Symbolic Computation of Sequential Equilibria
CoRR(2024)
摘要
The sequential equilibrium is a standard solution concept for extensive-form
games with imperfect information that includes an explicit representation of
the players' beliefs. An assessment consisting of a strategy and a belief is a
sequential equilibrium if it satisfies the properties of sequential rationality
and consistency.
Our main result is that both properties together can be written as a single
finite system of polynomial equations and inequalities. The solutions to this
system are exactly the sequential equilibria of the game. We construct this
system explicitly and describe an implementation that solves it using
cylindrical algebraic decomposition. To write consistency as a finite system of
equations, we need to compute the extreme directions of a set of polyhedral
cones. We propose a modified version of the double description method,
optimized for this specific purpose. To the best of our knowledge, our
implementation is the first to symbolically solve general finite imperfect
information games for sequential equilibria.
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