On Loeb measure spaces and their significance for non-cooperative game theory

In this expository paper, Loeb measure spaces are constructed on the basis of sequences, and shown to satisfy many useful properties, including some regularity properties of correspondences involving distribution and integration. It is argued that Loeb measure spaces can be effectively and systematically used for the analysis of game-theoretic situations in which ''strategic negligibility'' and/or ''diffuseness'' of information are substantive and essential issues. Positive results are presented, and the failure of analogous results for identical models based on Lebesgue measure spaces is illustrated by several examples. It is also pointed out that the requirement of Lebesgue measurability, by going against the non-cooperative element in the situation being modelled, is partly responsible for this failure.