arXiv subjects
Publications and source records attributed to Vikram Manjunath.
In allocating objects via lotteries, it is common to consider ordinal rules that rely solely on how agents rank degenerate lotteries. While ordinality is often imposed due to cognitive or informational constraints, we provide another justification from an axiomatic perspective: for three-agent problems, the combination of efficiency, strategy-proofness, non-bossiness, and a weak form of continuity collectively implies ordinality.
We study balanced exchange problems in which agents with responsive preferences are endowed with multiple indivisible objects and can trade without transfers (e.g. shift exchange, time-banking). Eliciting full preferences over bundles is infeasible, so mechanisms often rely solely on marginal preferences, that is, rankings of individual objects. We characterize when eliciting only marginal preferences is enough to unambiguously identify allocations that are efficient and individually rational in the sense that these properties hold with respect to any responsive preferences consistent with the elicited marginals. We parameterize domains of marginal preferences by which indifference classes can contain endowed and non-endowed objects. We show that the essentially unique maximal domain for which an unambiguously efficient and unambiguously individually rational marginal mechanism exists is trichotomous: agents rank objects in three tiers, with the bottom tier containing no endowed objects. We also consider incentives for truthful preference revelation. The maximal domain for which an efficient, individually rational, and strategy-proof mechanism exists is strongly trichotomous: agents rank objects in three tiers, with the bottom tier containing no endowed objects and the middle tier containing no non-endowed objects. The canonical marginal mechanism achieving our three desiderata on that domain is a serial dictatorship over individually rational allocations. When employed on the larger trichotomous domain, this mechanism still admits a weakly dominant strategy: reveal the top tier truthfully and omit non-endowed objects from the middle tier. We propose a family of gradual-revelation mechanisms that are also unambiguously efficient and individually rational on the trichotomous domain while providing better incentives for truthful revelation across all three tiers.
When allocating indivisible objects via lottery, planners often use ordinal mechanisms, which elicit agents' rankings of objects rather than their full preferences over lotteries. In such an ordinal informational environment, planners cannot differentiate between utility profiles that induce the same ranking of objects. We propose the criterion of unambiguous efficiency: regardless of how each agent extends their preferences over objects to lotteries, the allocation is Pareto efficient with respect to the extended preferences. We compare this with the predominant efficiency criterion used for ordinal mechanisms. As an application to mechanism design, we characterize all efficient and strategy-proof mechanisms satisfying certain regularity conditions.
Lexicographic composition is a natural way to build an aggregate choice function from component choice functions. As the name suggests, the components are ordered and choose sequentially. The sets that subsequent components select from are constrained by the choices made by earlier choice functions. The specific constraints affect whether properties like path independence are preserved. For several domains of inputs, we characterize the constraints that ensure such preservation.
Many centralized matching markets are preceded by interviews between participants. We study the impact on the final match of an increase in the number of interviews for one side of the market. Our motivation is the match between residents and hospitals where, due to the COVID-19 pandemic, interviews for the 2020-21 season of the National Residency Matching Program were switched to a virtual format. This drastically reduced the cost to applicants of accepting interview invitations. However, the reduction in cost was not symmetric since applicants, not programs, previously bore most of the costs of in-person interviews. We show that if doctors can accept more interviews, but the hospitals do not increase the number of interviews they offer, then no previously matched doctor is better off and many are potentially harmed. This adverse consequence is the result of what we call interview hoarding. We prove this analytically and characterize optimal mitigation strategies for special cases. We use simulations to extend these insights to more general settings.