Mechanism Design Problem Research Articles

Understanding Mechanism Design—Part 2 of 3: The Vickrey-Clarke-Groves Mechanism

As we saw in the first part of this short series, a mechanism design problem involves engineering the rules of a game so that, if participants then behave rationally in the game (by choosing strategies that maximize their expected utility, for example), then the result will satisfy some desired property. So far, however, we have said nothing about what these desirable properties might be, or what mechanisms might achieve them. Here, we will dig into these two issues in a little more detail.

On Incentive Compatibility in Dynamic Mechanism Design With Exit Option in a Markovian Environment

This paper studies dynamic mechanism design in a Markovian environment and analyzes a direct mechanism model of a principal-agent framework in which the agent is allowed to exit at any period. We consider that the agent’s private information, referred to as state, evolves over time. The agent makes decisions of whether to stop or continue and what to report at each period. The principal, on the other hand, chooses decision rules consisting of an allocation rule and a set of payment rules to maximize her ex-ante expected payoff. In order to influence the agent’s stopping decision, one of the terminal payment rules is posted-price, i.e., it depends only on the realized stopping time of the agent. This work focuses on the theoretical design regime of the dynamic mechanism design when the agent makes coupled decisions of reporting and stopping. A dynamic incentive compatibility constraint is introduced to guarantee the robustness of the mechanism to the agent’s strategic manipulation. A sufficient condition for dynamic incentive compatibility is obtained by constructing the payment rules in terms of a set of functions parameterized by the allocation rule. The payment rules are then pinned down up to a constant in terms of the allocation rule by deriving a first-order condition. We show cases of relaxations of the principal’s mechanism design problem and provide an approach to evaluate the loss of robustness of the dynamic incentive compatibility when the problem solving is relaxed due to analytical intractability. A case study is used to illustrate the theoretical results.

An adaptive fuzzy penalty method for constrained evolutionary optimization

Penalty function is well-known for constrained evolutionary optimization. An open question in the penalty function is how to tune the penalty coefficient. This paper proposes an adaptive fuzzy penalty method to address this issue, where the coefficient is adjusted at both the individual level and the population level. At the individual level, each individual chooses a penalty coefficient from a predefined domain according to some fuzzy rules. At the population level, the domain of the crisp output is adjusted adaptively by using population information. To enhance the population diversity, an effective mutation scheme is developed. Due to its numerous merits, differential evolution is used to design a search algorithm. By the above processes, a constrained optimization evolutionary algorithm called AFPDE is proposed. Since the objective function value and the degree of constraint violation are normalized, AFPDE is less problem-dependent than the seminal work of the fuzzy penalty method. AFPDE introduces a lower penalty value in the early stage of AFPDE while a higher one in the later stage. Thus, it can escape local optima in the infeasible region. Experiments on three well-known benchmark test sets and two mechanical design problems validate that AFPDE is competitive.

The Revelation Principle for Mechanism Design with Signaling Costs

The revelation principle is a key tool in mechanism design. It allows the designer to restrict attention to truthful mechanisms, greatly facilitating analysis. This is also borne out algorithmically, allowing certain computational problems in mechanism design to be solved in polynomial time. Unfortunately, when not every type can misreport every other type (the partial verification model) or—more generally—misreporting can be costly, the revelation principle can fail to hold. This also leads to NP-hardness results. The primary contribution of this article consists of characterizations of conditions under which the revelation principle still holds when reporting can be costly. (These are generalizations of conditions given earlier for the partial verification case [11, 21].) Furthermore, our results extend to cases where, instead of reporting types directly, agents send signals that do not directly correspond to types. In this case, we obtain conditions for when the mechanism designer can restrict attention to a given (but arbitrary) mapping from types to signals without loss of generality.

Terminal Ranking Games

We analyze a mean field tournament: a mean field game in which the agents receive rewards according to the ranking of the terminal value of their projects and are subject to cost of effort. Using Schrödinger bridges we are able to explicitly calculate the equilibrium. This allows us to identify the reward functions which would yield a desired equilibrium and solve several related mechanism design problems. We are also able to identify the effect of reward inequality on the players’ welfare as well as calculate the price of anarchy.

Two-facility Location Games with Minimum Distance Requirement

We study the mechanism design problem of a social planner for locating two facilities on a line interval [0, 1], where a set of n strategic agents report their locations and a mechanism determines the locations of the two facilities. We consider the requirement of a minimum distance 0 ≤ d ≤ 1 between the two facilities. Given the two facilities are heterogeneous, we model the cost/utility of an agent as the sum of his distances to both facilities. In the heterogeneous two-facility location game to minimize the social cost, we show that the optimal solution can be computed in polynomial time and prove that carefully choosing one optimal solution as output is strategyproof. We also design a strategyproof mechanism minimizing the maximum cost. Given the two facilities are homogeneous, we model the cost/utility of an agent as his distance to the closer facility. In the homogeneous two-facility location game for minimizing the social cost, we show that any deterministic strategyproof mechanism has unbounded approximation ratio. Moreover, in the obnoxious heterogeneous two-facility location game for maximizing the social utility, we propose new deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound (7 − d)/6 for any deterministic strategyproof mechanism. We also design a strategyproof mechanism maximizing the minimum utility. In the obnoxious homogeneous two-facility location game for maximizing the social utility, we propose deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound 4/3. Besides, in the two-facility location game with triple-preference, where each facility may be favorable, obnoxious, indifferent for any agent, we further motivate agents to report both their locations and preferences towards the two facilities truthfully, and design a deterministic group strategyproof mechanism with an approximation ratio 4.

Simple and Efficient Budget Feasible Mechanisms for Monotone Submodular Valuations

We study the problem of a budget limited buyer who wants to buy a set of items, each from a different seller, to maximize her value. The budget feasible mechanism design problem requires the design a mechanism that incentivizes the sellers to truthfully report their cost and maximizes the buyer’s value while guaranteeing that the total payment does not exceed her budget. Such budget feasible mechanisms can model a buyer in a crowdsourcing market interested in recruiting a set of workers (sellers) to accomplish a task for her. This budget feasible mechanism design problem was introduced by Singer in 2010. We consider the general case where the buyer’s valuation is a monotone submodular function. There are a number of truthful mechanisms known for this problem. We offer two general frameworks for simple mechanisms, and by combining these frameworks, we significantly improve on the best known results, while also simplifying the analysis. For example, we improve the approximation guarantee for the general monotone submodular case from 7.91 to 5 and for the case of large markets (where each individual item has negligible value) from 3 to 2.58. More generally, given an r approximation algorithm for the optimization problem (ignoring incentives), our mechanism is a r + 1 approximation mechanism for large markets, an improvement from 2 r 2 . We also provide a mechanism without the large market assumption, where we achieve a 4 r + 1 approximation guarantee. We also show how our results can be used for the problem of a principal hiring in a Crowdsourcing Market to select a set of tasks subject to a total budget.

Average-Case Approximation Ratio of Scheduling without Payments

Apart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the worst-case analysis and design of approximation schemes of Theoretical Computer Science. For instance, the approximation ratio, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs. In this paper, we take the average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design—the scheduling problem (Nisan and Ronen, in: Proceedings of the 31st annual ACM symposium on theory of computing (STOC), 1999). One version of this problem, which includes a verification component, is studied by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014). It was shown that the problem has a tight approximation ratio bound of (n+1)/2 for the single-task setting, where n is the number of machines. We show, however, when the costs of the machines to executing the task follow any independent and identical distribution, the average-case approximation ratio of the mechanism given by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014) is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio. It indicates that the optimal mechanism devised for a worst-case guarantee works well on average.

Solving integer programming problems by using population-based beetle antennae search algorithm

Beetle antennae search (BAS) algorithm is a newly proposed single-solution based metaheuristic technique inspired by the beetle preying process. Although BAS algorithm has shown good search abilities, it can be easily trapped into local optimum when it is used to solve hard optimization problems. With the intention to overcome this drawback, this paper presents a population-based beetle antennae search (PBAS) algorithm for solving integer programming problems. This method employs the population's capability to search diverse regions of the search space to provide better guarantee for finding the optimal solution. The PBAS method was tested on nine integer programming problems and one mechanical design problem. The proposed algorithm was compared to other state-of-the-art metaheuristic techniques. The comparisons show that the proposed PBAS algorithm produces better results for majority of tested problems.

Optimal Auction Design With Common Values: An Informationally Robust Approach

A profit‐maximizing seller has a single unit of a good to sell. The bidders have a pure common value that is drawn from a distribution that is commonly known. The seller does not know the bidders' beliefs about the value and thinks that beliefs are designed adversarially by Nature to minimize profit. We construct a strong maxmin solution to this joint mechanism design and information design problem, consisting of a mechanism, an information structure, and an equilibrium, such that neither the seller nor Nature can move profit in their respective preferred directions, even if the deviator can select the new equilibrium. The mechanism and information structure solve a family of maxmin mechanism design and minmax information design problems, regardless of how an equilibrium is selected. The maxmin mechanism takes the form of a proportional auction: each bidder submits a one‐dimensional bid, the aggregate allocation and aggregate payment depend on the aggregate bid, and individual allocations and payments are proportional to bids. We report a number of additional properties of the maxmin mechanisms, including what happens as the number of bidders grows large and robustness with respect to the prior over the value.

A Design Framework for Strongly χ²-Private Data Disclosure

In this paper, we study a stochastic disclosure control problem using information-theoretic methods. The useful data to be disclosed depend on private data that should be protected. Thus, we design a privacy mechanism to produce new data which maximizes the disclosed information about the useful data under a strong $\chi^2$-privacy criterion. For sufficiently small leakage, the privacy mechanism design problem can be geometrically studied in the space of probability distributions by a local approximation of the mutual information. By using methods from Euclidean information geometry, the original highly challenging optimization problem can be reduced to a problem of finding the principal right-singular vector of a matrix, which characterizes the optimal privacy mechanism. In two extensions we first consider a scenario where an adversary receives a noisy version of the user's message and then we look for a mechanism which finds $U$ based on observing $X$, maximizing the mutual information between $U$ and $Y$ while satisfying the privacy criterion on $U$ and $Z$ under the Markov chain $(Z,Y)-X-U$.

Bilateral trade with a benevolent intermediary

We study intermediaries who seek to maximize gains from trade in bilateral negotiations. Intermediaries are players: they cannot commit to act against their objective function and deny, in some cases, trade they believe to be beneficial. This impairs their ability to assist the parties relative to conventional mechanisms. We analyze this limited commitment environment as a standard mechanism design problem with an additional “credibility” constraint, requiring that every outcome be interim‐optimal conditional on available information. We investigate how such intermediaries communicate with the parties, analyze the tradeoffs they face, and study the bounds on what they can achieve.

Building a Foundation for Data-Driven, Interpretable, and Robust Policy Design using the AI Economist

Optimizing economic and public policy is critical to address socioeconomic issues and trade-offs, e.g., improving equality, productivity, or wellness, and poses a complex mechanism design problem.A policy designer needs to consider multiple objectives, policy levers, and behavioral responses from strategic actors who optimize for their individual objectives.Moreover, real-world policies should be explainable and robust to simulation-to-reality gaps, e.g., due to calibration issues.Existing approaches are often limited to a narrow set of policy levers or objectives that are hard to measure, do not yield explicit optimal policies, or do not consider strategic behavior, for example.Hence, it remains challenging to optimize policy in real-world scenarios.Here we show that the AI Economist framework enables effective, flexible, and interpretable policy design using two-level reinforcement learning (RL) and data-driven simulations.We validate our framework on optimizing the stringency of \USState{} policies and Federal subsidies during a pandemic, e.g., COVID-19, using a simulation fitted to real data.We find that log-linear policies trained using RL significantly improve social welfare, based on both public health and economic outcomes, compared to past outcomes.Their behavior can be explained, e.g., well-performing policies respond strongly to changes in recovery and vaccination rates.They are also robust to calibration errors, e.g., infection rates that are over or underestimated.As of yet, real-world policymaking has not seen adoption of machine learning methods at large, including RL and AI-driven simulations.Our results show the potential of AI to guide policy design and improve social welfare amidst the complexity of the real world.

Delegating learning

Learning is crucial to organizational decision making but often needs to be delegated. We examine a dynamic delegation problem where a principal decides on a project with uncertain profitability. A biased agent, who is initially as uninformed as the principal, privately learns the profitability over time and communicates to the principal. We formulate learning delegation as a dynamic mechanism design problem and characterize the optimal delegation scheme. We show that private learning gives rise to the trade‐off between how much information to acquire and how promptly it is reflected in the decision. We discuss implications on learning delegation for distinct organizations.

A Trial of Realization of Model Solutions to Mechanical Design Problems Using FEM 3D Printer

A Trial of Realization of Model Solutions to Mechanical Design Problems Using FEM 3D Printer

Uncertainty in Mechanism Design

This paper studies the design of mechanisms that are robust to misspecification. We introduce a novel notion of robustness that connects a variety of disparate approaches and study its implications in a wide class of mechanism design problems. This notion is quantifiable, allowing us to formalize and answer comparative statics questions relating the nature and degree of misspecification to sharp predictions regarding features of feasible mechanisms. This notion also has a behavioral foundation which reflects the perception of ambiguity, thus allowing the degree of misspecification to emerge endogenously. In a number of standard settings, robustness to arbitrarily small amounts of misspecification generates a discontinuity in the set of feasible mechanisms and uniquely selects simple, ex post incentive compatible mechanisms such as second-price auctions. Robustness also sheds light on the value of private information and the prevalence of full or virtual surplus extraction.

An Approximation Scheme for Data Monetization

The unprecedented rate at which data is being generated has led to the growth of data markets where valuable datasets are bought and sold. A salient feature of this market is that a data-buyer (agent) is endowed with multi-dimensional private information, namely her ``ideal'' record that she values the most and how her valuation for a given record changes as its distance from her ideal record changes. Consequently, the revenue-maximization problem faced by a data-seller (principal), who serves multiple buyers, is a multi-dimensional mechanism-design problem, which is well-recognized as being difficult to solve. Our main result in this paper is an approximation scheme that guarantees a revenue within as close a positive amount from the optimal revenue as desired. The scheme generates a posted-price menu consisting of a set of item-price pairs -- each entry in the menu consists of an item, i.e., a set of records from the dataset, and the price corresponding to that item. As a tradeoff, the length of the menu resulting from the scheme increases as the desired guarantee gets closer to zero. For convenience in practice, data-sellers may want the ability to limit the length of the menu used by the scheme. To facilitate this, we extend our analysis to obtain a general approximation guarantee corresponding to a menu of any given length. We also demonstrate how the seller can exploit buyers' preferences to generate intuitive and useful rules of thumb for an effective practical implementation of the scheme.

Smooth Design of 3D Self-Supporting Topologies Using Additive Manufacturing Filter and SEMDOT

The smooth design of self-supporting topologies has attracted great attention in the design for additive manufacturing (DfAM) field as it cannot only enhance the manufacturability of optimized designs but can obtain light-weight designs that satisfy specific performance requirements. This paper integrates Langelaar’s AM filter into the Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) algorithm—a new element-based topology optimization method capable of forming smooth boundaries—to obtain print-ready designs without introducing post-processing methods for smoothing boundaries before fabrication and adding extra support structures during fabrication. The effects of different build orientations and critical overhang angles on self-supporting topologies are demonstrated by solving several compliance minimization (stiffness maximization) problems. In addition, a typical compliant mechanism design problem—the force inverter design—is solved to further demonstrate the effectiveness of the combination between SEMDOT and Langelaar’s AM filter.

Technical Note—On Revenue Management with Strategic Customers Choosing When and What to Buy

In practice, when thinking about their purchasing decisions, customers usually strategize along two dimensions: (1) when to buy and (2) what to buy. That is, they might delay a purchase in anticipation of future price reductions, and/or they might purchase cheaper substitutes. Despite this, the literature has thus far dealt exclusively with either one of the two extremes whereby one of the two strategic dimension is missing. For example, a large body of work has studied forward-looking customers strategizing on when to buy but has done so merely within models in which customers have no alternatives to choose from. Conversely, another large body of work on assortment optimization and choice modeling has studied customers who choose what to buy from multiple product offerings but acting myopically. This paper takes a first step toward analyzing dynamic pricing when customers are fully strategic and choose both when and what to buy. Using a novel decomposition approach for the underlying multidimensional mechanism design problem, the paper presents theoretical and numerical performance analyses of static pricing policies.

Improved truthful mechanisms for combinatorial auctions with submodular bidders

A longstanding open problem in Algorithmic Mechanism Design is to design computationally-efficient truthful mechanisms for (approximately) maximizing welfare in combinatorial auctions with submodular bidders. The first such mechanism was obtained by Dobzinski, Nisan, and Schapira [STOC'06] who gave an O (log 2 m )-approximation where m is the number of items. This problem has been studied extensively since, culminating in an O ([EQUATION])-approximation mechanism by Dobzinski [STOC'16]. We present a computationally-efficient truthful mechanism with approximation ratio that improves upon the state-of-the-art by almost an exponential factor. In particular, our mechanism achieves an O ((log log m ) 3 )-approximation in expectation, uses only O ( n ) demand queries, and has universal truthfulness guarantee.