John Geanakoplos

Psychological games and sequential rationality

Abstract In psychological games the payoff to each player depends not only on what every player does but also on what he thinks every player believes, and on what he thinks they believe others believe, and so on. In equilibrium, beliefs are assumed to correspond to reality. Yet psychological games and psychological equilibria allow one to model belief-dependent emotions such as anger and surprise that are problematic for conventional game theory. We are particularly interested in issues of sequential rationality for psychological games. We show that although backward induction cannot be applied, and “perfect” psychological equilibria may not exist, subgame perfect and sequential equilibria always do exist.

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.

We can't disagree forever

Under the assumption of common priors, if the information partitions of two agents are finite, then simply by communicating back and forth and revising their posteriors the two agents will converge to a common equilibrium posterior, even though they may base their posteriors on quite different information. Furthermore, given any integer, n, one can construct an example in which the revision process not only takes n steps to converge, but no evident revision occurs n for (n-1) steps both agents repeat the same conflicting posteriors n until the last step when the two agents decide to agree. Common knowledge of each others posterior does not necessarily lead agents to the posterior they would have agreed upon had information been directly exchanged. On the other hand, the examples that are characterized by a discrepancy between the direct and indirect communication equilibrium are rare: with probability 1, the revision process constructed here leads the two agents in one step to the direct communication equilibrium.

Liquidity, Default and Crashes: Endogenous Contracts in General Equilibrium

The possibility of default limits available liquidity. If the potential default draws nearer, a liquidity crisis may ensue, causing a crash in asset prices, even if the probability of default barely changes, and even if no defaults subsequently materialize. 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 and shortens the horizon over which a fixed income asset may default, its drop in price may be much greater than its objective drop in value for two reasons: the drop in value reduces the relative wealth of its natural buyers and also endogenously raises the margin required for its purchase. The liquidity premium rises, and there may be spillovers in which other assets crash in price even though their probability of default did not change.

An introduction to general equilibrium with incomplete asset markets

I survey the major results in the theory of general equilibrium with incomplete asset markets. I also introduce the papers in this volume and offer a few suggestions for further work.

Real indeterminacy with financial assets

The purpose of this paper, which takes up after D. Cass (1984a, 1984b) is to find the degree of real indeterminacy inherent in models with purely financial assets. We solve the problem for the case where there are enough traders (precisely, the number of traders is larger than the number of bonds) and the asset returns structure is in general position. We find that if the number of bonds is non-zero and fewer than the number of states then, generically, the number of dimensions of real indeterminacy is S-1, one less than the number of states. There is something of a surprise in the above result, namely the dimension of real indeterminacy does not depend on the number of bonds (except in the two limit cases). Indeed one initial conjecture was S-B. This points to an intriguing qualitative discontinuity at the complete market configuration. If markets are financially complete then the model is determinate. Let just one bond be missing and the model become highly indeterminate. Thus, in this sense, the complete markets hypothesis lacks robustness.

Leverage Causes Fat Tails and Clustered Volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called ‘value investing’, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are approximately normally distributed and uncorrelated across time. This changes when the funds are allowed to leverage, i.e. borrow from a bank, which allows them to purchase more assets than their wealth would otherwise permit. During good times, funds that use more leverage have higher profits, increasing their wealth and making them dominant in the market. However, if a downward price fluctuation occurs while one or more funds is fully leveraged, the resulting margin call causes them to sell into an already falling market, amplifying the downward price movement. If the funds hold large positions in the asset, this can cause substantial losses. This in turn leads to clustered volatility: before a crash, when the value funds are dominant, they damp volatility, and after the crash, when they suffer severe losses, volatility is high. This leads to power-law tails, which are both due to the leverage-induced crashes and due to the clustered volatility induced by the wealth dynamics. This is in contrast to previous explanations of fat tails and clustered volatility, which depended on ‘irrational behavior’, such as trend following. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility becomes high, making these extreme fluctuations even worse.

Demography and the Long-Run Predictability of the Stock Market

Stock market price/earnings ratios should be influenced by demography. Since demography is predictable, stock returns should be as well. We provide a simple stochastic OLG model with a cyclical structure that generates cyclical P/E ratios. We calibrate the model to roughly fit the cyclical features of historical P/E ratios.

The revelation of information in strategic market games: A critique of rational expectations equilibrium

Abstract We criticize the R.E.E. approach to asymmetric information general equilibrium because it does not explain how information gets ‘into’ the prices. This leads to well-known paradoxes. We suggest a multiperiod game instead, where the flow of information into and out of prices is explicitly modeled. In our game Nash equilibria (N.E.) (1) generalize Walrasian equilibria to asymmetric information, (2) exist generically, (3) eliminate pure speculation, (4) allow prices to reveal information and markets to become more efficient over time, (5) are consistent with the weak efficient markets hypothesis that tracking past prices is not profitable, (6) yet always lead to higher utility for better informed agents (such as experts). Throughout the paper we use one concrete game. In the last section we prove that there is a broad range of games that would have the same properties.

Generic inefficiency of stock market equilibrium when markets are incomplete

A stock market is a mechanism by which the ownership and control of firms is determined through the trading of securities. It is on this market that many of the major risks faced by society are shared through the exchange of securities and the production decisions that influence the present and future supply of resources are determined. If the overall structure of markets is incomplete can the stock market be expected to perform its role of exchanging risks and allocating investment efficiently? It is this question that we seek to answer.