Welfare Maximization with Limited Interaction

We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model where agent's valuations are unknown to the central planner, and therefore communication is required to determine an efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is $n$, then $r$ rounds of interaction (with logarithmic bandwidth) suffice to obtain an $n^{1/(r+1)}$-approximation to the optimal social welfare. In particular, this implies that such markets converge to a stable state (constant approximation) in time logarithmic in the market size. We obtain the first multi-round lower bound for this setup. We show that even if the allowable per-round bandwidth of each agent is $n^{\epsilon(r)}$, the approximation ratio of any $r$-round (randomized) protocol is no better than $\Omega(n^{1/5^{r+1}})$, implying an $\Omega(\log \log n)$ lower bound on the rate of convergence of the market to equilibrium. Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of combinatorial auctions, for which the only known lower bound is for simultaneous ($r=1$) protocols [DNO14]

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Legal Transitions: Some Welfarist Remarks

This essay offers a sympathetic, utilitarian critique of Louis Kaplow\u27s famous argument for legal retroactivity in his 1986 article, An Economic Analysis of Legal Transitions. The argument, very roughly, is that the prospect of retroactivity is desirable if citizens are rational because it gives them a desirable incentive to anticipate legal change. My central claim is that this argument trades upon a dubious, objective view of probability that assumes rational citizens assign the same probabilities to states as rational governmental officials. But it is subjective, not objective probabilities that bear on rational choice, and the subjective probabilities of rational citizens can diverge from rational officials\u27. I imagine a simple case in which a single Social Planner structures both transition policy and substantive law in some domain. The legal change that the Planner anticipates she would enact in response to a given set of events, and the legal change that the Planner believes one or another citizen believes she (the Planner) will enact in response to those events, can differ. And this means, in turn, that there can be incentive costs to a retroactivity regime as well as a prospectivity regime, even if all actors are fully rational. The utilitarian case for retroactivity is more contingent than Kaplow thinks

Guest Worker Programs: A Theoretical Analysis of Welfare of the Host and Source Countries

This paper examines the interaction between migration policies of the host and source countries in the context of a model of guest-worker migration. For the host, the objective is to provide low-cost labor for its employers while avoiding illegal immigration. It optimizes over these objectives by setting the time limit of a guest-worker permit. The source country seeks remittance flows and return migration by offering fiscal benefits to returnees. Within this framework, we solve for the Nash equilibrium values of the migration policy instruments and compare them, to the extent possible, with the ones that emerge in a cooperative setting.Temporary Migration, Remittances, Migration Policy