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J Doyne Farmer's Blog

New: Best Reply Structure and Equilibrium Convergence in Generic Games

April 20, 2017 Comments (0)

Game theory often assumes rational players that play equilibrium strategies. But when the players have to learn their strategies by playing the game repeatedly, how often do the strategies converge? We analyze generic two player games using a standard learning algorithm, and also study replicator dynamics, which is closely related. We show that the frequency with which strategies converge to a fixed point can be understood by analyzing the best reply structure of the payoff matrix. A Boolean...

REVISION: A Taxonomy of Learning Dynamics in 2 × 2 Games

February 16, 2017 Comments (0)

Learning would be a convincing method to achieve coordination on an equilibrium. But does learning converge, and to what? We answer this question in generic 2-player, 2-strategy games, using Experience-Weighted Attraction (EWA), which encompasses many extensively studied learning algorithms. We exhaustively characterize the parameter space of EWA learning, for any payoff matrix, and we understand the generic properties that imply convergent or non-convergent behaviour in 2 × 2...

REVISION: A Taxonomy of Learning Dynamics in 2 × 2 Games

February 16, 2017 Comments (0)

Learning would be a convincing method to achieve coordination on an equilibrium. But does learning converge, and to what? We answer this question in generic 2-player, 2-strategy games, using Experience-Weighted Attraction (EWA), which encompasses many extensively studied learning algorithms. We exhaustively characterize the parameter space of EWA learning, for any payoff matrix, and we understand the generic properties that imply convergent or non-convergent behaviour in 2 × 2...

New: Macroprudential Policy in an Agent-Based Model of the UK Housing Market

February 16, 2017 Comments (0)

This paper develops an agent-based model of the UK housing market to study the impact of macroprudential policies on key housing market indicators. This approach enables us to tackle the heterogeneity in this market by modelling the individual behaviour and interactions of first-time buyers, home owners, buy-to-let investors, and renters from the bottom up, and observe the resulting aggregate dynamics in the property and credit markets. The model is calibrated using a large selection of...

New: Discounting the Distant Future

July 15, 2015 Comments (0)

If the historical average annual real interest rate is m > 0, and if the world is stationary, should consumption in the distant future be discounted at the rate of m per year? Suppose the annual real interest rate r(t) reverts to m according to the Ornstein Uhlenbeck (OU) continuous time process dr(t) = alpha[m - r(t)]dt kdw(t), where w is a standard Wiener process. Then we prove that the long run rate of interest is r_infinity = m-k^2/2alpha^2. This confirms the Weitzman-Gollier principle...

REVISION: Uncertain Growth and the Value of the Future

December 19, 2013 Comments (0)

For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount rate and has generated a major controversy as to the urgency for immediate action. We study analytically several standard interest rate models from finance and compare their properties to empirical...

REVISION: Uncertain Growth and the Value of the Future

December 19, 2013 Comments (0)

For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount rate and has generated a major controversy as to the urgency for immediate action. We study analytically several standard interest rate models from finance and compare their properties to empirical...

REVISION: How Efficiency Shapes Market Impact

December 19, 2013 Comments (0)

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the...

New: How Efficiency Shapes Market Impact

March 21, 2013 Comments (0)

J. Doyne FarmerSanta Fe Institute; LUISS Guido Carli UniversityAustin GerigUniversity of Oxford - Said Business SchoolFabrizio LilloUniversity of PalermoHenri WaelbroeckPortware LLCAbstractWe develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller...

New: Stability Analysis of Financial Contagion Due to Overlapping Portfolios

November 17, 2012 Comments (0)

Common asset holdings are widely believed to have been the primary vector of contagion in the recent financial crisis. We develop a network approach to the amplification of financial contagion due to the combination of overlapping portfolios and leverage, and we show how it can be understood in terms of a generalized branching process. By studying a stylized model we estimate the circumstances under which systemic instabilities are likely to occur as a function of parameters such as leverage, ma