Robust equilibrium outcomes in sequential games under almost common certainty of payoffs

Notes on “refinements and higher order beliefs”

“…An important recent paper of Takahashi and Tercieux (2018) studied-in the language of our survey-"robustness to all limit common knowledge elaborations" and developed a number of important tight characterizations of the connection between robustness and classical perturbation refinements in the tradition of Kohlberg and Mertens (1986). In particular, they show (roughly, translated into our language) that hyperstability is sufficient for robustness to all limit independent elaborations, that essentiality is sufficient for robustness to all canonical singleton elaborations and that stability is equivalent to robustness to all canonical, independent, singleton, known own payoff elaborations.…”

Equilibria in Schelling Games: Computational Hardness and Robustness

“…Analyzing the robustness of outcomes of decision processes has become more and more popular in algorithmic game theory over recent years [2,6,8,15,19,23,24,27]. For instance, in the context of hedonic games, Igarashi et al [16] studied stable outcomes that remain stable even after some agents have been deleted and, in the context of stable matching, Mai and Vazirani [20,21] and Chen et al [11] studied stable matchings that remain stable even if the agents' preferences partly change.…”

Sequentially Stable Outcomes

“…Our analysis does not consider payoff uncertainty, which is studied inFudenberg, Kreps, and Levine (1988). Recently,Takahashi and Tercieux (2020) have shown the existence of outcomes robust to payoff uncertainty for generic payoffs.6 Note that we assume, without loss of generality, that each action is available at a unique information set (otherwise, one can rename actions).7 Perfect recall requires that for all I I ∈ I with ι(I) = ι(I ) and all h ĥ ∈ I, if (h a) h for some h ∈ I and a ∈ A, then ( ĥ a) ĥ for some ĥ ∈ I , where (h a) h indicates that (h a) precedes or is equal to h.…”

“…55 Our analysis does not consider payoff uncertainty, which is studied in Fudenberg, Kreps, and Levine (1988). Recently, Takahashi and Tercieux (2020) have shown the existence of outcomes robust to payoff uncertainty for generic payoffs. …”

“…1515 Similarly, Fudenberg and Tirole (1991a, Theorems 14.5 and 14.6) show that, in normal‐form games, all outcomes of Nash equilibria are robust to payoff perturbations. By contrast, Takahashi and Tercieux (2020) show that requiring outcomes to be robust to payoff perturbations has significant selection power in extensive‐form games. However, robust outcomes do not exist for all games. …”