Blocks of coordinates, stochastic programming, and markets

摘要

Considered here are extremal convolutions concerned with allocative efficiency, risk sharing, or market equilibrium. Each additive term is upper semi-continuous, proper concave, maybe non-smooth, and possibly extended-valued. In a leading interpretation, each term, alongside its block of coordinates, is controlled by an independent economic agent. Vectors are construed as contingent claims or as bundles of commodities. These are diverse, divisible, and perfectly transferable. At every stage two randomly selected agents make bilateral direct exchanges. The amounts transferred between the two parties depend on the difference between their generalized gradients. The resulting process-and the associated convergence analysis-fits the frames of stochastic programming. Motivation stems from exchange markets.