On finding curb sets in extensive games
نویسنده
چکیده
We characterize strategy sets that are closed under rational behavior (curb) in extensive games of perfect information and finite horizon. It is shown that any such game possesses only one minimal curb set, which necessarily includes all its subgame perfect Nash equilibria. Applications of this result are twofold. First, it lessens computational burden while computing minimal curb sets. Second, it implies that the profile of subgame perfect equilibrium strategies is always stochastically stable in a certain class of games. April 10, 2003
منابع مشابه
Algorithms for Closed Under Rational Behavior (CURB) Sets
We provide a series of algorithms demonstrating that solutions according to the fundamental game-theoretic solution concept of closed under rational behavior (CURB) sets in two-player, normal-form games can be computed in polynomial time (we also discuss extensions to n-player games). First, we describe an algorithm that identifies all of a player’s best responses conditioned on the belief that...
متن کاملLearning by Adaptive and Forward-Looking Players with One Period Memory
We investigate how much simple-minded players with one period memory can learn for general stage games. The adaptive and one-step forward-looking behavior rules are sufficient for convergence to a minimal weak curb set. Weak curb sets are in general larger than the curb sets but the minimal ones coincide for many games including weakly acyclic games and supermodular games. We also provide an ex...
متن کاملAlgorithms for Rationalizability and CURB Sets
Significant work has been done on computational aspects of solving games under various solution concepts, such as Nash equilibrium, subgame perfect Nash equilibrium, correlated equilibrium, and (iterated) dominance. However, the fundamental concepts of rationalizability and CURB (Closed Under Rational Behavior) sets have not, to our knowledge, been studied from a computational perspective. Firs...
متن کاملEpistemically Stable Strategy Sets
This paper provides a definition of epistemic stability of sets of strategy profiles, and uses it to characterize variants of curb sets in finite games, including the set of rationalizable strategies and minimal curb sets.
متن کاملThe cutting power of preparation
In a strategic game, a curb set [Basu and Weibull, Econ. Letters 36 (1991) 141] is a product set of pure strategies containing all best responses to every possible belief restricted to this set. Prep sets [Voorneveld, Games Econ. Behav. 48 (2004) 403] relax this condition by only requiring the presence of at least one best response to such a belief. The purpose of this paper is to provide econo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Int. J. Game Theory
دوره 32 شماره
صفحات -
تاریخ انتشار 2003