Existence of Walrasian equilibria with discontinuous, non-ordered, interdependent and price-dependent preferences, without free disposal, and without compact consumption sets

We extend a result on existence of Walrasian equilibria in He and Yannelis (Econ Theory 61:497–513, 2016) by replacing the compactness assumption on consumption sets made there by the standard assumption that these sets are closed and bounded from below. This provides a positive answer to a question explicitly raised in He and Yannelis (Econ Theory 61:497–513, 2016). Our new equilibrium existence theorem generalizes many results in the literature as we do not require any transitivity or completeness or continuity assumption on preferences, initial endowments need not be in the interior of the consumption sets, preferences may be interdependent and price-dependent, and no monotonicity or local non satiation is needed for any of the agents.

Absence of Envy among “Neighbors” Can Be Enough

We assume that the set of agents is decomposed into several classes containing individuals related each other in some way, for example groups of neighbors. We propose a new definition of fairness by requiring efficiency and envy-freeness only within each group. We identify conditions under which absence of envy among “neighbors” is enough to ensure fairness in the entire society. We also show that equal-income Walrasian equilibria are the only fair allocations according to our notion, deriving as corollaries the equivalence theorems of Zhou (1992) and Cato (2010). The analysis is conducted in atomless economies as well as in mixed markets.

From Jungle to Civilized Economy: The Power Foundation of Exchange Economy Equilibrium

This article explores the evolution of a civilized exchange economy from an anarchistic environment. I analyze a model of stochastic jungle bargaining mechanism and show that it implements the Talmud Rule allocation (Aumann, R. J., and M. Maschler. 1985. “Game Theoretic Analysis of a Bankruptcy Problem from the Talmud.” Journal of Economic Theory 36 (2): 195–213.) in subgame perfect equilibrium. This Pareto-inefficient allocation constitutes the initial endowment of a stable exchange economy and supports stable Walrasian equilibria, implying that civilized economies could evolve from a Hobbesian state of nature without social contract or regulator. The moral implications of these results are also briefly discussed.