CeDEx
Centre for Decision Research and Experimental Economics

CeDEx workshop - Elias Tsakas (University of Maastricht)

Date(s)
Wednesday 15th February 2012 (14:00-15:00)
Description

Rational Belief in Hierarchies

Abstract:

We consider agents whose language can only express probabilistic beliefs that attach

a rational number to every event. We call these probability measures rational. We introduce

the notion of a rational belief hierarchy, where the first order beliefs are described

by a rational measure over the fundamental space of uncertainty, the second order beliefs

are described by a rational measure over the product of the fundamental space of uncertainty

and the opponent’s first order rational beliefs, and so on. Then, we derive the

corresponding (rational) type space model, thus providing a Bayesian representation of

rational belief hierarchies. Our first main result shows that this type-based representation

violates our intuitive idea of an agent whose language expresses only rational beliefs,

in that there are rational types associated with non-rational beliefs over the canonical

state space. We rule out these types by focusing on the rational types that satisfy common

certainty in the event that everybody holds rational beliefs over the canonical state

space. We call these types universally rational and show that they are characterized

by a bounded rationality condition which restricts the agents’ computational capacity.

Moreover, the universally rational types form a dense subset of the universal type space.

Finally, we show that the strategies rationally played under common universally rational

belief in rationality generically coincide with those satisfying correlated rationalizability.

Keywords: Epistemic game theory, bounded rationality, rational numbers, belief hierarchies,

type spaces, unawareness, computational capacity, common belief in rationality.

 

 

Centre for Decision Research and Experimental Economics

Sir Clive Granger Building
University of Nottingham
University Park
Nottingham, NG7 2RD

telephone: +44 (0)115 951 5458
Enquiries: jose.guinotsaporta@nottingham.ac.uk
Experiments: cedex@nottingham.ac.uk