Search in games with incomplete information: a case study using Bridge card play

摘要

We examine search algorithms in games with incomplete information, formalising a best defence model of such games based on the assumptions typically made when incomplete information problems are analysed in expert texts. We show that equilibrium point strategies for optimal play exist for this model, and define an algorithm capable of computing such strategies. Using this algorithm as a reference we then analyse search architectures that have been proposed for the incomplete information game of Bridge. These architectures select strategies by analysing some statistically significant collection of complete information sub-games. Our model allows us to clearly state the limitations of such architectures in producing expert analysis, and to precisely formalise and distinguish the problems that lead to sub-optimality. We illustrate these problems with simple game trees and with actual play situations from Bridge itself.