On Forward Induction and Evolutionary and Strategic Stability

Abstract

We analyze which normal form solution concepts capture the notion of forward induction, as de ned by v an Damme JET, 1989 in the class of generic two player normal form games preceded by an outside option. We nd that none of the known strategic stability concepts including Mertens stable sets and hyperstable sets captures this form of forward induction. On the other hand, we show that the evolutionary concept of EES set Swinkels, JET, 1992 is always consistent with forward induction.

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

“…As will become clear (see, for instance, Corollary 4), this will be enough to apply an analogue of Corollary 1 to the current context. 24 To recap, even though, as shown in AFHKT, the equilibrium behavior (which reports the state truthfully) is not robust to incomplete information, we show that the equilibrium outcome (full surplus extraction) is robust. Of course, as shown in AFHKT, we do have nearby priors under which we get undesirable equilibrium outcomes (i.e., where a significant fraction of the surplus cannot be extracted).…”

“…14 As we will see in the next section, other strategic stability notions that have appeared in the literature, known to be strictly weaker than hyperstability, are not sufficient for robustness. For example, the outcome T in Example 3 in Section 4.1 is fully stable in the sense of Kohlberg and Mertens (1986), but not robust; the outcome Out in the example of Hauk and Hurkens (2002) in Appendix A.3 is essential, but not robust; the outcome T in the example of van Damme (1989) in Online Appendix C.2 contains two stable sets in the sense of Mertens (1989) (as shown by Govindan and Wilson (2001)), but is not robust.…”

Game Theory Explorer: software for the applied game theorist

“…Interestingly, the larger component in this game has the property that it has index zero but is nevertheless strategically stable, that is, any perturbed game has equilibria near that component, as shown by Hauk and Hurkens (2002). The larger component in the game in Fig.…”

On Sustainable Equilibria

“…It follows from Demichelis and Ritzberger[4] that Hofbauer's second conjecture is false if we include all games: a necessary condition for a component of Nash equilibria to be asymptotically stable is that its index agree with its Euler characteristic; yet, there are examples (e.g [9]. Fig.8or[28] p. 325) where all components of equilibria are convex (and so have Euler characteristic +1), but no component has index +1.…”

“…Our game is inspired by the two player game in[9] fig 8 in which the +2 index was a component. By adding a player and strategies we can kill all equilibria of that component except τ 25.…”