On Invariant Games

CASCADING TO EQUILIBRIUM: HYDRAULIC COMPUTATION OF EQUILIBRIA IN RESOURCE SELECTION GAMES By

Drawing intuition from a (physical) hydraulic system, we present a novel framework, constructively showing the existence of a strong Nash equilibrium in resource selection games with nonatomic players, the coincidence of strong equilibria and Nash equilibria in such games, and the invariance of the cost of each given resource across all Nash equilibria. Our proofs allow for explicit calculation...

Two-Player Perfect-Information Shift-Invariant Submixing Stochastic Games Are Half-Positional

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the the payoff function is both shift-invariant and submixing, then the game is half-positional, i.e. the first player has an optimal strategy which is both deter...

Framework for Evaluating Loop Invariant Detection Games in Relation to Automated Dynamic Invariant Detectors

Extending Invariant Solutions

In this paper we show that an invariant solution for normal form games can be extended uniquely to an invariant solution for strategic form games. This result has Ž . the following consequence for the reduction of a normal form game. Suppose that Ž the pure strategies are removed that are payoff equivalent with some possibly . mixed strategy. Then, if one is concerned with an invariant solution...

Topologically Left Invariant Mean on Dual Semigroup Algebras

Invariant games

In the context of 2-player removal games, we define the notion of invariant game for which each allowed move is independent of the position it is played from. We present a family of invariant games which are variations of Wythoff’s game. The set of P -positions of these games are given by a pair of complementary Beatty sequences related to the irrational quadratic number αk = (1; 1, k). We also...