Interpreting Knowledge in the Backward Induction Problem

Episteme ◽  
2011 ◽  
Vol 8 (3) ◽  
pp. 248-261 ◽  
Author(s):  
Ken Binmore
Keyword(s):  
Common Knowledge ◽  
Perfect Information ◽  
Backward Induction ◽  
Finite Games ◽  
Common Knowledge Of Rationality

AbstractRobert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

From Common Knowledge of Rationality to Backward Induction

2003 ◽  
Vol 05 (02) ◽  
pp. 127-137 ◽  
Author(s):  
Antonio Quesada
Keyword(s):  
Common Knowledge ◽  
Perfect Information ◽  
Knowledge Structures ◽  
Backward Induction ◽  
Strict Sense ◽  
Strategy Profile ◽  
Induction Strategy ◽  
Common Knowledge Of Rationality ◽  
Epistemic Model

With the only assumption that a player knows the strategy he chooses, it is proved in a generalized version of Aumann's (1995) epistemic model that, in a generic game with perfect information, common knowledge of rationality is equivalent to common knowledge of the fact that the backward induction strategy profile is chosen. This result shows that Aumann's backward induction theorem holds without stipulating partition knowledge structures nor presuming that the epistemic operator defines knowledge in the strict sense.

Extensive Form Rationalizability

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Common Knowledge ◽  
Backward Induction ◽  
Forward Induction ◽  
Extensive Form ◽  
Extensive Form Games ◽  
Dominated Strategies ◽  
Extensive Form Game ◽  
Common Knowledge Of Rationality

The extensive form of a game is informationally richer than the normal form since players gather information that allows them to update their subjective priors as the game progresses. For this reason, the study of rationalizability in extensive form games is more complex than the corresponding study in normal form games. There are two ways to use the added information to eliminate strategies that would not be chosen by a rational agent: backward induction and forward induction. The latter is relatively exotic (although more defensible). Backward induction, by far the most popular technique, employs the iterated elimination of weakly dominated strategies, arriving at the subgame perfect Nash equilibria—the equilibria that remain Nash equilibria in all subgames. An extensive form game is considered generic if it has a unique subgame perfect Nash equilibrium. This chapter develops the tools of modal logic and presents Robert Aumann's famous proof that common knowledge of rationality (CKR) implies backward induction. It concludes that Aumann is perfectly correct, and the real culprit is CKR itself. CKR is in fact self-contradictory when applied to extensive form games.

scholarly journals Endogena korupcija kao ravnoteza sekvencijalne igre

2003 ◽  
Vol 44 (156) ◽  
pp. 21-43
Author(s):  
Milic Milovanovic
Keyword(s):  
Working Conditions ◽  
Perfect Information ◽  
Equilibrium Strategy ◽  
Backward Induction ◽  
Power Struggle ◽  
Extensive Form ◽  
Sequential Game ◽  
Privatized Firms ◽  
Motivational Structure ◽  
Insider Privatization

In this paper power struggle over the control of an insider privatized firm is modeled as a sequential game with perfect information. The endogenous corruption is a consequence of an insider privatization plan, where employees obtain majority of shares. In the post privatization game three players are dominant: managers, employees, and outside owners. Managers are by far the strongest player, with their key position in privatized firms despite their minority ownership stake. Since managers control working conditions of employees-cum-owners, they exercise an unparalleled power. Motivational structure is given for each player. Their ranked lists of goals and fears are necessary in order to specify parameters for the model. The game is modeled in an extensive form, and backward induction suggests a coalition of insiders (managers and employees) against the interests of outsiders. Under stated conditions, the equilibrium strategy results in an endogenous corruption.

DYNAMIC GAMES WITH COALITIONAL STRUCTURES

2006 ◽  
Vol 08 (02) ◽  
pp. 295-307 ◽  
Author(s):  
LEON PETROSJAN ◽  
SVETLANA MAMKINA
Keyword(s):  
Random Process ◽  
Dynamic Games ◽  
Perfect Information ◽  
Backward Induction ◽  
Multistage Games

The paper explores the properties of multistage games with perfect information, in which (unlike the classic Kuhnian definition) the conditional coalition partition at any vertex is determined by a chance move and remains unchanged until the random process repeats at the next vertex. A new value for such a game is proposed in terms of a PMS-vector. It is computed by backward induction using conditional partition and transition in the vertices. An illustrative example is provided.

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