📈 economics

Targeting Without Transfers

This paper characterizes the welfare-maximizing allocation of heterogeneous goods without monetary transfers, demonstrating that the optimal mechanism is either a simple menu of pure options or a menu augmented with a bundle, the latter being preferred when mixed allocations effectively target high-value agents based on their narrow preference margins.

Original authors: Filip Tokarski

Published 2026-07-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Filip Tokarski

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the manager of a charity that has a limited supply of different types of food (say, apples, bread, and cheese) to give away to a large group of people. You cannot ask people to pay money, and you don't know exactly how hungry each person is or how much they love apples versus bread. You just know that everyone has a private "value" for these items.

Your goal is to give out the food in a way that makes the most people happy (maximizing welfare), but you have a strict rule: you cannot take money from anyone to redistribute it. You can only give things away.

This paper, by Filip Tokarski, asks: What is the best way to hand out these goods without using money?

The Two Main Strategies

The paper explores two main ways to organize this giveaway:

1. The "Pick Your Favorite" Menu (Pure Options)
Imagine you set up a table with three baskets: one full of apples, one full of bread, and one full of cheese. You tell everyone, "You can only take from one basket. You can't mix them."

How it works: People who love apples the most grab apples. People who love bread grab bread.
The Paper's Finding: Surprisingly, this simple "pick one" system is often the best possible solution. It turns out that if the people who are most in need (have the highest total hunger) are also the people who are most picky about what they eat, then forcing them to choose just one thing is perfect. It naturally sorts the hungry people to the food they need most without needing to know their exact hunger levels.

2. The "Big Mixed Box" Strategy (Bundling)
Now, imagine a different scenario. Suppose the people who are most in need are actually the ones who are less picky. They are starving and would be happy with anything, whereas the less hungry people are very specific (e.g., "I only want cheese, nothing else").

The Paper's Finding: In this case, the simple "pick one" menu fails. The designer can do better by offering a third option: a big mixed box containing a little bit of everything.
Why it works: The "starving but flexible" people will happily trade their choice for a bigger total amount of food. They say, "I don't care if I get cheese or bread, just give me a huge box of both!" The "picky but less hungry" people will stick to their specific favorite.
The Result: By offering this mixed box, the designer can secretly target the people who need the most help (the flexible ones) without them having to lie about their needs. The mixed box acts as a filter: if you are willing to accept a mix, you get more stuff.

The Core Insight: "Picky" vs. "Flexible"

The paper's main discovery is that the best strategy depends entirely on the relationship between how much you need help and how picky you are.

Scenario A (The Picky Neediest): If the people who need the most help are also the most demanding ("I need this specific item"), then the simple "Pick One" menu is best. Trying to mix things up would actually hurt the people you are trying to help.
Scenario B (The Flexible Neediest): If the people who need the most help are the ones who are flexible ("I'll take whatever you have, just give me a lot"), then the designer should offer a "Big Mixed Box." This allows the designer to give more resources to the flexible, high-need group by letting them give up their specific choice.

Real-World Examples from the Paper

The author uses two specific examples to show where this matters:

Food Banks: In some systems, food banks bid for donations using fake money. The paper suggests that if food banks in poorer areas are less picky about which specific food they get (they just need more food), the system should offer them "discounted" large bundles of mixed food. This targets the neediest banks without needing to know their exact financial status.
Affordable Housing: When people apply for low-income housing, they often have to choose between waiting for a specific building or taking whatever is available. The paper suggests that if lower-income families are less picky about which unit they get (they just need a unit), the system should offer a "priority queue" where they give up their right to choose a specific unit in exchange for a faster, guaranteed placement. This targets the most needy families effectively.

Summary

In a world where you can't use money to sort people out, the best way to distribute goods depends on the personality of the people in need:

If the neediest people are picky, let them choose one thing.
If the neediest people are flexible, offer them a big mixed bundle in exchange for giving up their choice.

The paper proves mathematically when each of these strategies is the "winning move" and shows that the simple "pick one" approach is actually the winner in many common situations, but the "mixed bundle" trick is a powerful tool when the neediest people happen to be the most adaptable.

Technical Summary: Targeting Without Transfers

1. Problem Statement

The paper addresses the design of mechanisms for allocating heterogeneous goods among agents with private valuations when monetary transfers are prohibited. The designer aims to maximize utilitarian welfare (the sum of agents' cardinal values) subject to:

Incentive Compatibility (IC): Agents must truthfully reveal their preferences.
Aggregate Supply Constraints: The total allocation of each good cannot exceed its fixed supply.

Unlike much of the existing literature on allocation without money, which focuses on Pareto efficiency or ordinal rankings (e.g., Hylland and Zeckhauser, 1979; Abdulkadiro˘glu and S¨onmez, 1998), this framework explicitly incorporates cardinal welfare objectives. The central challenge is that the designer cannot directly observe agents' absolute levels of need (cardinal values) but must infer them from their revealed relative preferences over goods.

2. Methodology and Model

The author models the problem using a continuum of agents with value vectors $v \in \mathbb{R}^N_+$ . A key methodological innovation is the separation of absolute and relative values.

Renormalization: Since incentive compatibility in the absence of transfers implies that agents with proportional value vectors (same relative preferences) must receive proportional allocations, the author maps types to the simplex $\Gamma$ of relative-value profiles $\theta = v / \sum v_j$ .
Conditional Expectation: The designer's objective is reformulated in terms of $\lambda(\theta) = E[\sum V_j \mid \Theta = \theta]$ , which represents the expected total value (need) of agents with relative profile $\theta$ .
Optimization: The problem is transformed into maximizing a weighted integral of indirect utility over the simplex, subject to convexity constraints on the utility function and supply constraints. The analysis leverages tools from multidimensional screening, specifically optimal transport and stochastic dominance arguments (Daskalakis et al., 2013, 2017; Kleiner and Manelli, 2019).

3. Key Results

A. The Pure Option Mechanism

The paper first characterizes a "pure option" mechanism where each agent receives a quantity of exactly one good and zero of others.

Implementation: This mechanism is equivalent to a Competitive Equilibrium with Equal Incomes (CEEI), a Walrasian equilibrium of a representative endowment economy, or a choice-based lottery.
Optimality Conditions: The author derives necessary and sufficient conditions for this mechanism to be welfare-maximizing. These conditions are expressed via a rent measure $\mu$ $μ$ and a monotone transport plan.
- Specifically, the pure option mechanism is optimal if and only if, after a preprocessing step (analogous to "ironing" in one-dimensional screening), the negative part of the rent measure can be transported to the positive part by moving mass only toward the vertices of the simplex (i.e., toward more extreme relative preferences).
Sufficient Conditions: In symmetric settings with equal supplies, the pure option mechanism is optimal if agents with higher absolute values for their favorite good tend to be more selective (have stronger relative preferences). Intuitively, if high-value agents are pickier, distorting the allocation to offer bundles would inefficiently shift resources toward less selective (lower value) types.

B. The Optimal Mechanism with Two Goods

When there are exactly two goods, the problem reduces to a one-dimensional screening problem. The author fully characterizes the optimal mechanism:

Structure: The optimal mechanism is either the pure option mechanism or a menu containing two pure options and one mixed bundle.
The Bundle: The mixed bundle offers a larger total quantity of goods than the pure options. It is optimal to include the bundle when agents with narrower preference margins (less picky) tend to have higher total values.
Trade-off: Introducing a bundle creates allocative inefficiency (agents receive goods they value less), but it serves as a screening device. If less picky agents are systematically higher-value, the informational gain from targeting them via the bundle outweighs the efficiency loss from mixing.

C. Robustness and Perturbation

The paper demonstrates that the optimality of the pure option mechanism is not a "knife-edge" result of symmetry. Using a perturbation argument based on upper-set slack, the author shows that if the pure option mechanism is optimal for a baseline distribution, it remains optimal for small asymmetric perturbations of the primitives (distributions and supplies), provided the "slack" in the optimality conditions is maintained.

4. Significance and Contributions

The paper makes three primary contributions to the literature on allocation without transfers:

Welfare Maximization with Cardinal Values: It bridges the gap between mechanism design without money (traditionally ordinal) and welfare economics (cardinal). It shows that when policymakers care about targeting agents with high absolute need, the optimal mechanism depends critically on the statistical correlation between absolute need and relative preference intensity.
Characterization of Bundling: The paper provides a rigorous justification for why mixed bundles (or "discounts" for accepting less tailored allocations) might be optimal in non-monetary settings. It identifies the specific statistical condition—where high-value agents are less selective—under which such distortions improve welfare.
Connection to CEEI: It clarifies the relationship between the welfare-optimal mechanism and the Competitive Equilibrium with Equal Incomes (CEEI). While CEEI is known to be Pareto-efficient, the paper shows it is not always welfare-maximizing. However, it remains optimal in a broad class of environments where high-value agents are more selective, and it serves as a robust benchmark.

5. Applications Discussed

The author discusses the implications of these results for specific market design settings:

Food Banks: In systems like Feeding America, where food banks bid for donations using artificial currency, the results suggest that if food banks in low-donor areas are less selective about the specific food items they receive, the system could be improved by offering discounted bundles of pre-packaged assortments.
Affordable Housing: The model interprets waitlists and repeated lotteries as reduced-form mechanisms. The results suggest that offering applicants a choice between a priority queue (where they must accept any suitable unit) and a standard waitlist (where they can select specific units) could be welfare-improving if lower-income applicants are less selective.

The paper concludes by noting that while the baseline model abstracts from observable characteristics (like income), the framework could be extended to incorporate such labels, potentially leading to mechanisms with unequal incomes or segmented markets.