Sufficient conditions for pure-strategy Nash equilibria of finite games to be Ž . Lyapunov stable under a large class of evolutionary dynamics, the regular monotonic selection dynamics, are discussed. In particular, it is shown that in almost all finite extensive-form games, all the pure-strategy equilibria are stable. In such games, all mixed-strategy equilibria close to pure-strategy equilibr...

For repeated ultimatum bargaining, the Folk Theorem of repeated game theory suggests that there are many equilibria, among them equilibria in which the second mover, say, the buyer, appropriates all the surplus. This paper shows that the presence of outside options in form of alternative trading partners eliminates some of these equilibria by reducing the cope for extracting surplus in repeated...

For Hamiltonian systems with spherical symmetry there is a marked difference between zero and non-zero momentum values, and amongst all relative equilibria with zero momentum there is a marked difference between those of zero and those of non-zero angular velocity. We use techniques from singularity theory to study the family of relative equilibria that arise as a symmetric Hamiltonian which ha...

A class of nondegenerate n n bimatrix games is presented that have asymptotically more than 2:414 n = p n Nash equilibria. These are more equilibria than the 2 n ? 1 equilibria of the game where both players have the identity matrix as payoo matrix. This refutes the Quint{Shubik conjecture that the latter number is an upper bound on the number of equilibria of nondegenerate n n games. The rst c...

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward objectives, and their existence is undecidable with qualitative reachability objectives (and only three players). However, these results rely on the fact tha...

The huge multiplicity of equilibria given by the folk theorem motivates an obvious question: whywould players “deliberately” select on equilibria with bad outcomes if “better” equilibria are available? A simple answer to this is that individual rationality (along with the common knowledge of the game and strategic beliefs) does not take us further than equilibrium behavior. In particular, it do...

Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of an N-person game in which each player has two pure strategies. From the Nash-Tognoli Theorem it follows that every compact differentiable manifold can be encoded as the set of totally mixed Nash equilibria of some game. Moreove...

Dual reduction (Myerson, 1997) is a technique to reduce finite games in a way that selects among correlated equilibria. This technique is shown to be a useful tool to study Nash equilibria and correlated equilibria and its properties are investigated.