For economies in which goods are available in several (discrete) units, this paper identifies two notions of substitutes. The weaker notion guarantees monotonicity of tatonnement processses and convergence of clock auctions to a pseudo-equilibrium, but only the stronger notion, which treats each...

We distinguish two notions of substitutes for discrete inputs of a firm. Class substitutes are defined assuming that units of a given input have the same price while unitary substitutes treat each unit as a distinct input with its own price. Unitary substitutes is necessary and sufficient for...

How does renegotiation affect contracts between a principal and an agent subject to persistent private information and moral hazard? This paper introduces a concept of renegotiation-proofness, which adapts to stochastic games the concepts of weak renegotiation-proofness and internal consistency...

How does renegotiation affect contracts between a principal and an agent subject to persistent private information and moral hazard? This paper introduces a concept of renegotiationproofness, which adapts to stochastic games the concepts of weak renegotiation-proofness and internal consistency...