The Hangman's Paradox and Newcomb's Paradox as Psychological Games

We present a (hopefully) fresh interpretation of the Hangman's Paradox and Newcomb's Paradox by casting the puzzles in the language of modern game theory, instead of in the realm of epistemology. Game theory moves the analysis away from the formal logic of the puzzles toward more practical problems, such as: On what day would the executioner hang the prisoner if he wanted to surprise him as much as possible? How should a surprise test be administered? We argue that both the Hangman's Paradox and Newcomb's Paradox are analogous to a well-known phenomenon in game theory, that giving a player an additional attractive (even dominant) strategy may make him worse off. In the Hangman's Paradox, the executioner is determined to surprise the prisoner as much as possible, yet he cannot surprise him at all because he cannot commit in advance to a random schedule. The possibility of changing his mind (i.e., the presence of alternative strategies) superficially would seem to help the executioner, but because it changes the expectations of the prisoner, in the end it works dramatically to his disadvantage. In Newcomb's Paradox, a man given an extra dominant choice is worse off because it changes God's expectations about what he will do. Our analysis cannot be couched in terms of the standard Nash framework of games, but must instead be put in a recent extension called psychological games, where payoffs may depend on beliefs as well as on actions.

Greek Debt and American Debt: Graduation Speech at the University of Athens Economics and Business School

This is the graduation speech I gave on receiving an honorary doctorate at the University of Athens Economics and Business School. I talk about my Greek family, about how I got interested in economics, and then how in the 1990s I came to think about default, collateral, and leverage as the central features of the financial/macro economy, despite their complete absence (even now) from any textbooks. Finally I suggest that the Greek debt problem, and on a bigger scale, the American debt problem, can only be cured when lenders are prodded to forgive. That would be better for the borrowers but also for the lenders.Greek, Parents, Mathematical economics, Yale, Mortgage, Collateral, Securitization, Leverage, Foreclosure, Forgive, Principal

Solving the present crisis and managing the leverage cycle

Yale University professor John Geanakoplos discusses implications of “the leverage cycle”—a phenomenon in which leverage is excessive prior to a financial crisis and unacceptably low during the crisis—for regulatory policy and reform. Presented as the keynote address at "Central Bank Liquidity Tools and Perspectives on Regulatory Reform" a conference sponsored by the Federal Reserve Bank of New York, February 19-20, 2009.Financial market regulatory reform ; Assets (Accounting) ; Investments ; Equilibrium (Economics) ; Financial crises ; Housing - Prices ; Swaps (Finance) ; Default (Finance) ; Uncertainty ; Federal Reserve System

Promises Promises

In the classical general equilibrium model, agents keep all their promises, every good is traded, and competition prevents any agent from earning superior returns on investments in financial markets. In this paper I introduce the age-old problem of broken promises into the general equilibrium model, and I find that a new market dynamic emerges. Given the legal system and institutions, market forces of supply and demand will establish the collateral levels which are required to secure promises. Since physical collateral will typically be scarce, these collateral levels will be set so low that there is bound to be some default. Many kinds of promises will not be traded, because that also economizes on collateral. Scarce collateral thus creates a mechanism for determining endogenously which assets will be traded, thereby helping to resolve a long standing puzzle in general equilibrium theory. Finally, I shall show that under suitable conditions, in rational expectations equilibrium, some investors will be able to earn higher than normal returns on their investments. The legal system, in conjunction with the market, will be under constant pressure to expand the potential sources of collateral. This will lead to market innovation. I illustrate the theoretical points in this paper with some of my experiences on Wall Street as director of fixed income research at the firm of Kidder Peabody.

Overlapping Generations Models of General Equilibrium

The OLG model of Allais and Samuelson retains the methodological assumptions of agent optimization and market clearing from the Arrow-Debreu model, yet its equilibrium set has different properties: Pareto inefficiency, indeterminacy, positive valuation of money, and a golden rule equilibrium in which the rate of interest is equal to population growth (independent of impatience). These properties are shown to derive not from market incompleteness, but from lack of market clearing "at infinity;" they can be eliminated with land or uniform impatience. The OLG model is used to analyze bubbles, social security, demographic effects on stock returns, the foundations of monetary theory, Keynesian vs. real business cycle macromodels, and classical vs. neoclassical disputes.Demography, Inefficiency, Indeterminacy, Money, Bubbles, Cycles, Rate of interest, Impatience, Land, Infinity, Expectations, Social security, Golden rule

Solving the Present Crisis and Managing the Leverage Cycle

The present crisis is the bottom of a recurring problem that I call the leverage cycle, in which leverage gradually rises too high then suddenly falls much too low. The government must manage the leverage cycle in normal times by monitoring and regulating leverage to keep it from getting too high. In the crisis stage the government must stem the scary bad news that brought on the crisis, which often will entail coordinated write downs of principal; it must restore sane leverage by going around the banks and lending at lower collateral rates (not lower interest rates), and when necessary it must inject optimistic capital into firms and markets than cannot be allowed to fail. Economists and the Fed have for too long focused on interest rates and ignored collateral.Leverage, Collateral, Margins, Leverage cycle, Externality, Principal

The Ideal Inflation Indexed Bond and Irving Fisher's Impatience Theory of Interest in an Overlapping Generations World

Irving Fisher long advocated inflation indexed bonds. I prove in the context of a multicommodity CAPM world that the best welfare improving bond pays the minimum money needed to achieve the same utility, and not the minimum needed to buy an ideal commodity bundle. Irving Fisher also developed and advocated the impatience theory of interest. But in OLG economies, the rate of interest is determined by population growth, not impatience. I reconcile this contradiction by proving that in stationary OLG economies with land, the interest rate at the unique steady state does depend on impatience. Indeed, the proposition that greater impatience creates higher interest rates holds more generally in OLG with land than in Fisher's two-period model.Impatience, Theory of interest, Inflation indexed bond, Konus index, Capital asset pricing, Efficiency, Overlapping generations, Land

The Leverage Cycle

Equilibrium determines leverage, not just interest rates. Variations in leverage cause fluctuations in asset prices. This leverage cycle can be damaging to the economy, and should be regulated.Leverage, Collateral, Cycle, Crisis, Regulation

Liquidity, Default and Crashes: Endogenous Contracts in General Equilibrium

Introducing default and limited collateral into general equilibrium theory (GE) allows for a theory of endogenous contracts, including endogenous margin requirements on loans. This in turn allows GE to explain liquidity and liquidity crises in equilibrium. A formal definition of liquidity is presented. When new information raises the probability a fixed income asset may default, its drop in price may be much greater than its objective drop in value because the drop in value reduces the relative wealth of its natural buyers, who disproportiantely own the asset through leveraged purchases. When the information also shortens the horizon over which the asset might default, its price falls still further because the margin requirement for its purchase endogenously rises. There may be spillovers in which other assets also crash in price even though their probability of default did not change.Liquidity, default, collateral, crashes, general equilibrium, contracts, spillover, liquidity premium