Leontief function is one of the most widely used function in economic modeling, for both production and preferences. However it lacks the desirable property of diminishing returns. In this paper, we consider piecewise Leontief concave (p-Leontief) utility function which consists of a set of Leontief-type segments with decreasing returns and upper limits on the utility. Leontief is a special cas...

We reconsider the allocational invariance of equilibria to different formulations of market completeness. We identify the so-far neglected assumption of sophisticated behavior as crucial to this result. The paper studies three market structures. First, the Arrow-Debreu setting is considered. Second, sequentially complete markets are analyzed, where goods on the spot markets and all contingent o...

We present polynomial-time interior-point algorithms for solving the Fisher and Arrow-Debreu competitive market equilibrium problems with linear utilities and n players. Both of them have the arithmetic operation complexity bound of O(n log(1/2)) for computing an 2-equilibrium solution. If the problem data are rational numbers and their bit-length is L, then the bound to generate an exact solut...

We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities. Our algorithm views the allocation of money as flows and iteratively improves the balanced flow as in [Devanur et al. 2008] for Fisher’s model. We develop new methods to carefully deal with the flows and surpluses A preliminary version of this paper ...

Abstract In this article we combine Debreu’s (Proc Natl Acad Sci 38(10):886–893, 1952) social system with Hurwicz’s (Econ Design 1(1):1–14, 1994; Am Econ Rev 98(3):577–585, 2008) ideas of embedding a “desired” game form into “natural” that includes all feasible behavior, even if it is “illegal” according to the desired form. For resulting socio-legal extend concepts and its equilibria Debreu–Hu...

This article defines and analyzes a ‘‘sparse max’’ operator, which is a less than fully attentive and rational version of the traditional max operator. The agent builds (as economists do) a simplified model of the world which is sparse, considering only the variables of first-order importance. His stylized model and his resulting choices both derive from constrained optimization. Still, the spa...

Most philosophers of economics are hostile towards neoclassical economics in general and general equilibrium theory in the vein of Arrow and Debreu in particular. Especially the latter’s dismissal is justified by pointing out its lack of direct relevance for an understanding of real economies. Many recommend a more pragmatic approach along the lines of Keynes instead. The criterion of scientifi...

We provide a dual perspective on technical efficiency evaluation, in two respects. First, we build on the price assumptions implicitly associated with the notion of technical efficiency in a general equilibrium framework to characterize a set of appropriate references to be used in the technical efficiency evaluation of an inputoutput vector. Some existing evaluation methods always select an el...

Existing electricity market designs assume risk neutrality and lack risk-hedging instruments, which leads to suboptimal outcomes reduces the overall efficiency. This letter enables risk-trading in chance-constrained stochastic by introducing Arrow-Debreu Securities (ADS) derives a risk-averse market-clearing model with trading. To enable trading, probability space of underlying uncertainty is d...

The market equilibrium problem has a long and distinguished history. In 1874, Walras published the famous “Elements of Pure Economics”, where he describes a model for the state of an economic system in terms of demand and supply, and expresses the supply equals demand equilibrium conditions [62]. In 1936, Wald gave the first proof of the existence of an equilibrium for the Walrasian system, alb...