Counterbalancing Learning and Strategic Incentives in Allocation Markets

TL;DR

The paper tackles the inefficiency arising from information cascades in allocating a scarce, high-stakes object when agents hold private signals about quality. It shows that sequential first-come-first-served offers provoke herding and poor correctness, and proposes batching mechanisms that elicit truthful signals while balancing information gain and incentive compatibility. A central result proves that, when the private signal is sufficiently informative ($\mu<q$), there exists an incentive-compatible batching mechanism that strictly improves allocation correctness; when $\mu\ge q$, no batching scheme can beat the sequential benchmark. The authors present a greedy multi-batch algorithm that adaptively sets batch sizes based on posterior beliefs, demonstrate via theory and simulations that two batches often substantially improve correctness over sequential offering, and discuss practical implications for reducing organ-waste in real-world allocation systems.

Abstract

This paper considers the problem of offering a scarce object with a common unobserved quality to strategic agents in a priority queue. Each agent has a private signal over the quality of the object and observes the decisions made by other agents. We first show that, under the widely-used first-come-first-served sequential offering mechanism, herding behavior emerges: initial rejections create an information cascade resulting in inefficient waste. To address this issue, we then introduce a class of batching mechanisms. Agents in each batch report whether they would be willing to accept or reject the object based on their private signals and prior information. If the majority opts to accept, the object is randomly allocated within that batch. We prove that suitable batching mechanisms are incentive-compatible and improve efficiency. A key property of the mechanism is the gradual increase of the batch size after each failed allocation; the size is chosen so that it elicits as much information as possible without distorting the incentives of agents to report truthfully. Additionally, from a healthcare policy perspective, our results can shed light on the large wastage in organ allocation. In particular, wastage that arises due to herding may be reduced by applying adaptive simultaneous offering mechanisms.

Figures (4)

• Figure 1: Allocation outcome of the sequential offer mechanism ($V_\textsc{seq}$) based on the value of prior $\mu \in (0,1)$ with respect to signal precision $q.$ For low $\mu,$ the object is rejected by all agents, leading to discard. For intermediate $\mu,$ the allocation outcome depends on the initial two agents' private signals.
• Figure 2: Interval of incentive-compatible prior $\mathcal{I}_K$ for different batch sizes $K \in \{1, 3, \ldots\}$ as described in Lemma \ref{['lemma: ic-combined']}. The intervals $\mathcal{I}_K$ are decreasing (Lemma \ref{['lemma: ic-interval-decrease']}) with $K$ and the consecutive intervals $\mathcal{I}_K$ and $\mathcal{I}_{K+2}$ overlap (Lemma \ref{['lemma: ic-intervals-overlap']}) with each other.
• Figure 3: Via simulations, we compute the optimal incentive-compatible batch size $\overline{K}(\mu)$ for all possible priors $\mu \in (0,1)$ for three regimes: $q \in \{ 0.6, 0.7, 0.8\}$. In all regimes, $\overline{K}(\mu)$ decreases as $\mu$ increases. For low values of $\mu$, higher $q$ implies lower $\overline{K}(\mu)$.
• Figure 4: We compare the correctness $c(V)$ of mechanisms ${V \in \{V_\textsc{greedy}^1, V_\textsc{greedy}^2, V_\textsc{seq}, V_\textsc{all}\}}$ in a setting with population size $I=345.$$V_\textsc{all}$ represents the optimal mechanism in the absence of strategic incentives and achieves near-optimal correctness. The remaining $V_\textsc{greedy}^1$, $V_\textsc{greedy}^2$, and $V_\textsc{seq}$ assume strategic agents. We compute $c(V)$ for all $\mu \in (0,1)$ and three different regimes $q \in \{0.6,0.7,0.8\}.$ In all regimes, $V_\textsc{greedy}^1$ achieves higher correctness than $V_{\textsc{seq}}$ for all $\mu < {q}/{2} + {1}/{4}$. With one additional batch, $V_\textsc{greedy}^2$ further improves the correctness of $V_\textsc{greedy}^1$ and outperforms $V_{\textsc{seq}}$ for all $\mu < q$.

Theorems & Definitions (60)

• Lemma 3.1
• Proposition 1
• Theorem 1
• Definition 1
• Lemma 4.1
• Lemma 4.2
• Proposition 2
• Lemma 4.3
• Lemma 4.4
• Definition 2