### Abstract

We study games of incomplete information and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players—but not to the analyst—that certain hierarchies of beliefs are precluded. In particular, the players’ type structure can be viewed as a strict subset of the analyst’s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn’t change the analysis—i.e., every equilibrium of the players’ type structure can be associated with an equilibrium of the analyst’s type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)—and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied.

Original language | English (US) |
---|---|

Pages (from-to) | 1-40 |

Number of pages | 40 |

Journal | Economic Theory |

DOIs | |

State | Accepted/In press - Dec 22 2015 |

### Fingerprint

### Keywords

- Bayesian games
- Context
- Hierarchies of beliefs
- Robustness
- Universal type structure

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Economic Theory*, 1-40. https://doi.org/10.1007/s00199-015-0938-z

**The context of the game.** / Friedenberg, Amanda; Meier, Martin.

Research output: Contribution to journal › Article

*Economic Theory*, pp. 1-40. https://doi.org/10.1007/s00199-015-0938-z

}

TY - JOUR

T1 - The context of the game

AU - Friedenberg, Amanda

AU - Meier, Martin

PY - 2015/12/22

Y1 - 2015/12/22

N2 - We study games of incomplete information and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players—but not to the analyst—that certain hierarchies of beliefs are precluded. In particular, the players’ type structure can be viewed as a strict subset of the analyst’s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn’t change the analysis—i.e., every equilibrium of the players’ type structure can be associated with an equilibrium of the analyst’s type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)—and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied.

AB - We study games of incomplete information and argue that it is important to correctly specify the “context” within which hierarchies of beliefs lie. We consider a situation where the players understand more than the analyst: It is transparent to the players—but not to the analyst—that certain hierarchies of beliefs are precluded. In particular, the players’ type structure can be viewed as a strict subset of the analyst’s type structure. How does this affect a Bayesian equilibrium analysis? One natural conjecture is that this doesn’t change the analysis—i.e., every equilibrium of the players’ type structure can be associated with an equilibrium of the analyst’s type structure. We show that this conjecture is wrong. Bayesian equilibrium may fail an Extension Property. This can occur even in the case where the game is finite and the analyst uses the so-called universal structure (to analyze the game)—and, even, if the associated Bayesian game has an equilibrium. We go on to explore specific situations in which the Extension Property is satisfied.

KW - Bayesian games

KW - Context

KW - Hierarchies of beliefs

KW - Robustness

KW - Universal type structure

UR - http://www.scopus.com/inward/record.url?scp=84951845746&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951845746&partnerID=8YFLogxK

U2 - 10.1007/s00199-015-0938-z

DO - 10.1007/s00199-015-0938-z

M3 - Article

AN - SCOPUS:84951845746

SP - 1

EP - 40

JO - Economic Theory

JF - Economic Theory

SN - 0938-2259

ER -