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Discrete stop-or-go games

Author

Listed:
  • János Flesch

    (Maastricht University)

  • Arkadi Predtetchinski

    (Maastricht University)

  • William Sudderth

    (University of Minnesota)

Abstract

Dubins and Savage (How to gamble if you must: inequalities for stochastic processes, McGraw-Hill, New York, 1965) found an optimal strategy for limsup gambling problems in which a player has at most two choices at every state x at most one of which could differ from the point mass $$\delta (x)$$ δ ( x ) . Their result is extended here to a family of two-person, zero-sum stochastic games in which each player is similarly restricted. For these games we show that player 1 always has a pure optimal stationary strategy and that player 2 has a pure $$\epsilon $$ ϵ -optimal stationary strategy for every $$\epsilon > 0$$ ϵ > 0 . However, player 2 has no optimal strategy in general. A generalization to n-person games is formulated and $$\epsilon $$ ϵ -equilibria are constructed.

Suggested Citation

  • János Flesch & Arkadi Predtetchinski & William Sudderth, 2021. "Discrete stop-or-go games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 559-579, June.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:2:d:10.1007_s00182-021-00762-4
    DOI: 10.1007/s00182-021-00762-4
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    References listed on IDEAS

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    1. 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.
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    4. Lester E. Dubins & William D. Sudderth, 1977. "Persistently (epsilon)-Optimal Strategies," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 125-134, May.
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    6. William D. Sudderth, 1983. "Gambling Problems with a Limit Inferior Payoff," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 287-297, May.
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