Economics

Is efficiency consistent with fairness? Our approach to this question concerns the case where multiple individuals with diverse preferences are bound to consume the same bundle. Families are our lead example: the father, mother and children get to consume the same garden, kitchen, and vacations. We adapt each of the three most popular principles of fairness: envy-freeness, egalitarian-equivalence and the fair-share guarantee, in three different ways to the world of families. For any given criterion of fairness, an allocation is *unanimous-fair* if it is fair according to every individual member of each family, it is *aggregate-fair* if it is fair according to a particular aggregation of all family members' preferences, and it is *collective-fair* if it is fair according to the family's -- typically incomplete -- preferences, that rank a bundle above another bundle if and only if each member of the family ranks the first bundle above the second. While efficiency is generally incompatible with unanimous egalitarian equivalence, and incompatible with unanimous envy-freeness in economies with three or more families, unanimously envy-free efficient allocations always exist in economies with just two families. The unanimous fair share guarantee is easy to achieve: Under generic conditions the set of efficient allocations with the fair share guarantee contains some collectively envy-free and some collectively egalitarian equivalent allocations. We use modified versions of the traditional market equilibrium approach and lexicographic optimization to establish our results.

We propose a notion of fairness for allocation problems in which different agents may have different reservation utilities, stemming from different outside options, or property rights. Fairness is usually understood as the absence of envy, but this can be incompatible with reservation utilities. It is possible that Alice's envy of Bob's assignment cannot be remedied without violating Bob's participation constraint. Instead, we seek to rule out {\em justified envy}, defined as envy for which a remedy would not violate any agent's participation constraint. We show that fairness, meaning the absence of justified envy, can be achieved together with efficiency and individual rationality. We introduce a competitive equilibrium approach with price-dependent incomes obtaining the desired properties.

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state, and who observe some information structure. For two agents we introduce a quantitative version of Aumann's Agreement Theorem, and show that it is equivalent to a characterization of feasible distributions due to Dawid et al. (1995). For any number of agents, we characterize feasible distributions in terms of a "no-trade" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.

We say a model is continuous in utilities (resp., preferences) if small perturbations of utility functions (resp., preferences) generate small changes in the model's outputs. While similar, these two concepts are equivalent only when the topology satisfies the following universal property: for each continuous mapping from preferences to model's outputs there is a unique mapping from utilities to model's outputs that is faithful to the preference map and is continuous. The topologies that satisfy such a universal property are called final topologies. In this paper we analyze the properties of the final topology for preference sets. This is of practical importance since most of the analysis on continuity is done via utility functions and not the primitive preference space. Our results allow the researcher to extrapolate continuity in utility to continuity in the underlying preferences.

Efficiency and fairness are two desiderata in market design. Fairness requires randomization in many environments. Observing the inadequacy of Top Trading Cycle (TTC) to incorporate randomization, Yu and Zhang (2020) propose the class of Fractional TTC mechanisms to solve random allocation problems efficiently and fairly. The assumption of strict preferences in the paper restricts the application scope. This paper extends Fractional TTC to the full preference domain in which agents can be indifferent between objects. Efficiency and fairness of Fractional TTC are preserved. As a corollary, we obtain an extension of the probabilistic serial mechanism in the house allocation model to the full preference domain. Our extension does not require any knowledge beyond elementary computation.

Functional decision theory (FDT) is a fairly new mode of decision theory and a normative viewpoint on how an agent should maximize expected utility. The current standard in decision theory and computer science is causal decision theory (CDT), largely seen as superior to the main alternative evidential decision theory (EDT). These theories prescribe three distinct methods for maximizing utility. We explore how FDT differs from CDT and EDT, and what implications it has on the behavior of FDT agents and humans. It has been shown in previous research how FDT can outperform CDT and EDT. We additionally show FDT performing well on more classical game theory problems and argue for its extension to human problems to show that its potential for superiority is robust. We also make FDT more concrete by displaying it in an evolutionary environment, competing directly against other theories.

We present a fuzzy version of the Group Identification Problem ("Who is a J?") introduced by Kasher and Rubinstein (1997). We consider a class N={1,2,…,n} of agents, each one with an opinion about the membership to a group J of the members of the society, consisting in a function π:N→[0;1] , indicating for each agent, including herself, the degree of membership to J. We consider the problem of aggregating those functions, satisfying different sets of axioms and characterizing different aggregators. While some results are analogous to those of the originally crisp model, the fuzzy version is able to overcome some of the main impossibility results of Kasher and Rubinstein.

The resident matching algorithm, Gale-Shapley, currently used by SF Match and the National Residency Match Program, has been in use for over 50 years without fundamental alteration. The algorithm is a 'stable-marriage' method that favors applicant outcomes. However, in these 50 years, there has been a big shift in the supply and demand of applicants and programs. These changes along with the way the Match is implemented have induced a costly race among applicants to apply and interview at as many programs as possible. Meanwhile programs also incur high costs as they maximize their probability of matching by interviewing as many candidates as possible.

Players are statistical learners who learn about payoffs from data. They may interpret the same data differently, but have common knowledge of a class of learning procedures. I propose a metric for the analyst's "confidence" in a strategic prediction, based on the probability that the prediction is consistent with the realized data. The main results characterize the analyst's confidence in a given prediction as the quantity of data grows large, and provide bounds for small datasets. The approach generates new predictions, e.g. that speculative trade is more likely given high-dimensional data, and that coordination is less likely given noisy data.

We study network games in which players both create spillovers for one another and choose with whom to associate. The endogenous outcomes include both the strategic actions (e.g., effort levels) and the network in which spillovers occur. We introduce a framework and two solution concepts that extend standard approaches -- Nash equilibrium in actions and pairwise (Nash) stability in links. Our main results show that under suitable monotonicity assumptions on incentives, stable networks take simple forms. Our first condition concerns whether links create positive or negative payoff spillovers. Our second condition concerns whether actions and links are strategic complements or substitutes. Together, these conditions allow for a taxonomy of how network structure depends on economic primitives. We apply our model to understand the consequences of competition for status, to microfound matching models that assume clique formation, and to interpret empirical findings that highlight unintended consequences of group design.