arXiv subjects

Zhiming Feng

Publications and source records attributed to Zhiming Feng.

10 recordsLinked to original sources

arXiv2026

Decomposing Common Agency

This paper develops a decomposition methodology for common agency games in which each principal's payoff depends on her own outcome and the agent's type, but not on rivals' outcomes. The key step reduces each principal's best-response problem to a standard screening problem defined over the agent's indirect utility -- the upper envelope of her payoff over rivals' offerings. Individually best-responding mechanisms then assemble into a pure-menu perfect Bayesian equilibrium when a compatibility condition (utility-preserving recombination) ensures aligned tie-breaking across principals. Under a non-indifference condition, the decomposition recovers all equilibria except those sustained by menu items that no type of the agent actually selects but which nevertheless discipline the rival's screening problem. When principals' payoffs depend on the full allocation profile, the decomposition adapts only under substantive regularity conditions on the agent's off-path choice behavior, one of which coincides with Luce's choice axiom. I apply the methodology to two settings. In a quadratic-loss delegation model, equilibria feature one principal offering a finite menu of discrete ``regimes'' while the other receives piecewise full delegation within each regime. In a competitive bundling duopoly under intrinsic common agency, the decomposition yields equilibria exhibiting market splitting, in which firms specialize in complementary bundles, and asymmetric equilibria with a take-it-or-leave-it base contract paired with a nested or tree menu of upgrades.

econ.TH↗

arXiv2026

Self-Confirming Mechanisms

This paper studies mechanism design environments in which the designer does not know the distribution of agents' private information a priori and instead learns from agents' behavior induced by the mechanism itself. We formalize a notion of self-confirming mechanisms and a refinement thereof, capturing the idea that an equilibrium mechanism is optimal given the designer's belief and that this belief is consistent with the information produced by the mechanism. We establish a fictitious revelation principle, showing that any incentive-compatible mechanism can be represented as a direct mechanism with filtered type reports that preserve the original mechanism's informational content. Applying the framework to a monopoly problem, we show that, subject to an equilibrium refinement, dominant-strategy self-confirming mechanisms are exactly posted-price mechanisms with locally revenue-maximizing prices.

econ.TH↗

arXiv2025

A Constructive Characterization of Optimal Bundling

This paper studies a monopolist selling multiple goods to a consumer with one-dimensional private types. I provide a sufficient condition--single-crossing differences of virtual values together with monotonic differences of valuations--under which the monopolist's problem is equivalent to finding the upper envelope of the marginal revenue curves. This approach guarantees that the optimal mechanism is deterministic and can be implemented via a menu of bundles. I further characterize this upper envelope using a dominance notion. This characterization yields a constructive algorithm that computes the unique optimal menu by iteratively eliminating dominated bundles. As my main application, I use this framework to introduce and provide sufficient conditions for the optimality of tree bundling, a common but previously unmodeled sales strategy where the optimal menu contains a "root" bundle but features distinct upgrade paths. This structure captures prevalent sales practices across industries, from automobile manufacturers offering base models with customizable upgrade packages to software companies allowing modular feature additions.

econ.TH↗

arXiv2021

Globally conformally K\"ahler Einstein metrics on certain holomorphic bundles

The subject of this paper is the explicit momentum construction of complete Einstein metrics by ODE methods. Using the Calabi ansatz, further generalized by Hwang-Singer, we show that there are non-trivial complete conformally K\"ahler Einstein metrics on certain Hermitian holomorphic vector bundles and their subbundles over complete K\"ahler-Einstein manifolds. In special cases, we give the explicit expressions of of these metrics. These examples show that there is a compact K\"ahler manifold $M$ and its subvariety $N$ whose codimension is greater than 1 such that there is a complete conformally K\"ahler Einstein metric on $M-N$.

math.DG↗

arXiv2019

The regular quantizations of certain holomorphic bundles

In this paper, we study the regular quantizations of Kähler manifolds by using the first two coefficients of Bergman function expansions. Firstly, we obtain sufficient and necessary conditions for certain Hermitian holomorphic vector bundles and their ball subbundles to be regular quantizations. Secondly, we obtain that some projective bundles over the Fano manifolds $M$ admit regular quantizations if and only if $M$ are biholomorphically isomorphism to the complex projective spaces. Finally, we obtain the balanced metrics on certain Hermitian holomorphic vector bundles and their ball subbundles over the Riemann sphere.

math.CV↗

arXiv2018

Rawnsley's $\varepsilon$-function on some Hartogs type domains over bounded symmetric domains and its applications

The purpose of this paper is twofold. Firstly, we will compute the explicit expression of the Rawnsley's $\varepsilon$-function $\varepsilon_{(α,g(μ;ν))}$ of $\big(\big(\prod_{j=1}^kΩ_j\big)^{\mathbb{B}^{d_0}}(μ),g(μ;ν)\big)$, where $g(μ;ν)$ is a Kähler metric associated with the Kähler potential $-\sum_{j=1}^kν_j\ln N_{Ω_j}(z_j,\overline{z_j})^{μ_j}-\ln(\prod_{j=1}^kN_{Ω_j}(z_j,\overline{z_j})^{μ_j}-\|w\|^2)$ on the generalized Cartan-Hartogs domain $\big(\prod_{j=1}^kΩ_j\big)^{\mathbb{B}^{d_0}}(μ)$ and obtain necessary and sufficient conditions for $\varepsilon_{(α,g(μ;ν))}$ to become a polynomial in $1-\|\widetilde{w}\|^2$. Secondly, we study the Berezin quantization on $\big(\prod_{j=1}^kΩ_j\big)^{\mathbb{B}^{d_0}}(μ)$ with the metric $ g(μ;ν)$.

math.CV↗

arXiv2018

The first two coefficients of the Bergman function expansions for Cartan-Hartogs domains

Let $ϕ$ be a globally defined real Kähler potential on a domain $Ω\subset \mathbb{C}^d$, and $g_{F}$ be a Kähler metric on the Hartogs domain $ M=\{(z,w)\in Ω\times\mathbb{C}^{d_0}: \|w\|^2<e^{-ϕ(z)}\}$ associated with the Kähler potential $Φ_{F}(z,w)=ϕ(z)+F(ϕ(z)+\ln\|w\|^2)$. Firstly, we obtain explicit formulas of the coefficients $\mathbf{a}_j\;(j=1,2)$ of the Bergman function expansion for the Hartogs domain $( M,g_F)$ in a momentum profile $φ$. Secondly, using explicit expressions of $\mathbf{a}_j\;(j=1,2)$, we obtain necessary and sufficient conditions for the coefficients $\mathbf{a}_j\;(j=1,2)$ to be constants. Finally, we obtain all the invariant complete Kähler metrics on Cartan-Hartogs domains such that their the coefficients $\mathbf{a}_j\; (j=1,2)$ of the Bergman function expansions are constants.

math.CV↗

arXiv2015

Balanced metrics on the Fock-Bargmann-Hartogs domains

The Fock-Bargmann-Hartogs domain $D_{n,m}(μ)$ ($μ>0$) in $\mathbb{C}^{n+m}$ is defined by the inequality $\|w\|^2 0)$ on $D_{n,m}(μ)$, where $g(μ;ν)$ is the Kähler metric associated with the Kähler potential $Φ(z,w):=μν{\Vert z\Vert}^{2}-\ln(e^{-μ{\Vert z\Vert}^{2}}-\Vert w\Vert^2)$ ($ν>-1$) on $D_{n,m}(μ)$. The purpose of this paper is twofold. Firstly, we obtain an explicit formula for the Bergman kernel of the weighted Hilbert space of square integrable holomorphic functions on $(D_{n,m}(μ), g(μ;ν))$ with the weight $\exp\{-αΦ\}$ for $α>0$. Secondly, using the explicit expression of the Bergman kernel, we obtain the necessary and sufficient condition for the metric $αg(μ;ν)$ $(α>0)$ on the domain $D_{n,m}(μ)$ to be a balanced metric. So we obtain the existence of balanced metrics for a class of Fock-Bargmann-Hartogs domains.

math.CV↗

arXiv2014

Balanced metrics on some Hartogs type domains over bounded symmetric domains

The definition of balanced metrics was originally given by Donaldson in the case of a compact polarized Kähler manifold in 2001, who also established the existence of such metrics on any compact projective Kähler manifold with constant scalar curvature. Currently, the only noncompact manifolds on which balanced metrics are known to exist are homogeneous domains. The generalized Cartan-Hartogs domain $\big(\prod_{j=1}^kΩ_j\big)^{\mathbb{B}^{d_0}}(μ)$ is defined as the Hartogs type domain constructed over the product $\prod_{j=1}^kΩ_j$ of irreducible bounded symmetric domains $Ω_j$ $(1\leq j \leq k)$, with the fiber over each point $(z_1,...,z_k)\in \prod_{j=1}^kΩ_j$ being a ball in $\mathbb{C}^{d_0}$ of the radius $\prod_{j=1}^kN_{Ω_j}(z_j,\bar{z_j})^{\frac{μ_j}{2}}$ of the product of positive powers of their generic norms. Any such domain $\big(\prod_{j=1}^kΩ_j\big)^{\mathbb{B}^{d_0}}(μ)$ $(k\geq 2)$ is a bounded nonhomogeneous domain. The purpose of this paper is to obtain necessary and sufficient conditions for the metric $αg(μ)$ $(α>0)$ on the domain $\big(\prod_{j=1}^kΩ_j\big)^{\mathbb{B}^{d_0}}(μ)$ to be a balanced metric, where $g(μ)$ is its canonical metric. As the main contribution of this paper, we obtain the existence of balanced metrics for a class of such bounded nonhomogeneous domains.

math.CV↗

arXiv2014

On canonical metrics on Cartan-Hartogs domains

The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan-Hartogs domain $Ω^{B^{d_0}}(μ)$ endowed with the canonical metric $g(μ)$, we obtain an explicit formula for the Bergman kernel of the weighted Hilbert space $\mathcal{H}_α$ of square integrable holomorphic functions on $(Ω^{B^{d_0}}(μ), g(μ))$ with the weight $\exp\{-αφ\}$ (where $φ$ is a globally defined Kähler potential for $g(μ)$) for $α>0$, and, furthermore, we give an explicit expression of the Rawnsley's $\varepsilon$-function expansion for $(Ω^{B^{d_0}}(μ), g(μ)).$ Secondly, using the explicit expression of the Rawnsley's $\varepsilon$-function expansion, we show that the coefficient $a_2$ of the Rawnsley's $\varepsilon$-function expansion for the Cartan-Hartogs domain $(Ω^{B^{d_0}}(μ), g(μ))$ is constant on $Ω^{B^{d_0}}(μ)$ if and only if $(Ω^{B^{d_0}}(μ), g(μ))$ is biholomorphically isometric to the complex hyperbolic space. So we give an affirmative answer to a conjecture raised by M. Zedda.

math.CV↗