Virtual Valuation Research Articles

CVM을 이용한 부동산 중개서비스의 지불가능용의액 추정에 관한 연구

Consumers, real estate agents, and real estate platforms are in conflict as the burden of brokerage fees increases due to the increase in housing costs and the expansion of proptech services. This study focuses on resolving conflicts among parties of real estate transactions, and especially analyzes how consumers evaluate the value of brokerage fees incurred when using brokerage services and direct brokerage services, a core field of prop-tech. The research method employed the virtual valuation method, which is commonly used to measure the value of non-market goods such as difficult-to-measure goods and services. As an empirical measurement technique, the double bounded dichotomous choice question model was utilized in this case. A survey was used to collect analysis data and divided into five types to increase the validity of the research results. In addition, the secured sample was able to estimate the willingness to pay for real estate brokerage services using the logit model, a quantitative analysis model to measure the value and acceptability of such services. The analysis results revealed that the estimated willingness to pay for brokerage fees was 2,581,370 won for sales and 970,185 won for lease transactions.

A closer look at two conjectures about irregular marginal revenue

A common assumption in models where buyers have private information is for the buyers to draw their private values from distribution F with density f. Optimal mechanisms differ depending on whether the marginal revenue (buyer’s virtual valuation) is increasing (in which case F is said to be regular) or not increasing (in which case F is said to be irregular). This note examines two conjectures about sufficient conditions for irregularity made in the literature—made but not proven. We develop counterexamples to show that these conjectures are false, thereby reducing the set of distributions previously thought to be irregular.

Revenue-Optimal Deterministic Auctions for Multiple Buyers with Ordinal Preferences over Fixed-Price Items

In this article, we introduce a Bayesian revenue-maximizing mechanism design model where the items have fixed, exogenously given prices. Buyers are unit-demand and have an ordinal ranking over purchasing either one of these items at its given price or purchasing nothing. This model arises naturally from the assortment optimization problem, in that the single-buyer optimization problem over deterministic mechanisms reduces to deciding on an assortment of items to “show.” We study its multi-buyer generalization in the simplest setting of single-winner auctions or, more broadly, any service-constrained environment. Our main result is that if the buyer rankings are drawn independently from Markov chain choice models, then the optimal mechanism is computationally tractable, and structurally a virtual welfare maximizer. We also show that for ranking distributions not induced by Markov chains, the optimal mechanism may not be a virtual welfare maximizer. Finally, we apply our virtual valuation notion for Markov chains, in conjunction with existing prophet inequalities, to improve algorithmic guarantees for online assortment problems.

Optimal equity auction with interdependent valuations

This study considers a seller using an equity auction to sell an indivisible asset for which bidders have interdependent valuations. First, we introduce bidders’ conditional virtual valuations for this setting, and identify sufficient conditions for conditional virtual valuations’ monotonicity and single-crossing property. Then, we characterize the optimal equity mechanism, which is ex post incentive compatible and individually rational. In general symmetric case, English equity auction or two-round sealed bid equity auction with an endogenous take-it-or-leave-it contract can implement the optimal ex post equity auction; in asymmetric case, English auction with an endogenous discriminatory equity contract could be constructed for the implementation of the optimal ex post equity auction under certain conditions.

In the basic auction model, the optimal reserve price may depend on the number of bidders

A widespread claim in the auction literature about the most well known auction setting with i.i.d. private values is that the optimal reserve price for a second price auction is independent of the number n of bidders. This is indeed the case if the virtual valuation function is increasing, but this result fails to hold if the virtual valuation is non-monotone. In such case the optimal reserve price is weakly increasing in n and, as n tends to infinity, it tends to the highest regular valuation with zero virtual value.

Dynamic slot allocations with different patience levels

This study considers a mechanism design problem in which service slots are allocated over time to buyers arriving in different periods. Buyers have a multidimensional type representing their valuation and patience level. Some buyers can accept delayed service, whereas others cannot. The seller fully commits to a deterministic mechanism. We show that a mechanism is periodic ex-post incentive compatible if and only if the allocation rule is monotone in valuation and “price equivalence” holds. The dynamic pivot mechanism with reserve prices maximizes the seller's expected revenue if and only if the virtual valuation function is affine.

Optimal Auctions for Spiteful Bidders

Designing revenue-optimal auctions for various settings is perhaps the most important, yet sometimes most elusive, problem in mechanism design. Spiteful bidders have been intensely studied recently, especially because spite occurs in many applications in multiagent system and electronic commerce. We derive the optimal auction for such bidders (as well as bidders that are altruistic). It is a generalization of Myerson’s (1981) auction. It chooses an allocation that maximizes agents’ virtual valuations, but for a generalized definition of virtual valuation. The payment rule is less intuitive. For one, it takes each bidder’s own report into consideration when determining his payment. Moreover, bidders pay even if the seller keeps the item; a similar phenomenon has been shown in other settings with neg- ative externalities (Jehiel, Moldovanu, and Stacchetti 1996; Deng and Pekec 2011). On the other hand, a novel aspect of our auction is that it sometimes subsidizes losers when the item is sold to some other bidder. We also derive a revenue equivalence theorem for this setting. Using it, we generate a short proof of (a slight generalization of) the previously known result that, in two-bidder settings with independently uniformly drawn valuations, second-price auctions yield greater expected revenue than first-price auctions. Finally, we present a template for comparing the expected revenues of any two auction mechanisms that have the same allocation rule (for the valuations distributions at hand).

Pandora's Loot Box

Virtual worlds are a frontier unlike any other. But as virtual worlds grow exponentially in the internet age, they find more overlap with the real world and the laws that govern it. One such emerging intersection is the advent of “loot boxes.” Borrowing their design from the gambling industry, loot boxes operate as a hybrid between slot machines and packs of trading cards. A consumer pays real-world money to buy a virtual box without knowing its contents. Upon opening the box, the consumer receives a virtual good that may be of great value, but may also be a common or duplicate virtual good of little to no value. Such is the gamble that fuels this troubling and addictive virtual gaming mechanism. While scholars and government agencies have considered differing views regarding the ownership, property, and sale of virtual goods, few have considered the gambling perspective brought on by loot boxes. This Article offers a unique legal exploration of the overlaps between loot boxes and gambling by proposing that state gambling laws be updated to include the social science concept of perceived value that explains consumer behavior. By examining the perceived value of loot box rewards, it becomes clear that consumers are driven to gamble for virtual goods based on the value they bestow in the virtual world—irrespective of any real-world value. This framework of virtual valuation is key in properly regulating loot boxes as a form of gambling, which plays on the same psychological triggers as do slot machines. This new framework carries important implications outside of gambling regulation in virtual worlds, while also contributing to the developing literature exploring the ethical and economic dilemmas when software is designed to increase user engagement by exploiting psychological weaknesses.

Dynamic Slot Allocations with Different Patience Levels

This study considers a mechanism design problem in which service slots are allocated over time to buyers arriving at different periods. Some buyers can accept delayed service, whereas others cannot. Buyers have a multidimensional type representing their valuation and patience level. The seller fully commits to a mechanism with or without complete contingent contracts. We show that a deterministic mechanism is periodic ex-post incentive compatible if and only if the allocation rule is monotone in valuation and the equivalence holds. In cases both with and without contingent contracts, the dynamic pivot mechanism with a reserve price maximizes the seller's expected revenue under a regularity condition, which is characterized by the linearity of the virtual valuation function. When the regularity holds, the fully optimal mechanism with contingent contracts is multi-contracting-proof, whereas the constrained optimal mechanism without contingent contracts is not.

Truthful Mobile Crowdsensing for Strategic Users With Private Data Quality

Mobile crowdsensing has found a variety of applications (e.g., spectrum sensing, environmental monitoring) by leveraging the “wisdom” of a potentially large crowd of mobile users. An important metric of a crowdsensing task is data accuracy, which relies on the data quality of the participating users' data (e.g., users' received SNRs for measuring a transmitter's transmit signal strength). However, the quality of a user can be its private information (which, e.g., may depend on the user's location) that it can manipulate to its own advantage, which can mislead the crowdsensing requester about the knowledge of the data's accuracy. This issue is exacerbated by the fact that the user can also manipulate its effort made in the crowdsensing task, which is a hidden action that could result in the requester having incorrect knowledge of the data's accuracy. In this paper, we devise truthful crowdsensing mechanisms for Quality and Effort Elicitation (QEE), which incentivize strategic users to truthfully reveal their private quality and truthfully make efforts as desired by the requester. The QEE mechanisms achieve the truthful design by overcoming the intricate dependency of a user's data on its private quality and hidden effort. Under the QEE mechanisms, we show that the crowdsensing requester's optimal (RO) effort assignment assigns effort only to the best user that has the smallest “virtual valuation”, which depends on the user's quality and the quality's distribution. We also show that, as the number of users increases, the performance gap between the RO effort assignment and the socially optimal effort assignment decreases, and converges to 0 asymptotically. We further discuss some extensions of the QEE mechanisms. Simulation results demonstrate the truthfulness of the QEE mechanisms and the system efficiency of the RO effort assignment.

Performance bounds for optimal sales mechanisms beyond the monotone hazard rate condition

In mechanism design, Myerson’s classical regularity assumption is often too weak to imply quantitative results about the performance of sales mechanisms. For example, ratios between revenue and welfare, or sales probabilities may vanish at the boundary of Myerson regularity. Therefore, for quantitative results, many authors have resorted to much stronger assumptions such as the monotone hazard rate condition. This motivates us to explore performance bounds for sales mechanisms that follow from a quantitative version of Myerson regularity, which we call λ-regularity. The parameter λ interpolates from Myerson regularity to the monotone hazard rate condition and beyond. We provide four equivalent definitions of the concept. These rely on a growth condition on the virtual valuations function (known as α-strong regularity), a monotonicity condition on a generalized hazard rate, a ρ-concavity condition on survival functions and a comparison relation in the convex transform order. By highlighting the interplay between these different perspectives, we unify previous work in economics, computer science, applied mathematics and statistics. We demonstrate the usefulness of λ-regularity for quantitative mechanism design by proving various performance bounds for sales mechanisms. In addition, we briefly consider applications beyond auctions and mechanism design such as the measurement of inequality in populations.

Dynamic mechanism design of single forward-looking agent

The article mainly studies the optimal mechanism structure and nature of dynamic mechanism design. For forward-looking principals and agents, under the assumptions that the principal has the commitment, and the agent that participates cooperation in each cycle has the fixed-participation cost and the liquidity constraint, the article portrays the link between cycles, and comprehensively considering constraints such as incentive compatibility, a mechanism design model in a dynamic environment was established in the form of recursive equations. Then, the article proposes the concept of dynamic virtual valuation for multi-period problems, which fully considers the client's current income and future earnings. Furthermore, it is found that when the distribution of private information satisfies certain sufficient conditions, the dynamic virtual valuation will still have some special properties, and the structure of the optimal mechanism can be solved.

Optimal Deterministic Mechanism Design: Type-Independent Preference Orderings

We investigate revenue maximisation in general allocation problems with incomplete information, where we assume quasi-linearity, private values, independent type distributions and single-dimensionality of type spaces. We require a mechanism to be deterministic, strategy-proof and ex-post individually rational. We assume that each player has a type-independent preference ordering over deterministic allocations. We show that the Myerson’s technique to solve the incentive-constrained revenue maximisation problem in single-unit auctions can be applied to general allocation problems, where the incentive-constrained revenue maximisation problem can be reduced to the simple maximisation problem of the sum of players’ virtual valuations without imposing any incentive constraint.

Optimal profit sharing mechanisms with type-dependent outside options

This study considers a principal using a profit sharing mechanism to select one among multiple agents with type-dependent outside options to operate a project. Under mild conditions, we fully characterize revenue-maximizing profit sharing mechanisms. Moreover, we show that if the monotonicity of the virtual valuation holds, then optimal sharing mechanisms can be implemented by the first- and second-price share auctions with an optimally chosen reserve price. We further find that the principal’s expected revenue improves as outside options diminish and break-even shares become less responsive. When outside options are linear in types, full surplus extraction is obtained.

An Extensible and Flexible Truthful Auction Framework for Heterogeneous Spectrum Markets

In this paper, we propose an extensible and flexible truthful auction framework that is individually-rational and self-collusion resistant. By properly setting one simple parameter, this framework yields efficient auctions (like Vickery–Clarke–Groves), (sub)optimal auctions (like Myerson’s optimal mechanism), and budget-balanced double auctions; by carefully choosing virtual valuation functions for the bidders, it can produce attribute-aware auctions that take the channel diversity into consideration. The framework adopts a novel procedure that can prevent bidder self-collusion resulted from the bid diversity. In order to reduce the computational complexity of our framework, we propose a greedy auction scheme that possesses all the economic properties of our auction framework. We also prove the performance bound of the greedy algorithm under certain condition. Theoretical analysis and case studies demonstrate the strength of our auction framework in handling various considerations in a practical heterogeneous spectrum market.

Nonparametric tests for strictly increasing virtual valuations

ABSTRACTThis paper shows that for absolutely continuous valuation distributions the increasing virtual valuations is equivalent to the increasing odds rate. Based on this new characterization we develop two nonparametric tests for the strictly increasing virtual valuations by using the generalized total time on test transform. The empirical type I error rate and power performance of the two tests are examined through Monte Carlo simulations. As illustrations the two tests are also applied to two real data sets collected from eBay.

Automated Design of Revenue-Maximizing Combinatorial Auctions

Designing optimal—that is, revenue-maximizing—combinatorial auctions (CAs) is an important elusive problem. It is unsolved even for two bidders and two items for sale. Rather than pursuing the manual approach of attempting to characterize the optimal CA, we introduce a family of CAs and then seek a high-revenue auction within that family. The family is based on bidder weighting and allocation boosting; we coin such CAs virtual valuations combinatorial auctions (VVCAs). VVCAs are the Vickrey-Clarke-Groves (VCG) mechanism executed on virtual valuations that are affine transformations of the bidders’ valuations. The auction family is parameterized by the coefficients in the transformations. The problem of designing a CA is thereby reduced to search in the parameter space of VVCA—or the more general space of affine maximizer auctions. We first construct VVCAs with logarithmic approximation guarantees in canonical special settings: (1) limited supply with additive valuations and (2) unlimited supply. In the main part of the paper, we develop algorithms that design high-revenue CAs for general valuations using samples from the prior distribution over bidders’ valuations. (Priors turn out to be necessary for achieving high revenue.) We prove properties of the problem that guide our design of algorithms. We then introduce a series of algorithms that use economic insights to guide the search and thus reduce the computational complexity. Experiments show that our algorithms create mechanisms that yield significantly higher revenue than the VCG and scale dramatically better than prior automated mechanism design algorithms. The algorithms yielded deterministic mechanisms with the highest known revenues for the settings tested, including the canonical setting with two bidders, two items, and uniform additive valuations. 1

Welfare-maximizing assignment of agents to hierarchical positions

We allocate agents to three kinds of hierarchical positions: top, medium, and low. No monetary transfers are allowed. We solve for the incentive-compatible (IC) mechanisms that maximize a family of weighted social welfares that includes utilitarian and Rawlsian welfares. When the market is tough (all agents bear positive risk of obtaining a low position in any IC and feasible mechanism), then the pseudomarket mechanism with equal budgets (PM) and the Boston mechanism without priorities (BM) yield identical assignments which are always optimal. Otherwise, when the market is mild, PM and BM differ and each one implements the optimal rule under different assumptions on the curvature of virtual valuations. We also establish that both BM and PM mechanisms guarantee IC Pareto-optimal assignments for a domain of preference distributions satisfying weak assumptions.

Optimal crowdsourcing contests

We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the principal only benefits from the submission with the highest quality. We give a theory for optimal crowdsourcing contests that mirrors the theory of optimal auction design: the optimal crowdsourcing contest is a virtual valuation optimizer (the virtual valuation function depends on the distribution of contestant skills and the number of contestants). We also compare crowdsourcing contests with more conventional means of procurement. In this comparison, crowdsourcing contests are relatively disadvantaged because the effort of losing contestants is wasted. We show that the total wasted effort is at most the maximum effort which implies that crowdsourcing contests are a 2-approximation to an idealized model of conventional procurement.

On the optimality of pure bundling for a monopolist

This paper considers a monopolist selling two objects to a single buyer with privately observed valuations. We prove that if the virtual valuation for each object is non-negative for all possible types, then the optimal price schedule is such that the objects are sold only in a bundle. Under an additional regularity condition, pure bundling is the optimal sale mechanism among all individually rational and incentive compatible mechanisms.