The Rationale for Measurability

Robert J. Aumann

When modelling large economies by nonatomic measure spaces of agents, one defines "coalitions" as measurable - not arbitrary - sets of agents. Here we suggest a rationale for this restriction: "Real" economies have finitely many agents. In them, coalitions are associated with various measures, like total endowment, which play a vital role in the analysis. So in the model, too, one should be able to associate similar measures with coalitions; this means that they must be "measurable." Thus, though in the finite case a coalition is simply an arbitrary set of players, the appropriate generalization to the infinite case is not an arbitrary but a measurable set.

July, 2001
Published in: 
In G. Debreu, W. Neuefeind & W. Trockel (eds.) Economics Essays, A Festschrift for Werner Hildenbrand Springer, Berlin (2001), 5-7