Matching Dynamics with Constraints

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times. For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of "consistent" instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated. We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.Comment: Conference Version in WINE 201

New and simple algorithms for stable flow problems

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in which vertices express their preferences over their incident edges. A network flow is stable if there is no group of vertices that all could benefit from rerouting the flow along a walk. Fleiner established that a stable flow always exists by reducing it to the stable allocation problem. We present an augmenting-path algorithm for computing a stable flow, the first algorithm that achieves polynomial running time for this problem without using stable allocation as a black-box subroutine. We further consider the problem of finding a stable flow such that the flow value on every edge is within a given interval. For this problem, we present an elegant graph transformation and based on this, we devise a simple and fast algorithm, which also can be used to find a solution to the stable marriage problem with forced and forbidden edges. Finally, we study the stable multicommodity flow model introduced by Kir\'{a}ly and Pap. The original model is highly involved and allows for commodity-dependent preference lists at the vertices and commodity-specific edge capacities. We present several graph-based reductions that show equivalence to a significantly simpler model. We further show that it is NP-complete to decide whether an integral solution exists

Copyright, Private Copying, and Discrete Public Goods

Understanding if, and when, copyright should attempt to proscribe private copying deserves far more than the simplistic treatment it has so far received from a handful of courts. This Essay aims to begin that conversation. Part I begins by introducing simple models that compare the market and socially optimal production of continuous and discrete public goods models and discussing their implications for copyright. Part II will then focus on the limits of the market\u27s ability to produce efficiently discrete public goods in the absence of government intervention. Part III will then consider the implications of the discrete public goods model for copyright. Finally, in Part IV, I offer some concluding thoughts

Copyright, Private Copying, and Discrete Public Goods

Understanding if, and when, copyright should attempt to proscribe private copying deserves far more than the simplistic treatment it has so far received from a handful of courts. This Essay aims to begin that conversation. Part I begins by introducing simple models that compare the market and socially optimal production of continuous and discrete public goods models and discussing their implications for copyright. Part II will then focus on the limits of the market\u27s ability to produce efficiently discrete public goods in the absence of government intervention. Part III will then consider the implications of the discrete public goods model for copyright. Finally, in Part IV, I offer some concluding thoughts

Inclusive Economics and Home Loan Policies for Informal Workers

The United States has been suffering from a housing crisis that existed long before the proliferation of sub-prime loans and the Great Recession of 2008-2009. For decades, millions of gainfully employed workers have been institutionally excluded from homeownership, simply because they work in the informal economy. Because of this, the economic growth of households in this demographic has been stymied by discriminatory banking policies that heavily prioritize short-term profit maximization over borrower reliability, or loan viability. Many of those affected are historically disenfranchised people, who systematically have been excluded from the American dream of “a chicken in every pot and a car in every garage,” simply for failing to belong to the narrow demographic for whom home loans were originally designed. Approximately 37% of working adults in the United States today undertake some type of informal work, and 16% of working adults are employed on a full-time basis in the informal sector. It is a segment of the working population that funds an imposing amount of sales tax revenue. These are not the people who lost their homes in The Great Recession of 2008. Indeed, approximately 70% of the subprime loans issued in 2006 were to upper and upper-middle income borrowers in wealthy neighborhoods, and not middle-class working households, or middle-class neighborhoods. It is still the case today that, for workers of the informal economy, homeownership is largely unavailable due to institutional barriers, no matter how modest the home or neighborhood, and no matter how reliable the loan applicant is. This article describes the lost macro-economic opportunity in failing to provide home loans to qualified households in the informal economy, then providing a survey of solutions with successful track records. These solutions fall with a framework I refer to as inclusive economics. My analysis focuses on one segment of informal economy: the cultural economy, which largely operates in cash and exemplifies how inclusive economics can create wealth in a sustainable way that includes historically dis-enfranchised households

The Complexity of Matching Games: A Survey

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an overview of matching games and extensions, such as $b$-matching games and partitioned matching games; the latter originating from the emerging area of international kidney exchange. In this survey we focus on computational complexity aspects of various game-theoretical solution concepts, such as the core, nucleolus and Shapley value, when the input is restricted to some (generalized) matching game

Pairing games and markets

Pairing Games or Markets studied here are the non-two-sided NTU generalization of assignment games. We show that the Equilibrium Set is nonempty, that it is the set of stable allocations or the set of semistable allocations, and that it has has several notable structural properties. We also introduce the solution concept of pseudostable allocations and show that they are in the Demand Bargaining Set. We give a dynamic Market Procedure that reaches the Equilibrium Set in a bounded number of steps. We use elementary tools of graph theory and a representation theorem obtained here