Stable Matching with Evolving Preferences

We consider the problem of stable matching with dynamic preference lists. At each time step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an approximately stable matching (in terms of number of blocking pairs) at all times. The changes in the preference lists are not reported to the algorithm, but must instead be probed explicitly by the algorithm. We design an algorithm that in expectation and with high probability maintains a matching that has at most $O((log (n))^2)$ blocking pairs.Comment: 13 page

Stable Matching with Evolving Preferences

We consider the problem of stable matching with dynamic preference lists. At each time-step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an approximately stable matching, in terms of number of blocking pairs, at all time-steps. The changes in the preference lists are not reported to the algorithm, but must instead be probed explicitly. We design an algorithm that in expectation and with high probability maintains a matching that has at most O((log n)^2 blocking pairs

Incentivizing Resilience in Financial Networks

When banks extend loans to each other, they generate a negative externality in the form of systemic risk. They create a network of interbank exposures by which they expose other banks to potential insolvency cascades. In this paper, we show how a regulator can use information about the financial network to devise a transaction-specific tax based on a network centrality measure that captures systemic importance. Since different transactions have different impact on creating systemic risk, they are taxed differently. We call this tax a Systemic Risk Tax (SRT). We use an equilibrium concept inspired by the matching markets literature to show analytically that this SRT induces a unique equilibrium matching of lenders and borrowers that is systemic-risk efficient, i.e. it minimizes systemic risk given a certain transaction volume. On the other hand, we show that without this SRT multiple equilibrium matchings exist, which are generally inefficient. This allows the regulator to effectively stimulate a `rewiring' of the equilibrium interbank network so as to make it more resilient to insolvency cascades, without sacrificing transaction volume. Moreover, we show that a standard financial transaction tax (e.g. a Tobin-like tax) has no impact on reshaping the equilibrium financial network because it taxes all transactions indiscriminately. A Tobin-like tax is indeed shown to have a limited effect on reducing systemic risk while it decreases transaction volume.Comment: 38 pages, 9 figure

Selection mechanisms affect volatility in evolving markets

Financial asset markets are sociotechnical systems whose constituent agents are subject to evolutionary pressure as unprofitable agents exit the marketplace and more profitable agents continue to trade assets. Using a population of evolving zero-intelligence agents and a frequent batch auction price-discovery mechanism as substrate, we analyze the role played by evolutionary selection mechanisms in determining macro-observable market statistics. In particular, we show that selection mechanisms incorporating a local fitness-proportionate component are associated with high correlation between a micro, risk-aversion parameter and a commonly-used macro-volatility statistic, while a purely quantile-based selection mechanism shows significantly less correlation.Comment: 9 pages, 7 figures, to appear in proceedings of GECCO 2019 as a full pape

Evolutionary Game Theory

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