Popper's Axiomatic Probability System and the Value-Assignment Problem

Alternative Axiomatic Characterizations of the Grey Shapley Value

The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapl...

Axiomatic First-Order Probability

Most languages for the Semantic Web have their logical basis in some fragment of first-order logic. Thus, integrating first-order logic with probability is fundamental for representing and reasoning with uncertainty in the semantic web. Defining semantics for probability logics presents a dilemma: a logic that assigns a real-valued probability to any first-order sentence cannot be axiomatized a...

1.2 Axiomatic Approach to Probability and Properties of Probability Measure

Probabilistic Assignment: A Two-fold Axiomatic Approach

We study the problem of allocating objects by means of probabilistic mechanisms. Each agent has strict preferences over objects and ex post receives exactly one object. A standard approach in the literature is to extend agents' preferences over objects to preferences over lotteries de ned on those objects, using the rst-order stochastic dominance criterion, or the sd-extension. In a departure f...

The value of information - An axiomatic approach*

The following question is addressed: Given a real-valued function on the partitions of a measure space, what are necessary and sufficient conditions in order that it be the value of information function for a Bayesian decision maker? A characterization is provided, and the analysis reveals a close relationship to cooperative game theory. The tools developed for characterization can also be used...