On Game Theory Using Stochastic Tail Orders

TL;DR

This paper introduces a new family of distributions with tail orders based on hyper-real numbers, invariant to ultrafilter choice, and proves their density within all distributions with the same compact support.

Contribution

It constructs a distribution family with tail orders independent of ultrafilter models and establishes its density among distributions with identical support.

Findings

Distribution family is ultrafilter-invariant

Family is dense in all distributions with same support

Corrects previous models based on ultrafilter dependence

Abstract

We consider a family of distributions on which natural tail orders can be constructed upon a representation of a distribution by a (single) hyper-real number. Past research revealed that the ordering can herein strongly depend on the particular model of the hyperreals, specifically the underlying ultrafilter. Hence, our distribution family is constructed to order invariantly of an ultrafilter. Moreover, we prove that it lies dense in the set of all distributions with the (same) compact support, w.r.t. the supremum norm. Overall, this work resents a correction to [10, 12], in response to recent findings of [2].