Computing Normal Form Perfect Equilibria for Extensive Two-Person Games

Computing Normal Form Perfect Equilibria for Extensive Two-person Games

This paper presents an algorithm for computing an equilibrium of an extensive two-person game with perfect recall. The method is computationally efficient by virtue of using the sequence form, whose size is proportional to the size of the game tree. The equilibrium is traced on a piecewise linear path in the sequence form strategy space from an arbitrary starting vector. If the starting vector ...

Computing an Extensive-Form Perfect Equilibrium in Two-Player Games

Equilibrium computation in games is currently considered one of the most challenging issues in AI. In this paper, we provide, to the best of our knowledge, the first algorithm to compute a Selten’s extensive–form perfect equilibrium (EFPE) with two–player games. EFPE refines the Nash equilibrium requiring the equilibrium to be robust to slight perturbations of both players’ behavioral strategie...

Computing Equilibria for Two-person Games

Computing Equilibria for Two-Person Games

This paper is a self-contained survey of algorithms for computing Nash equilibria of two-person games given in normal form or extensive form. The classical Lemke{Howson algorithm for nding one equilibrium of a bimatrix game is presented graph-theoretically as well as algebraically in terms of complementary pivoting. Common deenitions of degenerate games are shown as equivalent. Enumeration of a...

On the Relation between Perfect Equilibria in Extensive Form Games and Proper Equilibria in Normal Form Games

This paper examines the question of the extent to which it is true that any equilibrium that is quasi-perfect in any extensive form game having a given normal form is necessarily proper. If one fixes not only the equilibrium in question but also a sequence of completely mixed strategies converging to that equilibrium then indeed the notions are equivalent. However the stronger result is not tru...