Subgame perfection in recursive perfect information games

Kuipers, Jeroen; Flesch, János; Schoenmakers, Gijs; Vrieze, Koos

doi:10.1007/s00199-020-01260-6

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…While two-player zero-sum Blackwell games and Blackwell games with perfect information are quite well understood (see, e.g., Martin [34,35], Mertens [38], Kuipers, Flesch, Schoenmakers, and Vrieze [25]), general multiplayer nonzero-sum Blackwell games have so far received relatively little attention.…”

Section: Introductionmentioning

confidence: 99%

Regularity of the minmax value and equilibria in multiplayer Blackwell games

Ashkenazi-Golan¹,

Flesch²,

Predtetchinski³

et al. 2022

Preprint

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A real-valued function ϕ that is defined over all Borel sets of a topological space is regular if for every Borel set W, ϕ(W) is the supremum of ϕ(C), over all closed sets C that are contained in W, and the infimum of ϕ (O), over all open sets O that contain W.We study Blackwell games with finitely many players. We show that when each player has a countable set of actions and the objective of a certain player is represented by a Borel winning set, that player's minmax value is regular.We then use the regularity of the minmax value to establish the existence of ε-equilibria in two distinct classes of Blackwell games. One is the class of n-player Blackwell games where each player has a finite action space and an analytic winning set, and the sum of the minmax values over the players exceeds n − 1. The other class is that of Blackwell games with bounded upper semi-analytic payoff functions, history-independent finite action spaces, and history-independent minmax values. For the latter class, we obtain a characterization of the set of equilibrium payoffs.

show abstract

Section: Introductionmentioning

confidence: 99%

Regularity of the minmax value and equilibria in multiplayer Blackwell games

Ashkenazi-Golan¹,

Flesch²,

Predtetchinski³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A general result for stochastic games with three or more players is lacking thus far. Flesch et al (2010) have demonstrated the existence of a subgame-perfect ε-equilibrium for every ε > 0 for the subclass of recursive stochastic games with non-negative utilities, whereas Kuipers et al (2021) obtain such a result for the subclass of recursive stochastic games with deterministic transitions.…”

Section: Introductionmentioning

confidence: 99%

Costless delay in negotiations

Herings

Houba

2021

Econ Theory

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We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect equilibrium in stationary strategies (SSPE) in case of costless delay. We present a characterization of SSPE that is valid for both costly and costless delay. We address the relationship between an SSPE under costless delay and the limit of SSPEs under vanishing costly delay. An SSPE always exists when delay is costly, but not necessarily so under costless delay, even when mixed strategies are allowed for. This is surprising as a quasi SSPE, a solution to the optimality conditions and the system of recursive equations, always exists. The problem is caused by the potential singularity of the system of recursive equations, which is intimately related to the possibility of perpetual disagreement in the bargaining process.

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Regularity of the minmax value and equilibria in multiplayer Blackwell games

Ashkenazi-Golan,

Flesch,

Predtetchinski

et al. 2024

Isr. J. Math.

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A real-valued function φ that is defined over all Borel sets of a topological space is regular if for every Borel set W, φ(W) is the supremum of φ(C), over all closed sets C that are contained in W, and the infimum of φ(O), over all open sets O that contain W.We study Blackwell games with finitely many players. We show that when each player has a countable set of actions and the objective of a certain player is represented by a Borel winning set, that player’s minmax value is regular.We then use the regularity of the minmax value to establish the existence of ε-equilibria in two distinct classes of Blackwell games. One is the class of n-player Blackwell games where each player has a finite action space and an analytic winning set, and the sum of the minmax values over the players exceeds n − 1. The other class is that of Blackwell games with bounded upper semi-analytic payoff functions, history-independent finite action spaces, and history-independent minmax values. For the latter class, we obtain a characterization of the set of equilibrium payoffs.

show abstract

Subgame perfection in recursive perfect information games

Cited by 3 publications

References 21 publications

Regularity of the minmax value and equilibria in multiplayer Blackwell games

Regularity of the minmax value and equilibria in multiplayer Blackwell games

Costless delay in negotiations

Regularity of the minmax value and equilibria in multiplayer Blackwell games

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