Abstract: There are many diverse examples of groups with a large number of competing participants. As early as 1944, in their famous book "Theory of Games and Economic Behavior", von Neumann and Morgenstern emphasized the importance of studying mass phenomena arising from the interaction of a large number of participants. To model the idea that the influence of individuals is negligible in very large societies, Milnor and Shapley in 1961 used a non-atomic measure space to represent "a continuum of infinitesimal minor players." Since then, many new results have been obtained in the continuum setting that would fail in the case of a fixed finite number of agents. It has been discovered recently, however, that the usual continuum model such as Lebesgue space may not appropriately capture limiting phenomena for the interaction of a large, but finite, number of agents. Examples include the disappearance of Nash equilibria for games with many players, and the lack of a limiting model for many agents with independent risks. This talk will show how rich measure spaces, such as Loeb measure spaces, can be used not only to resolve these problems, but also to go beyond them to discover unexpected new connections in economics as well as in mathematics.