Competitive pricing and the core: With reference to matching

Lloyd Shapley's contributions with respect to the core are interpreted as subdifferentiability characterizations of the pricing of individuals that is similar to the pricing of commodities in economic models of exchange with transferable utility. Differentiability of the core is interpreted as perfect substitutability with respect to the pricing of individuals. Differentiability implies, but is not implied by, equivalence of the core and Walrasian equilibria. Differentiability eliminates opportunities for strategic misrepresentation of utilities. The assignment model with transferable utility is framed in the setting of exchange economies and its individual and commodity pricing is extended to non-transferable utility.