Regret testing: learning to play Nash equilibrium without knowing you have an opponent

A learning rule is uncoupled if a player does not condition his strategy on the opponent's payoffs. It is radically uncoupled if a player does not condition his strategy on the opponent's actions or payoffs. We demonstrate a family of simple, radically uncoupled learning rules whose period-by-period behavior comes arbitrarily close to Nash equilibrium behavior in any finite two-person game.Learning, Nash equilibrium, regret, bounded rationality

Contagion in financial networks

The recent financial crisis has prompted much new research on the interconnectedness of the modern financial system and the extent to which it contributes to systemic fragility. Network connections diversify firms' risk exposures, but they also create channels through which shocks can spread by contagion. We review the extensive literature on this issue, with the focus on how network structure interacts with other key variables such as leverage, size, common exposures, and short-term funding. We discuss various metrics that have been proposed for evaluating the susceptibility of the system to contagion and suggest directions for future research

Stochastic learning dynamics and speed of convergence in population games

We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium

How safe are central counterparties in credit default swap markets?

We propose a general framework for estimating the vulnerability to default by a central counterparty (CCP) in the credit default swaps market. Unlike conventional stress testing approaches, which estimate the ability of a CCP to withstand nonpayment by its two largest counterparties, we study the direct and indirect effects of nonpayment by members and/or their clients through the full network of exposures. We illustrate the approach for the U.S. credit default swaps market under shocks that are similar in magnitude to the Federal Reserve’s stress tests. The analysis indicates that conventional stress testing approaches may underestimate the potential vulnerability of the main CCP for this market

The Cost of Stability in Coalitional Games

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the \emph{core}--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which is interested in having the players work together, offers a supplemental payment to the grand coalition (or, more generally, a particular coalition structure). This payment is conditional on players not deviating from their coalition(s). The sum of this payment plus the actual gains of the coalition(s) may then be divided among the agents so as to promote stability. We define the \emph{cost of stability (CoS)} as the minimal external payment that stabilizes the game. We provide general bounds on the cost of stability in several classes of games, and explore its algorithmic properties. To develop a better intuition for the concepts we introduce, we provide a detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings. Finally, we extend our model and results to games with coalition structures.Comment: 20 pages; will be presented at SAGT'0

Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games

We consider repeated multiplayer games in which players repeatedly and simultaneously choose strategies from a finite set of available strategies according to some strategy adjustment process. We focus on the specific class of weakly acyclic games, which is particularly relevant for multiagent cooperative control problems. A strategy adjustment process determines how players select their strategies at any stage as a function of the information gathered over previous stages. Of particular interest are “payoff-based” processes in which, at any stage, players know only their own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know the actions taken by other players and do not know the structural form of payoff functions. We introduce three different payoff-based processes for increasingly general scenarios and prove that, after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage with arbitrarily high probability. We also show how to modify player utility functions through tolls and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a simulation of distributed routing over a network

The speed of innovation diffusion in social networks

New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In practice, the topology may not be known with any precision, and it is constantly in flux as links are formed and severed. Here, we establish an upper bound on the expected waiting time until a given proportion of the population has adopted that holds independently of the network structure. Kreindler and Young (2014) demonstrated such a bound for regular networks when agents choose between two options: the innovation and the status quo. Our bound holds for directed and undirected networks of arbitrary size and degree distribution, and for multiple competing innovations with different payoffs

Anatomy of the Repo Rate Spikes in September 2019

Repurchase agreement (repo) markets represent one of the largest sources of funding and risk transformation in the US financial system. Despite the large volume, repo rates can be quite volatile, and in the extreme, they have exhibited intraday spikes that are five to 10 times the rate on a typical day. This paper uses a unique combination of intraday timing data from the repo market to examine the potential causes of the dramatic spike in repo rates in mid-September 2019. We conclude that, in large part, the spike resulted from a confluence of factors that, when taken individually, would not have been nearly as disruptive. Our work highlights how a lack of information transmission across repo segments and stickiness in customer-to-dealer markets most likely exacerbated the spike. These findings are instructive in the context of repo market liquidity, demonstrating how the segmented structure of the market can contribute to its fragility