Dominant Strategy Incentive Compatibility Research Articles

Selecting a winner with external referees

We consider a problem of mechanism design without money, where a planner selects a winner among a set of agents with binary types and receives outside signals (like the report of external referees). We show that there is a gap between the optimal Dominant Strategy Incentive Compatible (DSIC) mechanism and the optimal Bayesian Incentive Compatible (BIC) mechanism. In the optimal BIC mechanism, the planner can leverage the outside signal to elicit information about agents' types. BIC mechanisms are lexicographic mechanisms, where the planner first shortlists agents who receive high reports from the referees and then uses agents' reports to break ties among agents in the shortlist. We compare the “self-evaluation” mechanism with a “peer evaluation” mechanism where agents evaluate other agents, and show that for the same signal precision, the self- evaluation mechanism outperforms the peer evaluation mechanism. We show that optimal Ex Post Incentive Compatible (EPIC) mechanisms give the planner an intermediate value between the optimal DSIC and BIC mechanisms

Truthful Mechanisms for Two-Sided Markets via Prophet Inequalities

We design novel mechanisms for welfare maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our mechanisms are designed based on a powerful correspondence between two-sided markets and prophet inequalities. They satisfy individual rationality, dominant-strategy incentive compatibility, and budget balance constraints and give constant factor approximations to the optimal social welfare. We improve previous results in several settings. Our main focus is on matroid double auctions. Here, sellers hold identical items, and the set of buyers that obtain an item needs to be independent in a matroid. We construct two mechanisms, the first being a 1/3 approximation of the optimal social welfare-satisfying strong budget balance and requiring the agents to trade in a customized order and the second being a 1/2 approximation weakly budget balanced and able to deal with online arrival determined by an adversary. In addition, we construct constant factor approximations in two-sided markets with identical items when buyers need to fulfill a knapsack constraint. Also, in combinatorial double auctions with heterogeneous items, where buyers have valuation functions over item bundles instead of being interested in only one item, using similar techniques, we design a mechanism that is a 1/2 approximation of the optimal social welfare, is strongly budget balanced, and can deal with the online arrival of agents in an adversarial order. Funding: A. Braun was funded by the Deutsche Forschungsgemeinschaft [Grant 437739576].

Incentive-Compatible Forecasting Competitions

We initiate the study of incentive-compatible forecasting competitions in which multiple forecasters make predictions about one or more events and compete for a single prize. We have two objectives: (1) to incentivize forecasters to report truthfully and (2) to award the prize to the most accurate forecaster. Proper scoring rules incentivize truthful reporting if all forecasters are paid according to their scores. However, incentives become distorted if only the best-scoring forecaster wins a prize, since forecasters can often increase their probability of having the highest score by reporting more extreme beliefs. In this paper, we introduce two novel forecasting competition mechanisms. Our first mechanism is incentive compatible and guaranteed to select the most accurate forecaster with probability higher than any other forecaster. Moreover, we show that in the standard single-event, two-forecaster setting and under mild technical conditions, no other incentive-compatible mechanism selects the most accurate forecaster with higher probability. Our second mechanism is incentive compatible when forecasters’ beliefs are such that information about one event does not lead to belief updates on other events, and it selects the best forecaster with probability approaching one as the number of events grows. Our notion of incentive compatibility is more general than previous definitions of dominant strategy incentive compatibility in that it allows for reports to be correlated with the event outcomes. Moreover, our mechanisms are easy to implement and can be generalized to the related problems of outputting a ranking over forecasters and hiring a forecaster with high accuracy on future events.This paper was accepted by Yan Chen, behavioral economics and decision analysis.Funding: This work was supported by the European Research Council [Grant ERC StG 307036] and the National Science Foundation [Grant CCF-1445755].

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.

Pareto efficient combinatorial auctions: Dichotomous preferences without quasilinearity

We consider a combinatorial auction model where preferences of agents over bundles of objects and payments need not be quasilinear. However, we restrict the preferences of agents to be dichotomous. An agent with dichotomous preference partitions the set of bundles of objects as acceptable and unacceptable, and at the same payment level, she is indifferent between bundles in each class but strictly prefers acceptable to unacceptable bundles. We show that there is no Pareto efficient, dominant strategy incentive compatible (DSIC), individually rational (IR) mechanism satisfying no subsidy if the domain of preferences includes all dichotomous preferences. However, a generalization of the VCG mechanism is Pareto efficient, DSIC, IR and satisfies no subsidy if the domain of preferences contains only positive income effect dichotomous preferences. We show tightness of this result: adding any non-dichotomous preference (satisfying some natural properties) to the domain of quasilinear dichotomous preferences brings back the impossibility result.

The capacity constrained facility location problem

We initiate the study of the capacity constrained facility location problem from a mechanism design perspective. In the capacity constrained setting, the facility can serve only a subset of the population, assumed to be the k-closest with respect to agents' true locations (this can be justified as the essentially unique equilibrium outcome of a first-come-first game induced by the facility location). The main result is a complete characterization of dominant-strategy incentive compatible (DIC) mechanisms via the family of generalized median mechanisms (GMMs). Thus, the framework we introduce surprisingly provides a new characterization of GMMs, and is responsive to gaps in the current social choice literature highlighted by Border and Jordan (1983) and Barberà et al. (1998). We also provide algorithmic results and study the performance of DIC mechanisms in optimizing welfare. Adopting a worst-case approximation measure, we attain tight lower bounds on the approximation ratio of any DIC mechanism.

Monotonic norms and orthogonal issues in multidimensional voting

We study issue-by-issue voting by majority and incentive compatibility in multidimensional frameworks where privately informed agents have preferences induced by general norms and where dimensions are endogenously chosen. We uncover the deep connections between dominant strategy incentive compatibility (DIC) on the one hand, and several geometric/functional analytic concepts on the other. Our main results are: 1) Marginal medians are DIC if and only if they are calculated with respect to coordinates defined by a basis such that the norm is orthant-monotonic in the associated coordinate system. 2) Equivalently, marginal medians are DIC if and only if they are computed with respect to a basis such that, for any vector in the basis, any linear combination of the other vectors is Birkhoff-James orthogonal to it. 3) We show how semi-inner products and normality provide an analytic method that can be used to find all DIC marginal medians. 4) As an application, we derive all DIC marginal medians for lp spaces of any finite dimension, and show that they do not depend on p (unless p=2).

Efficient multiunit auctions for normal goods

I study multiunit auction design when bidders have private values, multiunit demands, and non‐quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. I give conditions under which we can design a mechanism that retains the Vickrey auction's desirable incentive and efficiency properties: (1) individual rationality, (2) dominant strategy incentive compatibility, and (3) Pareto efficiency. I show that there is a mechanism that retains the desired properties of the Vickrey auction if there are two bidders who have single‐dimensional types. I also present an impossibility theorem that shows that there is no mechanism that satisfies Vickrey's desired properties and weak budget balance when bidders have multidimensional types.

General Competing Mechanisms with Frictions

This paper studies the class of robust equilibria in a general competing mechanism game for decentralized markets with frictions in which non-deviating sellers punish a deviator with dominant strategy incentive compatible (DIC) direct mechanisms. Given one-dimensional, independent, and private types, the lower bound of a seller's payoff in such equilibria is his minmax value over all DIC direct mechanisms if a seller can deviate to a contract that determines a menu of any complex mechanisms conditional on buyers' messages and he chooses a mechanism he wants from it. In applications, the number of sellers is endogenized given a number of buyers and fixed entry costs. As the number of buyer increases, a unique equilibrium emerges and the equilibrium ratio of buyers to sellers converges to the point where a seller's net profit is zero with the monopoly terms of trade.

Multi-Unit Bilateral Trade

We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular.Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1 − e) approximation mechanism, matching the best known bounds for the single-item setting.

Simple mechanisms for subadditive buyers via duality

A central problem in mechanism design is how to design simple and approximately revenue-optimal auctions in multi-item multi-buyer settings. Prior to our work, all results only apply to cases where the buyers' valuations are linear over the items. We unify and improve all previous results, as well as generalize the results to accommodate non-linear valuations [Cai and Zhao 2017]. In particular, we prove that a simple, deterministic and Dominant Strategy Incentive Compatible (DSIC) mechanism, namely, the sequential posted price with entry fee mechanism, achieves a constant fraction of the optimal revenue among all randomized, Bayesian Incentive Compatible (BIC) mechanisms, when buyers' valuations are XOS (a superclass of submodular valuations) over independent items. If the buyers' valuations are subadditive over independent items, the approximation factor degrades to O (log m ), where m is the number of items. We obtain our results by first extending the Cai-Devanur-Weinberg duality framework to derive an effective benchmark of the optimal revenue for subadditive buyers, and then developing new analytic tools that combine concentration inequality of subadditive functions, prophet-inequality type of arguments, and a novel decomposition of the benchmark.

Robust bilateral trade with discrete types

Bilateral trade problem is the most common market interaction in which a seller and a buyer bargain over an indivisible object, and the valuation of each agent about the object is private information. We investigate the cases where mechanisms satisfying Dominant Strategy Incentive Compatibility (DIC) and Ex-post Individual Rationality (EIR) properties can exhibit robust performance in the face of imprecision in prior structure. We start with the general mathematical formulation for the bilateral trade problem with DIC, EIR properties. We derive necessary and sufficient conditions for DIC, EIR mechanisms to be Ex-post efficient at the same time. Then, we define a new property—Allocation Maximality—and prove that the Posted Price mechanisms are the only mechanisms that satisfy DIC, EIR and Allocation Maximal properties. We also show that Posted Price mechanism is not the only mechanism that satisfies DIC and EIR properties. The last part of the paper introduces different sets of priors for agents’ types and consequently allows ambiguity in the problem framework. We derive robust counterparts and solve them numerically for the proposed objective function under box and ϕ -divergence ambiguity specifications. Results suggest that restricting the feasible set to Posted Price mechanisms can decrease the objective value to different extents depending on the uncertainty set.

A subsidized Vickrey auction for cost sharing

It is well-known that there is no cost-sharing mechanism that is budget balanced, efficient, and dominant strategy incentive compatible (DSIC). The Vickrey auction is DSIC and efficient, but raises surplus revenue. In an environment where players have constant marginal values, we introduce a subsidized Vickrey auction (SVA) that uses surplus revenue to offset some of the production costs. By compromising efficiency, our SVA improves the players’ payoffs over the Vickrey auction. We show that the SVA is DSIC, budget balanced, and value effective (awarding quantity only to the player who values it most), and it Pareto dominates any other mechanism with these three properties. We demonstrate that there is no welfare ranking between the SVA and the non-value effective serial cost-sharing mechanism.

Modularity and greed in double auctions

Designing double auctions is a complex problem, especially when there are restrictions on the sets of buyers and sellers that may trade with one another. The goal of this paper is to develop a modular approach to the design of double auctions, by relating it to the exhaustively-studied problem of designing one-sided mechanisms with a single seller (or, alternatively, a single buyer).We consider several desirable properties of a double auction: feasibility, dominant-strategy incentive compatibility, the still stronger incentive constraints offered by a deferred-acceptance implementation, exact and approximate welfare maximization, and budget balance. For each of these properties, we identify sufficient conditions on two one-sided algorithms—one for ranking the buyers, one for ranking the sellers—and on a method for their composition into trading pairs, which guarantee the desired property of the double auction.Our framework also offers new insights into classic double auction designs, such as the VCG and McAfee auctions with unit-demand buyers and unit-supply sellers.

On public good provision mechanisms with dominant strategies and balanced budget

Consider a mechanism for the binary public good provision problem that is dominant strategy incentive compatible (DSIC), ex-post individually rational (EPIR), and ex-post budget balanced (EPBB). It is well known that if there are only two agents, then any such mechanism must have a threshold (or fixed cost-sharing) form, providing the public good if and only if both agents have values that are at least their respective thresholds. When there are more than two agents, there are mechanisms that are DSIC, EPIR, and EPBB that are not of the threshold form. Any DSIC, EPIR, and EPBB mechanism that additionally satisfies that the lowest types expect zero net utility from participating are again of the threshold form. This additional condition arises endogenously when maximizing expected welfare subject to DSIC, EPIR, and EPBB.

Complexity, and New Dynamic-Pricing 'Learning' Models that Reduce Antitrust Liability, Deadweight Losses, Regret and GPS-Manipulation In the 'Sharing Economy'

During 2005-2018, the “Sharing Economy” (which includes Airbnb; Apple; Alibaba, Uber; WeWork; Liquidspace, Lyft; Ebay; Didi Chuxing; Taxify; Amazon; HomeAway; etc.) blossomed across the world, triggered structural changes in industries and significantly affected international capital flows primarily by disobeying a wide variety of statutes laws in many countries and illegally reducing and changing the nature of competition in many industries often to the detriment of social welfare. Furthermore, Uber’s and Airbnb’s pricing systems are not efficient and can generate deadweight-losses and Regret. Other “sharing economy companies” (“SEOs”) also face similar pricing, antitrust, deadweight-loss and Regret issues (eg. WeWork; Lyft; Taxify; LiquidSpace; ShareDesk; Homeaway; etc.). This article: i) develops new dynamic pricing models for the Sharing Economy companies; ii) derives some stability properties of mixed games and dynamic algorithms that are inherent in new dynamic pricing models introduced herein which eliminate antitrust liability for SEOs and also reduce deadweight losses, greed, Regret and GPS manipulation - that is, the new dynamic pricing models exhibit “Multi-Stability”. The new dynamic pricing models have desirable properties such as individual rationality; exact and approximate welfare maximization; strong budget balance; dominant-strategy incentive compatibility of sellers and buyers; pareto optimality and feasibility – and thus, each model contravenes the Myerson-Satterthwaite Impossibility Theorem. The pricing models include multi-sided auctions wherein at any time t, several auctions can simultaneously occur, and the payoff functions of any buyer-seller pair in any auction depends on the bidding done by at least another buyer-seller pair either at the same time, or at a different time (this “long-memory” bias of buyers and sellers is new in the literature). More importantly the issues and models discussed herein have or can have significant implications for inequality, labor mobility and income dynamics (for employees of SEOs).

Spanning tree auctions: A complete characterization

We consider a mechanism design problem over a connected graph in private value environment where the type of an agent is a single number. The preference over transfers is quasi-linear for every agent. We give a complete characterization of dominant strategy incentive compatible mechanisms for this problem. Further, by imposing a suitable version of anonymity and non-bossiness along with dominant strategy incentive compatibility, we find that the only mechanisms satisfying all these conditions are the Groves mechanisms.

Optimal Voting Rules

We study dominant strategy incentive compatible (DIC) and deterministic mechanisms in a social choice setting with several alternatives. The agents are privately informed about their preferences, and have single-crossing utility functions. Monetary transfers are not feasible. We use an equivalence between deterministic, DIC mechanisms and generalized median voter schemes to construct the constrained-efficient, optimal mechanism for an utilitarian planner. Optimal schemes for other welfare criteria such as, say, a Rawlsian maximin can be analogously obtained.

Efficient Multi-Unit Auctions for Normal Goods

I study efficient multi-unit auction design when bidders have private values, multi-unit demands, and non-quasilinear preferences. Without quasilinearity, the Vickrey auction loses its desired incentive and efficiency properties. Instead of assuming that bidders have quasilinear preferences, I assume that bidders have positive wealth effects. This nests cases where bidders are risk averse, face financial constraints, or have budgets.With two bidders, I show that there is a mechanism that retains the desirable properties of the Vickrey auction if and only if bidders have single dimensional types. If bidders have multi-dimensional types, there is no mechanism that satisfies (1) individual rationality, (2) dominant strategy incentive compatibility, (3) ex-post Pareto efficiency, and (4) weak budget balance. When there are more than two bidders, I show that there is no mechanism with desirable incentive and efficiency properties, even if bidders have single dimensional types.

Efficient Constrained Combinatorial Auctions

The seminal work by Green and Laffont [(1977) characterization of satisfactory mechanisms for the revelation of preferences for public goods, Econometrica 45, 427–438] shows that efficient mechanisms with Vickrey–Clarke–Groves prices satisfy the properties of dominant-strategy incentive compatible (DSIC) and individually rational in the quasilinear utilities model. Nevertheless in many real-world situations some players have a gap between their willingness to pay and their ability to pay, i.e., a budget. We show that once budgets are integrated into the model then Green and Laffont’s theorem ceases to apply. More specifically, we show that even if only a single player has budget constraints then there is no deterministic efficient mechanism that satisfies the individual rationality and DSIC properties. Furthermore, in a quasilinear utilities model with [Formula: see text] nonidentical items and [Formula: see text] players with multidimensional types, we characterize the sufficient and necessary conditions under which Green and Laffont’s theorem holds in the presence of budget-constrained players. Interestingly our characterization is similar in spirit to that of Maskin [(2000) Auctions, development and privatization: Efficient auctions with liquidity-constrained buyers, Eur. Econ. Rev. 44, 667–681] for Bayesian single-item constrained-efficiency auctions.