An Epistemic Rationale for Order-Independence

Publication Type

Journal contribution (peer reviewed)

Authors

Trost, Michael

Year of publication

2014

Published in

International Game Theory Review

Band/Volume

16/01

DOI

10.1142/S0219198914400027

The issue of the order dependence of iterative deletion procedures is well known in thegame theory community, and conditions on the dominance concept underlying theseprocedures have meanwhile been detected which ensure order independence (see, e.g.,the criteria of Gilboaet al.(1990) and Apt (2011)). While this kind of research dealswith the technical issue whether certain iterative deletion procedures are order indepen-dent, or not, our focus is on the normative issue whether there are weighty reasons forapplying order-independent iterative deletion procedures to strategic games. We tacklethis question from an epistemic perspective and attempt to figure out whether orderindependence contains some specific epistemic meaning. It turns out that, under fairlygeneral conditions on the choice rules underlying the iterative deletion procedures, theirorder independence coincides with the epistemic characterization of their solutions bythe common belief of choice rule following behavior. Presumably, the most challeng-ing condition of this coincidence is the property of independence of unfavorable acts.We also examine the consequences of two weakenings of this property on our epistemicmotivation for order independence. Although the coincidence mentioned above does nothold for both weakenings, there still exist links between the order independence of iter-ative deletion procedures and their epistemic characterization by the common belief offollowing the choice rules on which these procedures are based.