Joosten*, Robin Meijboom

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

We present and analyze a stochastic game in which transition probabilities between states are not fixed as in standard stochastic games, but depend on the history of the play, i.e., the players’ past action choices. For the limiting average reward criterion we determine the set of jointly convergent pure-strategy rewards which can be supported by equilibria involving threats. For expository purposes we analyze a stylized fishery game. Each period, two agents choose between catching with restraint or without. The resource is in either of two states, High or Low. Restraint is harmless to the fish, but it is a dominated action at each stage. The less restraint shown during the play, the higher the probabilities that the system moves to or stays in Low. The latter state may even become “absorbing temporarily,”’ i.e., transition probabilities to High temporarily become zero while transition probabilities to Low remain nonzero.
Original languageEnglish
Title of host publicationMathematical programming and game theory
EditorsS.K. Neogy, Ravandra B. Bapat, Dipti Dubey
Place of PublicationSingapore
PublisherSpringer
Pages205-226
Number of pages22
ISBN (Electronic)978-981-13-3059-9
ISBN (Print)978-981-13-3058-2
DOIs
Publication statusPublished - 28 Nov 2018

Publication series

NameIndian Statistical Institute Series
PublisherSpringer
ISSN (Print)2523-3114

Fingerprint

Transition probability
Stochastic games
Reward
Threat
Fish
Fisheries
Resources
Pure strategies

Cite this

Joosten, R., & Meijboom, R. (2018). Stochastic games with endogenous transitions. In S. K. Neogy, R. B. Bapat, & D. Dubey (Eds.), Mathematical programming and game theory (pp. 205-226). (Indian Statistical Institute Series). Singapore: Springer. https://doi.org/10.1007/978-981-13-3059-9
Joosten, Reinoud ; Meijboom, Robin. / Stochastic games with endogenous transitions. Mathematical programming and game theory. editor / S.K. Neogy ; Ravandra B. Bapat ; Dipti Dubey. Singapore : Springer, 2018. pp. 205-226 (Indian Statistical Institute Series).
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Joosten, R & Meijboom, R 2018, Stochastic games with endogenous transitions. in SK Neogy, RB Bapat & D Dubey (eds), Mathematical programming and game theory. Indian Statistical Institute Series, Springer, Singapore, pp. 205-226. https://doi.org/10.1007/978-981-13-3059-9

Stochastic games with endogenous transitions. / Joosten, Reinoud; Meijboom, Robin.

Mathematical programming and game theory. ed. / S.K. Neogy; Ravandra B. Bapat; Dipti Dubey. Singapore : Springer, 2018. p. 205-226 (Indian Statistical Institute Series).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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AB - We present and analyze a stochastic game in which transition probabilities between states are not fixed as in standard stochastic games, but depend on the history of the play, i.e., the players’ past action choices. For the limiting average reward criterion we determine the set of jointly convergent pure-strategy rewards which can be supported by equilibria involving threats. For expository purposes we analyze a stylized fishery game. Each period, two agents choose between catching with restraint or without. The resource is in either of two states, High or Low. Restraint is harmless to the fish, but it is a dominated action at each stage. The less restraint shown during the play, the higher the probabilities that the system moves to or stays in Low. The latter state may even become “absorbing temporarily,”’ i.e., transition probabilities to High temporarily become zero while transition probabilities to Low remain nonzero.

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Joosten R, Meijboom R. Stochastic games with endogenous transitions. In Neogy SK, Bapat RB, Dubey D, editors, Mathematical programming and game theory. Singapore: Springer. 2018. p. 205-226. (Indian Statistical Institute Series). https://doi.org/10.1007/978-981-13-3059-9