Suppose that there are n states, each denoted by i. This paper shows that the function [p_{i|E}] is a homeomorphism from the set of conditional probability systems onto the convex hull of all permutations of the n-dimensional vector (0,1,2,... n-1).

A "dispersion" specifies the relative probability between any two elements of a finite domain. It thereby partitions the domain into equivalence classes separated by infinite relative probability. The paper's novelty is to numerically represent not only the order of the equivalence classes, but...

This paper offers two characterizations of the Kreps-Wilson concept of consistent beliefs. One is primarily of applied interest: beliefs are consistent iff they can be constructed by multiplying together vectors of monomials which induce the strategies. The other is primarily of conceptual...

We introduce three definitions. First, we let a "basement" be a set of nodes and actions that supports at least one assessment. Second, we derive from an arbitrary basement its implied "plausibility" (i.e. infinite-relative-likelihood) relation among the game's nodes. Third, we say that this...

This paper defines and develops the concept of a product dispersion over any finite number of dimensions. The concept itself is nontrivial because products over several dimensions cannot be constructed by an iterative binary operation. Yet the paper's most important contribution is to...

This paper derives two characterizations of the Kreps-Wilson concept of consistent beliefs. In the first, beliefs are shown to be consistent iff they can be constructed from the elements of monomial vectors which converge to the strategies. In the second, beliefs are shown to be consistent iff...

The nodes of an extensive-form game are commonly specified as sequences of actions. Rubinstein calls such nodes histories. We find that this sequential notation is superfl uous in the sense that nodes can also be specified as sets of actions. The only cost of doing so is to rule out games with...

In a discounted expected-utility problem, tomorrow's utilities are aggregated across tomorrow's states by the expectation operator. In our problems, this aggregation is accomplished by a Choquet integral of the form iudP a, where a specifies uncertainty aversion. We solve all finite-state...

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