Prudent Rationalizability in Generalized Extensive-form Games with Unawareness

AbstractWe define a cautious version of extensive-form rationalizability for generalized extensive-form games with unawareness that we call prudent rationalizability. It is an extensive-form analog of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.

Download Full-text

An Algorithm for Constructing and Solving Imperfect Recall Abstractions of Large Extensive-Form Games

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/130 ◽

2017 ◽

Cited By ~ 2

Author(s):

Jiri Cermak ◽

Branislav Bošanský ◽

Viliam Lisý

Keyword(s):

Relative Size ◽

Fictitious Play ◽

Perfect Recall ◽

Extensive Form ◽

Extensive Form Games ◽

Imperfect Recall ◽

Information Sets ◽

Information Set ◽

Zero Sum ◽

Large Extensive Form Games

We solve large two-player zero-sum extensive-form games with perfect recall. We propose a new algorithm based on fictitious play that significantly reduces memory requirements for storing average strategies. The key feature is exploiting imperfect recall abstractions while preserving the convergence rate and guarantees of fictitious play applied directly to the perfect recall game. The algorithm creates a coarse imperfect recall abstraction of the perfect recall game and automatically refines its information set structure only where the imperfect recall might cause problems. Experimental evaluation shows that our novel algorithm is able to solve a simplified poker game with 7.10^5 information sets using an abstracted game with only 1.8% of information sets of the original game. Additional experiments on poker and randomly generated games suggest that the relative size of the abstraction decreases as the size of the solved games increases.

Download Full-text