A Stay-in-a-Set Game without a Stationary Equilibrium Mikhail Raskin - - PowerPoint PPT Presentation
A Stay-in-a-Set Game without a Stationary Equilibrium Mikhail Raskin , raskin@mccme.ru 1 Kristoffer Arnsfelt Hansen September 3, 2019 1 The author has received funding from ERC under the EU H2020 programme grant No 787367 (PaVeS) and from the
Kristoffer Arnsfelt Hansen Mikhail Raskin, raskin@mccme.ru 1 September 3, 2019
1The author has received funding from ERC under the EU H2020 programme grant
No 787367 (PaVeS) and from the ANR project GraphEn / ANR-15-CE40-0009.
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Turn-based (perfect information) Finite Stochastic Independent safety goals
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Exact Nash equilibrium exists with bounded memory Remember who has lost
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Induction 1 player: Markov decision process Arbitrary positional strategy for each player in case of loss Uniform bound on time until someone loses or loss becomes impossible Payoffs at that point: by inductive assumption (or obvious)
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For 2 players, is there always zero memory Nash equilibrium (instead
(i.e. equilibrium in stationary strategies)
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Discounted payoffs: stationary equilibrium Deterministic game: stationary equilibrium Recursive/imperfect information games: no stationary ε-Nash equilibrium
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1 2 L2 W L c q 1/4 1/2 1/4 c q 1/4 3/4 1/4 1/4 1/2
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If cycle is left, both P1 and P2 prefer that P1 leaves For P1 best case is staying For P2 staying means loss Note that ε-equilibrium exists
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(for two players) Stationary ε-equilibrium? Stationary equilibrium for reachability conditions? Stationary equilibrium for deterministic recursive games with reachability conditions?
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Discounted payoffs: stationary equilibrium Deterministic game: stationary equilibrium Recursive/imperfect information games: no stationary ε-Nash equilibrium Two-player turn-based stay-in-a-set game: no stationary equilibrium Stationary ε-equilibrium? Stationary equilibrium for reachability conditions? Stationary equilibrium for deterministic recursive games with reachability conditions?
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