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Complex Preferences in Matching Markets and Auctions

Final Report Summary - CPMMA (Complex Preferences in Matching Markets and Auctions)

Our contribution is to the theory of "trading networks", a general new framework which subsumes many "classical" matching and auction settings. Roughly speaking, trading networks allow us to model a decentralized market in which each agent can be simultaneously a buyer and a seller and any two agents may interact with each other through bilateral contracts.

Our first project investigates various forms of substitutability, a key restriction on the preferences that agents are allowed to express, which is essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ canonical definitions of substitutability to trading networks and we show that all these definitions are equivalent. We introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We then prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability. Our full substitutability condition is very general, and in particular allows for certain complementarities, which in turn may allow agents to express richer preferences. For instance, in the entry-level labour market for junior doctors, it may be possible to express the preferences of couples. Or, in an auction setting, a central bank, in it’s capacity of lender of last resort for commercial banks, may be able to run a single auction for both “good” and “bad” collateral (as opposed to having two separate auctions, one for each type of collateral), which in turn may allow commercial banks to express richer preferences over mixes of good and bad collateral.

Our second project, considers some of the issues with various canonical solution concepts in the trading networks framework. First, cooperative solution concepts in game theory such as stability often rely on coordinated deviations by large groups of agents, including, in some cases, all the agents in the economy. A natural question when considering such deviations is how and whether such coalitions can in fact form. Second, a different yet related issue arises when considering the concept of competitive equilibrium with personalized prices. Competitive equilibrium requires specifying prices for all possible goods and trades in the economy — even those that are not actually traded. Third, a parallel set of issues arises in applied work: An econometrician may want to estimate parameters of interest and would like to use conditions arising from cooperative solution concepts or from equilibrium requirements. Similarly, an econometrician may want to test whether an outcome in a particular market satisfies those conditions. In such cases, when using cooperative solution concepts, does an econometrician need to consider deviations by all possible groups of agents? When studying competitive equilibrium, does he need to “fill out” all the “missing” prices for the trades that do not take place? We answer all these questions in the negative and we show that chains of contracts which have a well-defined linear structure are the “essential” blocking sets that one needs to consider to evaluate the stability of an outcome or its consistency with competitive equilibrium. Thus, our results show that much of the complexity faced by applied work in trading networks can be sidestepped.