scholarly journals A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information

2017 ◽  
Vol 42 (4) ◽  
pp. 1162-1179 ◽  
Author(s):  
János Flesch ◽  
Arkadi Predtetchinski
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
Perfect Equilibrium

THE CENTIPEDE OF ROSENTHAL

2007 ◽  
Vol 09 (02) ◽  
pp. 341-345
Author(s):  
EZIO MARCHI
Keyword(s):  
Equilibrium Points ◽  
Short Note ◽  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
Private Communication ◽  
Perfect Equilibrium ◽  
Payoff Functions ◽  
The Relationship ◽  
Extensive Games

In this short note we extend the very well known Centipede game of Rosenthal to the same extensive games with perfect information. The only difference that here the Centipede games have instead of numbers as payoff functions, they have variables. We introduce and study the relationship between the structure of subgame perfect equilibrium points (see Osborne (1994), Binmore (1994)) and the friendly equilibrium points due to Marchi (2004a) and (2004b). We solve an Asheim's conjecture (private communication).

scholarly journals ON GAMES OF PERFECT INFORMATION: EQUILIBRIA, ε–EQUILIBRIA AND APPROXIMATION BY SIMPLE GAMES

2005 ◽  
Vol 07 (04) ◽  
pp. 491-499 ◽  
Author(s):  
GUILHERME CARMONA
Keyword(s):  
Payoff Function ◽  
Perfect Information ◽  
Perfect Equilibrium ◽  
Simple Games ◽  
Original Game ◽  
Approximation Sequence ◽  
Perfect Equilibria

We show that every bounded, continuous at infinity game of perfect information has an ε–perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing from the original game only on the payoff function. In addition, this approach yields a new characterization of perfect equilibria: A strategy f is a perfect equilibrium in such a game G if and only if it is an 1/n–perfect equilibrium in Gn for all n, where {Gn} stands for our approximation sequence.

scholarly journals BACKWARD INDUCTION: MERITS AND FLAWS

2017 ◽  
Vol 50 (1) ◽  
pp. 9-24
Author(s):  
Marek M. Kamiński
Keyword(s):  
Infinite Number ◽  
Nash Equilibria ◽  
Complex Structure ◽  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
Backward Induction ◽  
Perfect Equilibrium ◽  
Sequential Games ◽  
Theoretical Predictions

Abstract Backward induction (BI) was one of the earliest methods developed for solving finite sequential games with perfect information. It proved to be especially useful in the context of Tom Schelling’s ideas of credible versus incredible threats. BI can be also extended to solve complex games that include an infinite number of actions or an infinite number of periods. However, some more complex empirical or experimental predictions remain dramatically at odds with theoretical predictions obtained by BI. The primary example of such a troublesome game is Centipede. The problems appear in other long games with sufficiently complex structure. BI also shares the problems of subgame perfect equilibrium and fails to eliminate certain unreasonable Nash equilibria.

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