Posted Price Mechanism Research Articles

Selling to a manager and a budget-constrained agent

We analyze a model of selling a single object to a manager-agent pair who want to acquire the object for a firm. The manager and the agent have different assessments of the object’s value to the firm. The agent is budget-constrained while the manager is not. The agent participates in the mechanism, but she can (strategically) approach the manager for decision-making. We derive the revenue-maximizing mechanism in a two-dimensional type space (values of the agent and the manager). We show that below a threshold budget, a mechanism involving two posted prices and three outcomes (one of which involves randomization) is the optimal mechanism for the seller. Otherwise, a single posted price mechanism is optimal.

Buying from a Group

A buyer procures a good owned by a group of sellers whose heterogeneous cost of trade is private information. The buyer must either buy the whole good or nothing, and sellers share the transfer in proportion to their share of the good. We characterize the optimal mechanism: trade occurs if and only if the buyer’s benefit of trade exceeds a weighted average of sellers’ virtual costs. These weights are endogenous, with sellers who are ex ante less inclined to trade receiving higher weight. This mechanism always outperforms posted-price mechanisms. An extension characterizes the entire Pareto frontier. (JEL D44, D63, D82, Q15, Q24)

Fully Dynamic Online Selection through Online Contention Resolution Schemes

We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial constraints. In the classical ``incremental'' version of the problem, selected elements remain active until the end of the input sequence. On the other hand, in the fully dynamic version of the problem, elements stay active for a limited time interval, and then leave. This models, for example, the online matching of tasks to workers with task/worker-dependent working times, and sequential posted pricing of perishable goods. A successful approach to online selection problems in the adversarial setting is given by the notion of Online Contention Resolution Scheme (OCRS), that uses a priori information to formulate a linear relaxation of the underlying optimization problem, whose optimal fractional solution is rounded online for any adversarial order of the input sequence. Our main contribution is providing a general method for constructing an OCRS for fully dynamic online selection problems. Then, we show how to employ such OCRS to construct no-regret algorithms in a partial information model with semi-bandit feedback and adversarial inputs.

Stateful Posted Pricing with Vanishing Regret via Dynamic Deterministic Markov Decision Processes

An online problem called dynamic resource allocation with capacity constraints (DRACC) is introduced and studied in the realm of posted price mechanisms. This problem subsumes several applications of stateful pricing, including but not limited to posted prices for online job scheduling and matching over a dynamic bipartite graph. Because existing online learning techniques do not yield vanishing regret for this problem, we develop a novel online learning framework over deterministic Markov decision processes with dynamic state transition and reward functions. Following that, we prove, based on a reduction to the well-studied problem of online learning with switching costs, that if the Markov decision process admits a chasing oracle (i.e., an oracle that simulates any given policy from any initial state with bounded loss), then the online learning problem can be solved with vanishing regret. Our results for the DRACC problem and its applications are then obtained by devising (randomized and deterministic) chasing oracles that exploit the particular structure of these problems. Funding: The work of Y. Emek was supported in part by the Israel Science Foundation [Grant 1016/17]. The work of R. Lavi was partially supported by the Israel Science Foundation [Grant 2560/17] and the National Natural Science Foundation of China [Grant 2560/17]. The work of R. Niazadeh was supported by the University of Chicago Booth School of Business. The work of Y. Shi was partially supported at the Technion by the Council for Higher Education [fellowship], and at Shandong University by the Science Fund Program of Shandong Province for Distinguished Oversea Young Scholars [Grant 2023HWYQ-006].

Bilateral Trade: A Regret Minimization Perspective

Bilateral trade, a fundamental topic in economics, models the problem of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. In this paper, we cast the bilateral trade problem in a regret minimization framework over T rounds of seller/buyer interactions, with no prior knowledge on their private valuations. Our main contribution is a complete characterization of the regret regimes for fixed-price mechanisms with different feedback models and private valuations, using as a benchmark the best fixed price in hindsight. More precisely, we prove the following tight bounds on the regret: [Formula: see text] for full-feedback (i.e., direct revelation mechanisms). [Formula: see text] for realistic feedback (i.e., posted-price mechanisms) and independent seller/buyer valuations with bounded densities. [Formula: see text] for realistic feedback and seller/buyer valuations with bounded densities. [Formula: see text] for realistic feedback and independent seller/buyer valuations. [Formula: see text] for the adversarial setting. Funding: This work was partially supported by the European Research Council Advanced [Grant 788893] AMDROMA “Algorithmic and Mechanism Design Research in Online Markets”, the Ministero dell’Istruzione, dell’Università e della Ricerca PRIN project ALGADIMAR “Algorithms, Games, and Digital Markets”, the AI Interdisciplinary Institute ANITI (funded by the French “Investing for the Future—PIA3” program under the [Grant agreement ANR-19-PI3A-0004], the project BOLD from the French national research agency (ANR), the EU Horizon 2020 ICT-48 research and innovation action ELISE (European Learning and Intelligent Systems Excellence, [Grant agreement 951847].

Promoting Spatial Coordination in Flood Buyouts in the United States: Four Strategies and Four Challenges from the Economics of Land Preservation Literature

Managed retreat in the form of voluntary flood-buyout programs provides homeowners with an alternative to repairing and rebuilding residences that have sustained severe flood damage. Buyout programs are most economically efficient when groups of neighboring properties are acquired because they can then create unfragmented flood control areas and reduce the cost of providing local services. However, buyout programs in the United States often fail to acquire such efficient, unfragmented spaces, for various reasons, including long administrative timelines, the way in which buyout offers are made, desires for community cohesion, and attachments to place. Buyout programs have relied primarily on posted price mechanisms involving offers that are accepted or rejected by homeowners with little or no negotiation. In this paper, we describe four alternative strategies that have been used successfully in land-preservation agricultural–environmental contexts to increase acceptance rates and decrease fragmentation: agglomeration bonuses, reverse auctions, target constraints, and hybrid approaches. We discuss challenges that may arise during their implementation in the buyout context—transaction costs, equity and distributional impacts, unintended consequences, and social pressure—and recommend further research into the efficiency and equity of applying these strategies to residential buyout programs with the explicit goal of promoting spatial coordination.

Comparison of four mechanisms for request exchange in collaborative transportation

AbstractThis paper presents frameworks for auction‐based and posted price mechanisms for exchanging requests between carriers operating in the same geographical areas. Similar mechanisms have been studied before in a rather isolated manner. In this work, all mechanisms are tested within the same scenario and by comparing their results; the aim is to obtain insights regarding the efficiency gains they offer to the network and the required information for their application. Moreover, this comparison provides a clear idea of what is needed to implement each mechanism and the results to expect if one invests in the mentioned implementation, i.e., how much would the net profit be affected. The mechanisms' main objective is to give carriers the chance to improve their original sets of requests in order to increase their overall efficiency. Due to the nature of routing problems, requests usually have different costs for different carriers, depending on the location of the depots as well as on the requests that have to be serviced. The exchange mechanism should find a new allocation such that carriers obtain requests with higher value (i.e., lower cost) for them. Results obtained here show that individual auction‐based mechanisms provide similar results, on average, to centralized auction‐based mechanisms, both outperforming posted price mechanisms. Nevertheless, this improvement difference comes at the cost of providing more information (included in the carriers' bids). Readers can use the presented comparison and results to improve decisions taken prior to collaboration, specifically deciding which mechanism is the best option for a specific situation.

Online revenue maximization for server pricing

Efficient and truthful mechanisms to price resources on servers/machines have been the subject of much work in recent years due to the importance of the cloud market. This paper considers revenue maximization in the online stochastic setting with non-preemptive jobs and a unit capacity server. One agent/job arrives at every time step, with parameters drawn from the underlying distribution. We design a posted-price mechanism which can be efficiently computed and is revenue-optimal in expectation and in retrospect, up to additive error. The prices are posted prior to learning the agent’s type, and the computed pricing scheme is deterministic, depending only on the length of the allotted time interval and on the earliest time the server is available. We also prove that the proposed pricing strategy is robust to imprecise knowledge of the job distribution and that a distribution learned from polynomially many samples is sufficient to obtain a near-optimal truthful pricing strategy.

Treating Symmetric Buyers Asymmetrically

We investigate a finite-horizon dynamic pricing problem of a seller under limited commitment. Even when the buyers are ex-ante symmetric to the seller, the seller can charge different prices to different buyers. We show that under the class of posted-price mechanisms this asymmetric treatment of symmetric buyers strictly revenue-dominates symmetric treatment. The seller im- plements this by using a priority-based deterministic tie-breaking rule instead of using a random tie-breaking rule. The effect of asymmetric treatment on revenue increment increases monotonically as we increase the time horizon of the game.

Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms

How to optimize posted price mechanisms? The sequential posted-price (SPP) mechanism is one of the widely used selling mechanisms in practice. In this mechanism, the seller presents each buyer with a price sequentially and the buyer can either accept or reject the mechanism's offer. Despite the widespread use of the SPP mechanism, the problem of optimizing prices in this mechanism has not been fully addressed. In a paper entitled, “Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms,” H. Beyhaghi, N. Golrezaei, R. Paes Leme, M. Pal, and B. Sivan construct SPP mechanisms by considering the best of two simple pricing rules: one that imitates the optimal mechanism and the other that posts a uniform price (same price for every buyer). Their simple pricing rules can be easily generalized to the setting with multiple units and yield the first improvement over long-established approximation factors.

Multidimensional bargaining and posted prices

A seller and a buyer bargain over the quantities and prices of multiple goods. Both agents have private information about their preferences. Utility is quasilinear in money. We show that a deterministic mechanism satisfies (i) dominant-strategy incentive compatibility, (ii) ex-post individual rationality and (iii) ex-post budget balance if and only if it is a posted-price mechanism. A similar, more general result holds if (iii) is replaced by ex-post collusion-proofness and a no-free lunch condition. We provide a unified proof of both findings via the property of non-bossiness.

Reinforcement Learning of Sequential Price Mechanisms

We introduce the use of reinforcement learning for indirect mechanisms, working with the existing class of sequential price mechanisms, which generalizes both serial dictatorship and posted price mechanisms and essentially characterizes all strongly obviously strategyproof mechanisms. Learning an optimal mechanism within this class forms a partially-observable Markov decision process. We provide rigorous conditions for when this class of mechanisms is more powerful than simpler static mechanisms, for sufficiency or insufficiency of observation statistics for learning, and for the necessity of complex (deep) policies. We show that our approach can learn optimal or near-optimal mechanisms in several experimental settings.

Online Posted Pricing with Unknown Time-Discounted Valuations

We study the problem of designing posted-price mechanisms in order to sell a single unit of a single item within a finite period of time. Motivated by real-world problems, such as, e.g., long-term rental of rooms and apartments, we assume that customers arrive online according to a Poisson process, and their valuations are drawn from an unknown distribution and discounted over time. We evaluate our mechanisms in terms of competitive ratio, measuring the worst-case ratio between their revenue and that of an optimal mechanism that knows the distribution of valuations. First, we focus on the identical valuation setting, where all the customers value the item for the same amount. In this setting, we provide a mechanism M_c that achieves the best possible competitive ratio, discussing its dependency on the parameters in the case of linear discount. Then, we switch to the random valuation setting. We show that, if we restrict the attention to distributions of valuations with a monotone hazard rate, then the competitive ratio of M_c is lower bounded by a strictly positive constant that does not depend on the distribution. Moreover, we provide another mechanism, called M_pc, which is defined by a piecewise constant pricing strategy and reaches performances comparable to those obtained with M_c. This mechanism is useful when the seller cannot change the posted price too often. Finally, we empirically evaluate the performances of our mechanisms in a number of experimental settings.

The Higher Risk, The Higher Price? A Theoretical and Empirical Analysis of Pricing Strategy in P2P Lending

As an increasing number of P2P lending platforms choose posted-price mechanisms (the platform determines the interest rate), a crucial but unanswered question is: how do interest rates affect market outcomes? Because P2P lending platforms are characterized by two-sidedness and information asymmetry, the effects of interest rate pricing on market outcomes may differ from the traditional one-sided market. We address our research question theoretically and empirically. We first construct a simple general model to investigate the effect of interest rate on the platform profit and investment risk, taking into account the participation decisions of lenders and borrowers and platform pricing strategies (i.e., transaction fees to users on both sides). Our model implies that the investment risk has a non-monotonic relationship with interest rates. Inspired by our theoretical analyses, we then conduct a robust and solid counterfactual econometric analysis and empirically show that an inverted U-shaped non-monotonic interest rate design demonstrates its advantages in reducing credit risks and improving the platform’s profits by 33.89%. This study extends our understanding of the role of price in two-sided platforms with platform mandated price mechanisms and information asymmetry; the findings have important policy implications for interest rate regulation in the P2P lending industry from the perspective of two-sided platforms.

DPoS: Decentralized, Privacy-Preserving, and Low-Complexity Online Slicing for Multi-Tenant Networks

Network slicing is the key to enable virtualized resource sharing among vertical industries in the era of 5G communication. Efficient resource allocation is of vital importance to realize network slicing in real-world business scenarios. To deal with the high algorithm complexity, privacy leakage, and unrealistic offline setting of current network slicing algorithms, in this paper we propose a fully decentralized and low-complexity online algorithm, DPoS, for multi-resource slicing. We first formulate the problem as a global social welfare maximization problem. Next, we design the online algorithm DPoS based on the primal-dual approach and posted price mechanism. In DPoS, each tenant is incentivized to make its own decision based on its true preferences without disclosing any private information to the mobile virtual network operator and other tenants. We provide a rigorous theoretical analysis to show that DPoS has the optimal competitive ratio when the cost function of each resource is linear. Extensive simulation experiments are conducted to evaluate the performance of DPoS. The results show that DPoS can not only achieve close-to-offline-optimal performance, but also have low algorithmic overheads.

Bidding behavior in auctions versus posted prices: comparisons of mean and marginal effects

Abstract Economic experiments have been widely used to elicit individuals' evaluation for various commodities. Common elicitation methods include auction and posted price mechanisms. A field experiment is designed to compare willingness-to-pay (WTP) estimates between these two mechanisms. Despite both of these formats being theoretically incentive compatible and demand revealing, results from 115 adult consumers indicate that WTP estimates obtained from an auction are 32–39 percent smaller than those from a posted price mechanism. A comparison in statistical significance shows that auctions require a smaller sample size than posted price mechanisms in order to detect the same preference change. Nevertheless, the signs of marginal effects for different product characteristics are consistent in both mechanisms.

Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals

The classic prophet inequality states that, when faced with a finite sequence of nonnegative independent random variables, a gambler who knows the distribution and is allowed to stop the sequence at any time, can obtain, in expectation, at least half as much reward as a prophet who knows the values of each random variable and can choose the largest one. In this work, we consider the situation in which the sequence comes in random order. We look at both a nonadaptive and an adaptive version of the problem. In the former case, the gambler sets a threshold for every random variable a priori, whereas, in the latter case, the thresholds are set when a random variable arrives. For the nonadaptive case, we obtain an algorithm achieving an expected reward within at least a 0.632 fraction of the expected maximum and prove that this constant is optimal. For the adaptive case with independent and identically distributed random variables, we obtain a tight 0.745-approximation, solving a problem posed by Hill and Kertz in 1982. We also apply these prophet inequalities to posted price mechanisms, and we prove the same tight bounds for both a nonadaptive and an adaptive posted price mechanism when buyers arrive in random order.

Efficient mechanisms for level-k bilateral trading

This paper revisits Myerson and Satterthwaite's (1983) classic analysis of mechanism design for bilateral trading, replacing equilibrium with a level-k model of strategic thinking and focusing on direct mechanisms. The revelation principle fails for level-k models, so restricting attention to direct mechanisms and imposing incentive-compatibility are not without loss of generality. If, however, only direct, level-k-incentive-compatible mechanisms are feasible and traders' levels are observable, Myerson and Satterthwaite's characterization of mechanisms that maximize traders' total surplus subject to incentive constraints generalizes qualitatively to level-k models. If only direct, level-k-incentive-compatible mechanisms are feasible but traders' levels are not observable, generically a particular posted-price mechanism maximizes traders' total expected surplus subject to incentive constraints. If direct, non-level-k-incentive-compatible mechanisms are feasible and traders best respond to them, total expected surplus-maximizing mechanisms may take completely different forms.

Robust multidimensional pricing: separation without regret

We study a robust monopoly pricing problem with a minimax regret objective, where a seller endeavors to sell multiple goods to a single buyer, only knowing that the buyer’s values for the goods range over a rectangular uncertainty set. We interpret this pricing problem as a zero-sum game between the seller, who chooses a selling mechanism, and a fictitious adversary or ‘nature’, who chooses the buyer’s values from within the uncertainty set. Using duality techniques rooted in robust optimization, we prove that this game admits a Nash equilibrium in mixed strategies that can be computed in closed form. The Nash strategy of the seller is a randomized posted price mechanism under which the goods are sold separately, while the Nash strategy of nature is a distribution on the uncertainty set under which the buyer’s values are comonotonic. We further show that the restriction of the pricing problem to deterministic mechanisms is solved by a deteministic posted price mechanism under which the goods are sold separately.

Special Section on the 48th Annual ACM Symposium on Theory of Computing (STOC 2016)

Special Section on the 48th Annual ACM Symposium on Theory of Computing (STOC 2016)