scholarly journals Equivalence of Stochastic and Deterministic Mechanisms

Econometrica ◽  
2019 ◽  
Vol 87 (4) ◽  
pp. 1367-1390 ◽  
Author(s):  
Yi-Chun Chen ◽  
Wei He ◽  
Jiangtao Li ◽  
Yeneng Sun
Keyword(s):  
Mechanism Design ◽  
Type Distribution ◽  
Incentive Compatible ◽  
Monetary Transfers ◽  
Ex Ante ◽  
Finite Set ◽  
Multidimensional Types ◽  
Social Surplus ◽  
Interdependent Valuations ◽  
Incentive Compatible Mechanism

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.

Learning and Mechanism Design: An Experimental Test of School Matching Mechanisms with Intergenerational Advice

2019 ◽  
Vol 129 (623) ◽  
pp. 2779-2804 ◽  
Author(s):  
Tingting Ding ◽  
Andrew Schotter
Keyword(s):  
Social Learning ◽  
Mechanism Design ◽  
Experimental Test ◽  
Real World ◽  
Dominant Strategy ◽  
Truth Telling ◽  
The Real ◽  
Incentive Compatible ◽  
Short Period ◽  
Incentive Compatible Mechanism

Abstract While the mechanisms that economists design are typically static, one-shot games, in the real world, mechanisms are used repeatedly by generations of agents who engage in them for a short period of time and then pass on advice to their successors. Hence, behaviour evolves via social learning and may diverge dramatically from that envisioned by the designer. We demonstrate that this is true of school matching mechanisms—even those for which truth-telling is a dominant strategy. Our results indicate that experience with an incentive-compatible mechanism may not foster truthful revelation if that experience is achieved via social learning.

Monopoly Regulation Under Relaxed Pareto Efficiency

2017 ◽  
Vol 5 (2) ◽  
pp. 162-176
Author(s):  
Ismail Saglam
Keyword(s):  
Marginal Cost ◽  
Regulatory Environment ◽  
Pareto Dominance ◽  
Incentive Compatible ◽  
Monopoly Regulation ◽  
Dominance Relationships ◽  
Ex Post ◽  
Ex Ante ◽  
Pareto Axiom ◽  
Set Of Points

Baron and Myerson (BM; 1982, Econometrica, 50(4), 911–930) propose an incentive-compatible, individually rational and ex ante socially optimal direct-revelation mechanism to regulate a monopolistic firm with unknown costs. Their mechanism is not ex post Pareto dominated by any other feasible direct-revelation mechanism. However, there also exist an uncountable number of feasible direct-revelation mechanisms that are not ex post Pareto dominated by the BM mechanism. To investigate whether the BM mechanism remains in the set of ex post undominated mechanisms when the Pareto axiom is slightly weakened, we introduce the ∈-Pareto dominance. This concept requires the relevant dominance relationships to hold in the support of the regulator’s beliefs everywhere except for a set of points of measure ∈, which can be arbitrarily small. We show that a modification of the BM mechanism which always equates the price to the marginal cost can ∈-Pareto dominate the BM mechanism at uncountably many regulatory environments, while it is never ∈-Pareto dominated by the BM mechanism at any regulatory environment.

scholarly journals Deterministic, Strategyproof, and Fair Cake Cutting

2017 ◽  
Author(s):  
Vijay Menon ◽  
Kate Larson
Keyword(s):  
Mechanism Design ◽  
Impossibility Result ◽  
Restricted Class ◽  
Piecewise Constant ◽  
Incentive Compatible ◽  
Negative Results ◽  
Cake Cutting ◽  
Design Perspective ◽  
A Minor ◽  
Cutting Problem

We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show that for even the restricted class of piecewise constant valuations there exists no direct-revelation mechanism that is strategyproof and even approximately proportional. Subsequently, we remove the non-wasteful constraint and show another impossibility result stating that there is no strategyproof and approximately proportional direct-revelation mechanism that outputs contiguous allocations, again, for even the restricted class of piecewise constant valuations. In addition to the above results, we also present some negative results when considering an approximate notion of strategyproofness, show a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and finally also present a (minor) modification to the well-known Even-Paz algorithm that has better incentive-compatible properties for the cases when there are two or three agents.

A Note on the Multidimensional Monopolist Problem and Intertemporal Price Discrimination

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Mariano G Runco
Keyword(s):  
Price Discrimination ◽  
Price Strategy ◽  
Incentive Compatible ◽  
Step Functions ◽  
Intertemporal Price Discrimination ◽  
Ex Ante ◽  
Posted Prices ◽  
Price Discriminate ◽  
Heterogeneous Consumers ◽  
Over Time

This note analyzes a model of a monopolist selling multiple goods to a continuum of heterogeneous consumers. The implementation of Direct Revelation Mechanisms is analyzed in that setting, finding that it is possible for the monopolist to implement all Stochastic Incentive Compatible Mechanisms by committing to post a decreasing sequence of prices. The posted prices depend on time and have the desirable property of being step functions. When the optimal mechanisms are stochastic, it is optimal for the monopolist to price discriminate over time, contrary to the conventional wisdom that a single-good monopolist committed to an ex-ante price strategy will not price discriminate.

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