Rodney Garratt

The intraday liquidity management game

Abstract We use a game theoretical framework to analyze the intraday behavior of banks with respect to settlement of interbank claims in a real-time gross settlement setting. The game played by banks depends upon the intraday credit policy of the central bank and it encompasses two well-known game theoretical paradigms: the prisoners dilemma and the stag hunt. The former arises in a collateralized credit regime where banks have an incentive to postpone payments when daylight liquidity is costly, an outcome that is socially inefficient. The latter arises in a priced credit regime where the postponement of payments can be socially efficient. Banks are risk neutral, but we show that most of the results are unaffected by risk aversion.

Collusion Via Resale

The English auction is susceptible to tacit collusion when post-auction inter-bidder resale is allowed. We show this by constructing equilibria where, with positive probability, one bidder wins the auction without any competition and divides the spoils by optimally reselling the good to the other bidders. These equilibria interim Pareto dominate (among bidders) the standard value-bidding equilibrium, without requiring the bidders to make any commitment on bidding behavior or post-bidding spoil-division.

Public Finance of Private Goods: The Case of College Education

This paper describes a contract theory of public finance of college education that explains why everyone pays for the college education of a lucky minority. The contract provides gambles that families desire. Optimizing the contract determines the taxes paid by all members of society, fees paid by those whose children go to college, the fraction of children who are admitted to college, and the quality of college education. Changes in wealth lead to changes in taxes and admissions, but fees and quality are invariant. The practice of using a cutoff level of precollege achievement to determine admission to college is justified by the theory.

Mapping Systemic Risk in the International Banking Network

Systemic risk among the network of international banking groups arises when financial stress threatens to criss-cross many national boundaries and expose imperfect international co-ordination. To assess this risk, we apply an information theoretic map equation due to Martin Rosvall and Carl Bergstrom to partition banking groups from 21 countries into modules. The resulting modular structure reflects the flow of financial stress through the network, combining nodes that are most closely related in terms of the transmission of stress. The modular structure of the international banking network has changed dramatically over the past three decades. In the late 1980s four important financial centres formed one large supercluster that was highly contagious in terms of transmission of stress within its ranks, but less contagious on a global scale. Since then the most influential modules have become significantly smaller and more broadly contagious. The analysis contributes to our understanding as to why defaults in US sub-prime mortgages had such large global implications.

Decentralizing Lottery Allocations in Markets With Indivisible Commodities

SummaryIn economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common “sunspot device” as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.

Equilibrium Prices when the Sunspot Variable is Continuous

We analyze sunspot-equilibrium prices in nonconvex economies with perfect markets and a continuous sunspot variable. Our primary result is that every sunspot equilibrium allocation can be supported by prices that, when adjusted for probabilities, are constant across states. This result extends to the case of a finite number of equally probable states under weak nonsatiation conditions, but does not extend to general discrete state spaces. We use our primary result to establish the equivalence of the set of sunspot equilibrium allocations based on a continuous sunspot variable and the set of lottery equilibrium allocations

On Market Games When Agents Cannot Be in Two Places at Once

Abstract We consider markets in which agents supply their time or the services of a capital good and the duration of the market is limited. We show that a coalitional game can be generated by such a market if and only if the characteristic function of the game is superadditive. Journal of Economic Literature Classification Numbers: C71, D51.

Mapping Change in the Federal Funds Market

We use an information-theoretic approach to describe changes in lending relationships between federal funds market participants around the time of the Lehman Brothers failure. Unlike previous work that conducts maximum-likelihood estimation on undirected networks, our analysis distinguishes between borrowers and lenders and looks for broader lending relationships (multibank lending cycles) that extend beyond the immediate counterparties. We find that significant changes in lending patterns emerge following implementation of the Interest on Reserves policy by the Federal Reserve on October 9, 2008.

A Characterization of Robust Sunspot Equilibria

In nonconvex environments, a sunspot equilibrium can sometimes be destroyed by the introduction of new extrinsic information. We provide a simple test for determining whether or not a particular equilibrium survives, or is robust to, all possible re…nements of the state space. We use this test to provide a characterization of the set of robust sunspot-equilibrium allocations of a given economy: it is equivalent to the set of equilibrium allocations of the associated lottery economy.

Efficient Bilateral Trade

We re-examine the canonical question of Myerson and Satterthwaite (1983) whether two parties can trade an indivisible good in a Pareto efficient way when they are both privately-informed about their valuations for the good. Relaxing the assumption that utilities are quasi-linear, we show that efficient trade is generically possible if agents’ utility functions are not too responsive to private information. In natural examples efficient trade is possible even when agents’ utility functions are highly responsive to their private information. The analysis relies on new methods we introduce.