An “Ethical” Game-Theoretic Solution Concept for Two-Player Perfect-Information Games

A syntactic formalism for the modeling of belief revision in perfect information games is presented that allows to define the rationality of a player's choice of moves relative to the beliefs he holds as his respective decision nodes have been reached. In this setting, true common belief in the structure of the game and rationality held before the start of the game does not imply that backward induction will be played. To derive backward induction, a “forward belief” condition is formulated in terms of revised rather than initial beliefs. Alternative notions of rationality as well as the use of knowledge instead of belief are also studied within this framework.

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Best-Response Cycles in Perfect Information Games

Mathematics of Operations Research ◽

10.1287/moor.2016.0808 ◽

2017 ◽

Vol 42 (2) ◽

pp. 427-433

Author(s):

P. Jean-Jacques Herings ◽

Arkadi Predtetchinski

Keyword(s):

Perfect Information ◽

Best Response ◽

Perfect Information Games ◽

Information Games

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Best Response Cycles in Perfect Information Games

SSRN Electronic Journal ◽

10.2139/ssrn.2621979 ◽

2015 ◽

Author(s):

P. Jean-Jacques Herings ◽

Arkadi Predtetchinski

Keyword(s):

Perfect Information ◽

Best Response ◽

Perfect Information Games ◽

Information Games

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Several Remarks on Banach–Mazur Games and its Applications Ewa Drabik

Foundations of Management ◽

10.2478/fman-2014-0002 ◽

2013 ◽

Vol 5 (1) ◽

pp. 21-25

Author(s):

Ewa Drabik

Keyword(s):

Perfect Information ◽

Perfect Information Games ◽

Information Games

Abstract Certain type of perfect information games (PI-games), the so-called Banach-Mazur games, so far have not been applied in economy. The perfect information positional game is defined as the game during which at any time the choice is made by one of the players who is acquainted with the previous decision of his opponent. The game is run on the sequential basis. The aim of this paper is to discuss selected Banach-Mazur games and to present some applications of positional game

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Algorithms for Closed Under Rational Behavior (CURB) Sets

Journal of Artificial Intelligence Research ◽

10.1613/jair.3070 ◽

2010 ◽

Vol 38 ◽

pp. 513-534 ◽

Cited By ~ 3

Author(s):

M. Benisch ◽

G. B. Davis ◽

T. Sandholm

Keyword(s):

Nash Equilibrium ◽

Polynomial Time ◽

Solution Concept ◽

Rational Behavior ◽

Strategy Space ◽

Normal Form Games ◽

Polynomial Time Algorithms ◽

Game Theoretic ◽

Theoretic Solution ◽

Best Responses

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 players best responses conditioned on the belief that the other player will play from within a given subset of its strategy space. This algorithm serves as a subroutine in a series of polynomial-time algorithms for finding all minimal CURB sets, one minimal CURB set, and the smallest minimal CURB set in a game. We then show that the complexity of finding a Nash equilibrium can be exponential only in the size of a games smallest CURB set. Related to this, we show that the smallest CURB set can be an arbitrarily small portion of the game, but it can also be arbitrarily larger than the supports of its only enclosed Nash equilibrium. We test our algorithms empirically and find that most commonly studied academic games tend to have either very large or very small minimal CURB sets.

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