Mechanism Design for Team Formation

Team formation is a core problem in AI. Remarkably, little prior work has addressed the problem of mechanism design for team formation, accounting for the need to elicit agents' preferences over potential teammates. Coalition formation in the related hedonic games has received much attention, but only from the perspective of coalition stability, with little emphasis on the mechanism design objectives of true preference elicitation, social welfare, and equity. We present the first formal mechanism design framework for team formation, building on recent combinatorial matching market design literature. We exhibit four mechanisms for this problem, two novel, two simple extensions of known mechanisms from other domains. Two of these (one new, one known) have desirable theoretical properties. However, we use extensive experiments to show our second novel mechanism, despite having no theoretical guarantees, empirically achieves good incentive compatibility, welfare, and fairness.Comment: 12 page

Computing large market equilibria using abstractions

Computing market equilibria is an important practical problem for market design (e.g. fair division, item allocation). However, computing equilibria requires large amounts of information (e.g. all valuations for all buyers for all items) and compute power. We consider ameliorating these issues by applying a method used for solving complex games: constructing a coarsened abstraction of a given market, solving for the equilibrium in the abstraction, and lifting the prices and allocations back to the original market. We show how to bound important quantities such as regret, envy, Nash social welfare, Pareto optimality, and maximin share when the abstracted prices and allocations are used in place of the real equilibrium. We then study two abstraction methods of interest for practitioners: 1) filling in unknown valuations using techniques from matrix completion, 2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market. We find that in real data allocations/prices that are relatively close to equilibria can be computed from even very coarse abstractions

A comparison of optimal tax policies when compensation or responsibility matter

This paper examines optimal redistribution in a model with high and low-skilled individuals with heterogeneous tastes for labor, that either work or not. With such double heterogeneity, traditional Welfarist criteria including Utilitarianism fail to take the compensation-responsibility trade-off into account. As a response, several other criteria have been proposed in the literature. This paper is the first to compare the extent to which optimal policies based on different normative criteria obey the principles of compensation (for differential skills) and responsibility (for preferences for labor), when labor supply is along the extensive margin. The criteria from the social choice literature perform better in this regard than the traditional criteria, both in first and second best. More importantly, these equality of opportunity criteria push the second best policy away from an Earned Income Tax Credit and in the direction of a Negative Income tax.optimal income taxation, equality of opportunity, heterogeneous preferences for labor

An incentive mechanism to break the low-skill immigration deadlock

public good, inequality aversion, immigration policy

An Incentive Mechanism to Break the Low-skill Immigration Deadlock

Although movements of capital, goods and services are growing in importance, workers movements are impeded by restrictive policies in rich countries. Such regulations carry substantial economic costs for developing countries, and prevent global inequality from declining. Even if rich countries are averse to global inequality, a single country lacks incentives to welcome additional migrants as it would bear the costs alone while the benefits accrue to all rich states. Aversion to global inequality confers a public good nature to the South-North migration of low-skill workers. We propose an alternative allocation of labor maximizing global welfare subject to the constraints that the rich countries are at least as well off as in the current "nationalist" (or "Nashionalist") situation. This "no regret" allocation can be decentralized by a tax-subsidy scheme which makes people internalize the fact that as soon as a rich country welcomes an additional migrant, global inequalities are reduced, and each citizen in the rich world is better off too. Our model is calibrated using statistics on immigration, working-age population and output. We simulate the proposed scheme on different sets of rich countries.Public Good, Inequality Aversion, Immigration policy

Proportionality in Approval-Based Participatory Budgeting

The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the satisfaction of a voter consider (i) the number of approved projects and (ii) the total cost of approved projects, respectively. In general, it is difficult to decide which measure of satisfaction best reflects the voters' true utilities. In this paper, we study proportionality axioms with respect to large classes of approval-based satisfaction functions. We establish logical implications among our axioms and related notions from the literature, and we ask whether outcomes can be achieved that are proportional with respect to more than one satisfaction function. We show that this is impossible for the two commonly used satisfaction functions when considering proportionality notions based on extended justified representation, but achievable for a notion based on proportional justified representation. For the latter result, we introduce a strengthening of priceability and show that it is satisfied by several polynomial-time computable rules, including the Method of Equal Shares and Phragm\`en's sequential rule