A competitive market mechanism is a prominent example of a non-binary social choice rule, typically defined for a special class of economic environments in which each social state is an economic allocation of private goods, and individuals' preferences concern only their own personal consumption. This chapter begins by discussing which Pareto efficient allocations can be characterized as competitive equilibria with lump-sum transfers. It also discusses existence and characterization of such equilibria without lump-sum transfers. The second half of the chapter focuses on continuum economies, for which such characterization results are much more natural given that agents have negligible influence over equilibrium prices
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