arXiv subjects

Debasis Mishra

Publications and source records attributed to Debasis Mishra.

13 recordsLinked to original sources

arXiv2026

Strategy-proof and Efficient Job Matching with Participation Constraints

We study the design of strategy-proof and efficient mechanisms satisfying participation constraints in the job-matching problem. Each firm can hire multiple workers and each worker can be employed at only one firm. While firm utilities over subsets of workers are common knowledge, worker disutilities for working at each firm are private information. The VCG mechanism is the unique mechanism that is strategy-proof, efficient, and individually rational for workers; however, it may not be individual rational for firms. We show that the VCG mechanism is individually rational for firms if and only if firm utilities satisfy a condition called weak substitutes. We then strengthen participation constraints of firms to {\sl strong individual rationality}, which requires that each firm has no incentive to fire some of the workers assigned to it. The VCG mechanism is strongly individual rational if and only if firm utilities satisfy submodularity.

econ.TH↗

arXiv2026

Equity in auction design with unit-demand agents and non-quasilinear preferences

We study a model of auction design where a seller is selling a set of objects to a set of agents who can be assigned no more than one object. Each agent's preference over (object, payment) pair need not be quasilinear. If the domain contains all classical preferences, we show that there is a unique mechanism, the minimum Walrasian equilibrium price (MWEP) mechanism, which is strategy-proof, individually rational, and satisfies equal treatment of equals, no-wastage (every object is allocated to some agent), and no-subsidy (no agent is subsidized). This provides an equity-based characterization of the MEWP mechanism, and complements the efficiency-based characterization of the MWEP mechanism known in the literature.

econ.TH↗

arXiv2025

Robust Procurement: Bayesian Design under Worst-Case Approval Constraints

We study optimal procurement when a Bayesian designer must obtain approval from a non-Bayesian authority that shares the designer's objective but is uncertain about the value of the good and the supplier's cost. The designer uses a conjectured model to compute expected payoffs but is constrained to select among mechanisms delivering the largest payoff guarantee to the authority. This robustness requirement reshapes the tradeoff between efficiency and rent extraction: it reduces procurement from sellers with intermediate costs but may increase it from those with a high cost. When the good is sold in a market, we show that quantity regulation dominates price regulation if markups under the conjectured model are large, whereas price regulation dominates when demand uncertainty is substantial.

econ.TH↗

arXiv2025

Teacher transfers: equalizing deficits across schools

The Right to Free and Compulsory Education Act (2009) (RTE) of the Government of India prescribes student-teacher ratios for state-run schools. One method advocated by the Act to achieve its goals is the redeployment of teachers from surplus to deficit (in teacher strength) schools. We consider a model where teachers can either remain in their initially assigned schools or be transferred to a deficit school in their acceptable set. The planner's objective is specified in terms of the post-transfer deficit vector that can be achieved. We show that there exists a transfer whose post-transfer deficit vector Lorenz dominates all achievable post-transfer deficit vectors. We provide a two-stage algorithm to derive the Lorenz-dominant post-transfer deficit vector, and show that this algorithm is strategy-proof for teachers.

econ.TH↗

arXiv2024

Undominated monopoly regulation

We study undominated mechanisms with transfers for regulating a monopolist who privately observes the marginal cost of production. We show that in any undominated mechanism, there is a quantity floor, which depends only on the primitives, and the regulator's operation decision is stochastic only if the monopolist produces at the quantity floor. We provide a near-complete characterization of the set of undominated mechanisms and use it to (a) provide a foundation for deterministic mechanisms, (b) show that the efficient mechanism is dominated, and (c) derive a max-min optimal regulatory mechanism.

econ.TH↗

arXiv2022

Rank-preserving Multidimensional Mechanisms: an equivalence between identical-object and heterogeneous-object models

We show that the mechanism-design problem for a monopolist selling multiple, heterogeneous objects to a buyer with ex ante symmetric and additive values is equivalent to the mechanism-design problem for a monopolist selling identical objects to a buyer with decreasing marginal values. We derive three new results for the identical-objects model: (i) a new condition for revenue monotonicity of stochastic mechanisms, (ii) a sufficient condition on priors, such that prices in optimal deterministic mechanism are not increasing, and (iii) a simplification of incentive constraints for deterministic mechanisms. We use the equivalence to establish corresponding results in the heterogeneous-objects model.

econ.TH↗

arXiv2022

Symmetric reduced form voting

We study a model of voting with two alternatives in a symmetric environment. We characterize the interim allocation probabilities that can be implemented by a symmetric voting rule. We show that every such interim allocation probabilities can be implemented as a convex combination of two families of deterministic voting rules: qualified majority and qualified anti-majority. We also provide analogous results by requiring implementation by a symmetric monotone (strategy-proof) voting rule and by a symmetric unanimous voting rule. We apply our results to show that an ex-ante Rawlsian rule is a convex combination of a pair of qualified majority rules.

econ.TH↗

arXiv2022

Selling to a principal and a budget-constrained agent

We analyze a model of selling a single object to a principal-agent pair who want to acquire the object for a firm. The principal and the agent have different assessments of the object's value to the firm. The agent is budget-constrained while the principal is not. The agent participates in the mechanism, but she can (strategically) delegate decision-making to the principal. We derive the revenue-maximizing mechanism in a two-dimensional type space (values of the agent and the principal). 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.

econ.TH↗

arXiv2020

Ordinal Bayesian incentive compatibility in random assignment model

We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is a uniform prior, then a large class of random mechanisms are OBIC with respect to this prior -- this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent priors in some neighborhood of a given independent prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.

econ.TH↗

arXiv2020

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 the 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.

econ.TH↗

arXiv2020

Selling Two Identical Objects

It is well-known that optimal (i.e., revenue-maximizing) selling mechanisms in multidimensional type spaces may involve randomization. We obtain conditions under which deterministic mechanisms are optimal for selling two identical, indivisible objects to a single buyer. We analyze two settings: (i) decreasing marginal values (DMV) and (ii) increasing marginal values (IMV). Thus, the values of the buyer for the two units are not independent. We show that under a well-known condition on distributions~(due to McAfee and McMillan (1988)), (a) it is optimal to sell the first unit deterministically in the DMV model and (b) it is optimal to bundle (which is a deterministic mechanism) in the IMV model. Under a stronger sufficient condition on distributions, a deterministic mechanism is optimal in the DMV model. Our results apply to heterogeneous objects when there is a specified sequence in which the two objects must be sold.

econ.TH↗

arXiv2016

Balanced Ranking Mechanisms

In the private values single object auction model, we construct a satisfactory mechanism - a symmetric, dominant strategy incentive compatible, and budget-balanced mechanism. Our mechanism allocates the object to the highest valued agent with more than 99% probability provided there are at least 14 agents. It is also ex-post individually rational. We show that our mechanism is optimal in a restricted class of satisfactory ranking mechanisms. Since achieving efficiency through a dominant strategy incentive compatible and budget-balanced mechanism is impossible in this model, our results illustrate the limits of this impossibility.

cs.GT↗

arXiv2010

Roberts' Theorem with Neutrality: A Social Welfare Ordering Approach

We consider dominant strategy implementation in private values settings, when agents have multi-dimensional types, the set of alternatives is finite, monetary transfers are allowed, and agents have quasi-linear utilities. We show that any implementable and neutral social choice function must be a weighted welfare maximizer if the type space of every agent is an $m$-dimensional open interval, where $m$ is the number of alternatives. When the type space of every agent is unrestricted, Roberts' theorem with neutrality \cite{Roberts79} becomes a corollary to our result. Our proof technique uses a {\em social welfare ordering} approach, commonly used in aggregation literature in social choice theory. We also prove the general (affine maximizer) version of Roberts' theorem for unrestricted type spaces of agents using this approach.

cs.GT↗