Equivalence of Stochastic and Deterministic Mechanisms

Abstract

We consider a general social choice environment that has multiple agents, a finite set of alternatives, independent types, and atomless type distribution. We show that for any Bayesian incentive compatible mechanism, there exists an equivalent deterministic mechanism that (1) is Bayesian incentive compatible; (2) delivers the same interim expected allocation probabilities and the same interim expected utilities for all agents; and (3) delivers the same ex ante expected social surplus. This result holds in settings with a rich class of utility functions, multidimensional types, interdependent valuations, and in settings without monetary transfers. To prove our result, we develop a novel methodology of mutual purification, and establish its link with the mechanism design literature.

Efficient sequential screening with informational externalities

“…The first is to the set of indirect deterministic mechanisms. In an indirect deterministic mechanism if agents play mixed strategies then the direct mechanism, that mimics the equilibrium strategies of the indirect mechanism, is not deterministic, see, e.g., Strausz (2003), Jarman and Meisner (2017), and Chen et al (2019). I find that all the results of the paper still hold even if we consider indirect deterministic mechanisms.…”

Tools for Estimation of “Deterministic Chaos” of Economic Sectoral Mesodynamic

“…The results of the experiment gave a representative assessment of the adequacy of the adopted methodology and the proposed tools. The authors tested the principle of synergetic deterministic chaos [ 1 – 3 ] and several models of econophysics based on mesodynamic data from 12 main economical sectors over 78 regions of Russia during the period from 2005 to 2017 [ 13 ]. Time series of the following industries are considered: construction and building, retail trade, natural resources extraction and mining, crude oil and gas extraction, metal ores extraction, industry and manufacturing, chemical industry, production of rubber and plastics, pharmacy, metallurgy, production of electronics and optical devices.…”

Loeb extension and Loeb equivalence

“…The Loeb measure construction ( [Loe75]) has many fruitful applications in various areas in mathematics such as probability theory (see [And76], [AR78], [Per81], [Kei84], [Sto86], [Lin90], [Lin04], [DRW18], [ADS18] etc), statistical decision theory (see [DR18]), potential theory ( [Loe76]), mathematical physics (see [AHKFL86]) and mathematical economics (see [BR74], [Kha74], [BR75], [KR75], [Kha76], [Ras78], [Emm84], [And85], [And88], [And91], [Sun96], [AKRS97], [Sun99], [KS99], [AKS03], [Rau07], [DS07], [AR08], [Sun16], [DQS18], [CHLS19], among others). 1 These applications are made possible by a well-developed theory of integration (see [Loe75] and [And76]), representation of measures (see [And82] and [Sti97]) and a Fubini theorem for Loeb measures (see [Kei84]).…”