An Epistemic Rationale for Order-Independence
The issue of the order-dependence of iterative deletion processes is well-known in the game theory community, and meanwhile conditions on the dominance concept underlying these processes have been detected which ensure order-independence (see e.g. the criteria of Gilboa et al., 1990 and Apt, 2011). While this kind of research deals with the technical issue, whether certain iterative deletion processes are order-independent, or not, our focus is on the normative issue, whether there are good reasons for employing order-independent iterative deletion processes on strategic games. We tackle this question from an epistemic perspective and attempt to figure out, whether order-independence contains some specific epistemic meaning. It turns out that, under fairly general preconditions on the choice rules underlying the iterative deletion processes, the order-independence of these deletion processes coincides with the epistemic characterization of their solutions by the common belief of choice-rule following behavior. The presumably most challenging precondition of this coincidence is the property of the independence of irrelevant acts. We also examine the consequences of two weakenings of this property on our epistemic motivation for order-independence. Although the coincidence mentioned above breaks down for both weakenings, still there exist interesting links between the order-independence of iterative deletion processes and the common belief of following the choice rules, on which these processes are based.
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