Object-based unawareness: Axioms

This paper provides foundations for a model of unawareness, called object-based unawareness (OBU) structures, that can be used to distinguish between what an agent is unaware of and what she simply does not know. At an informal level, this distinction plays a key role in a number of papers such as Tirole (2009) and Chung & Fortnow (2016). In this paper, we give the model-theoretic description of OBU structures by showing how they assign truth conditions to every sentence of the formal language used. We then prove a model-theoretic sound and completeness theorem, which characterizes OBU structures in terms of a system of axioms. We then verify that agents in OBU structures do not violate any of the introspection axioms that are generally considered to be necessary conditions for a plausible notion of unawareness. Applications are provided in our companion paper.

Axioms concerning uncertain disagreement points in 2-person bargaining problems

We consider 2-person bargaining situations in which the feasible set is known, but the disagreement point is uncertain. We investigate the implications of various axioms concerning uncertain disagreement points and characterize the family of linear solutions, which includes the egalitarian, lexicographic egalitarian, Nash, and Kalai-Rosenthal solutions. We also show that how the important subfamilies (or members) of this family can be singled out by imposing additional axioms or strengthening the axioms used in the characterizations.

Dream teams and the Apollo effect

We model leadership selection, competition, and decision making in teams with heterogeneous membership composition. We show that if the choice of leadership in a team is imprecise or noisy--which may arguably be the case if appointment decisions are made by non-expert administrators--then it is not necessarily the case that the best individuals should be selected as team members. On the contrary, and in line with what has been called the "Apollo effect," a "dream team" consisting of unambiguously higher-performing individuals may perform worse in terms of team output than a group composed of lower performers. We characterize the properties of the leadership selection and production processes that lead to the Apollo effect. Finally, we clarify when the opposite effect occurs in which supertalent performs better than comparatively less qualified groups.

A deferred acceptance mechanism for decentralized, fast, and fair childcare assignment

We design and implement a program-proposing deferred acceptance mechanism with ties (DAT) and apply it to childcare assignment in two German cities. The mechanism can accommodate complementarities in providers' preferences, is fast to terminate even in larger cities, is difficult to manipulate in practice, and produces stable allocations. It can be further sped up by introducing two new features. First, allowing for an arbitrary share of facilities who participate in a centralized manner by submitting a rank-order-list over applicants. Second, by breaking ties in applicants' rank-order-lists on a first-come-first-serve basis, which sets incentives for programs to propose faster. We provide and evaluate simulation results.

On the degree of distortions under second-degree price discrimination

This paper highlights the limitations and applicability of results developed by Chao & Nahata (2015) for nonlinear pricing. Although Chao and Nahata appear to provide necessary and sufficient conditions for general utility functions, we show that one of their results leads only to a restatement of two constraints, and another result may not be valid when consumers can freely dispose of the good. Their model allows for the possibility that higher quantities will have a lower price than smaller quantities. We provide conditions under free disposal that preclude this anomaly. Our analysis suggests that further research on violations of the single-crossing condition should be encouraged.

Matching with compatibility constraints: The case of the Canadian medical residency match

The Canadian medical residency match has received considerable attention in the medical community as several students go unmatched every year. Simultaneously, multiple residency positions go unfilled, largely in Quebec, the Francophone province of Canada. In Canada, positions are designated with a language restriction, a phenomenon that has not been described previously in the matching literature. We develop a model of matching with compatibility constraints, where, based on a dual-valued characteristic, a subset of students is incompatible with a subset of hospitals, and show how such constraints lead to inefficiency. We derive a lower bound for the number of Anglophone and Francophone residency positions such that every student is matched for all instances of (a form of) preferences. Our analysis suggests that to guarantee a stable match for every student, a number of positions at least equal to the population of bilingual students must be left unfilled.

Rights and rents in local commons

Motivated by management problems in national fisheries, we examine management of renewable resources in local or regional commons. This paper suggests that property rights, or lack thereof, be replaced by well-defined user rights. It shows that the use of commons can be conditioned, paid for, or valued, via market mechanisms. To that end, direct deals and double auctions are expedient. Either institution can distribute, restore and secure resource rent. Either can also focalize debates as to which assignments, regulations or taxation of rights might be fair or legitimate.

On a class of linear-state differential games with subgame individually rational and time consistent bargaining solutions

We consider n-person pure bargaining games in which the space of feasible payoffs is constructed via a normal form differential game. At the beginning of the game the agents bargain over strategies to be played over an infinite time horizon. An initial cooperative solution (a strategy tuple) is called subgame individually rational (SIR) if it remains individually rational throughout the entire game and time consistent (TC) if renegotiating it at a later time instant yields the original solution. For a class of linear-state differential games we show that any solution which is individually rational at the beginning of the game satisfies SIR and TC if the space of admissible cooperative strategies is restricted to constants. We discuss an application from environmental economics.

On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints

When a government intervenes in markets by setting a target amount of goods/services traded, its tax/subsidy policy is optimal if it entices the market participants to obey the policy target while achieving the highest possible social welfare. For the model of job market interventions by Kojima et al. (2019), we establish the existence of optimal taxes/subsidies as well as their characterization. Our methodological contribution is to introduce a discrete version of Karush-Kuhn-Tucker's saddle-point theorem based on the techniques in discrete convex analysis. We have two main results: we (i) characterize the optimal taxes/subsidies and the corresponding equilibrium salaries as the minimizers of a Lagrange function, and (ii) prove that the function satisfies a notion of discrete convexity (called L#-convexity). These results together with others imply that an optimal tax/subsidy level exists and can be calculated via a computationally efficient algorithm.

Implementation with ex post hidden actions

We study implementation in settings where agents take strategic actions that influence preferences over mechanism outcomes and yet are hidden from the mechanism designer. We show that such settings can arise in entry auctions for markets, and that the Vickery-Clarke-Groves mechanism is not necessarily truthful. In this paper we first formalize so-called ex post hidden actions, we then characterize social choice functions that can be implemented in a way that is robust with respect to ex post hidden actions, and finally we propose a mechanism to do so. The model allows agents to have multi-dimensional types and to have quasi-linear utilities in money. We showcase these results by identifying social choice functions that can and cannot be implemented in entry auctions for Cournot competition models.