Envelope Theorems for Arbitrary Choice Sets

By Paul R. Milgrom, Ilya Segal. 2002

1,417 citations recorded by the source corpus.

Subfields: Management Information Systems, Management Science and Operations Research, Marketing, Mathematical Optimization, Economics & Operations Research

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Citations in the corpus

Wasserstein GAN (2017, background): “We know that by a simple envelope theorem ([12], Theorem 1) that for any f ∈ X ∗ ( θ ) when both terms are well-deﬁned.”
Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach (2015, methodology): “From the envelope theorem [14], it follows that dH ( y ) dy = λ, is Lipschitz in y , with constant C ( x, a )+ γM .”
Efficient Allocations in Dynamic Private Information Economies with Persistent Shocks: A First-Order Approach (2013, methodology): “Since (3.2) holds, Ŝt(θ t−1, θ̂t, θt) is maximized at θ̂t = θt and by Theorem 2 of Milgrom and Segal (2002), it can be represented by an integral of its derivative.”
Managerial Turnover in a Changing World (2012, background): “The same sequence of inequalities as in theorem 2 of Milgrom and Segal ð2002Þ then implies the result.”
The Theory of Optimal Delegation With an Application to Tariff Caps (2013, neutral): “Then, we write constraint (23) as two inequalities:∫ γ γ π(γ̃)dγ̃ +U − γπ(γ)− b(π(γ)) ≤ 0 for all γ ∈ Γ (25) − ∫ γ γ π(γ̃)dγ̃ −U + γπ(γ)+ b(π(γ)) ≤ 0 for all γ ∈ Γ (26) 47See Milgrom and Segal (2002).”
Spatial pricing in ride-sharing networks (2017, neutral): “48 Electronic copy available at: https://ssrn.com/abstract=2868080 Thus, it follows from Bonnans and Shapiro (2013) and Milgrom and Segal (2002) (Corollary 5) that for some primal optimal solution (p?,Y?, δ?)”
Generalized Energy Based Models (2020, methodology): “We are in position to apply Milgrom and Segal (2002)(Theorem 3) which ensures thatK(θ) admits left and right partial derivatives given by ∂ e K(θ)= lim t>0 t→0 ∂θLθ(E θ+te)e, ∂− e K(θ)= lim t<0 t→0 ∂θLθ(E θ+te)e, (28)”
Dynamic Mechanism Design: A Myersonian Approach (2014, neutral): “Furthermore, by U-ELC, ICFOCi,t+1, and F-BIR all the derivatives above are bounded.”