The capital asset pricing model as a general equilibrium with incomplete markets

We recast the capital asset pricing model (CAPM) in the broader context of general equilibrium with incomplete markets (GEI). In this setting we give proofs of three properties of CAPM equilibria: they are efficient, asset prices lie on a security market line, and all agents hold the same two mutual funds. The first property requires a riskless asset, the latter two do not. We show that across all GEI only one of these three properties of equilibrium is generally valid: asset prices depend on covariances, not variances. We extend CAPM to many consumption goods in such a way that all three properties hold. But now the definition of a riskless asset depends on preferences and endowments, and so cannot be specifieda priori.We wish to acknowledge assistance of NSF Grant No. 88-12051, and a referee's comments. We are grateful for conversations with H. Polemarchakis, especially concerning Section II.4.     

Games of Status

A status game is a cooperative game in which the outcomes are rank orderings of the players. They are a good model for certain situations in which players care about how their "status" compares with that of other players.
We present several formal models within this class. Included are authoritarian status games (where coalitions may assign positions in the rank ordering to nonmembers) and oligarchic status games (where they are unableto do so). We consider the issues of a value concept for authoritarian games and that of core existence for oligarchic games. We then add a transferable resource to the models, obtaining "games of wealth and status."
Finally, we consider an interesting variant, called a "secession game," where coalitions have the right to secede from the grand coalition and form their own smaller "subsocieties," each with its own hierarchy.     

Efficiency properties of strategies market games: An axiomatic approach

The paper investigates the conditions under which an abstractly given market game will have the property that if there is a continuum of traders then every noncooperative equilibrium is Walrasian. In orther words, we look for a general axiomatization of Cournot's well-known result. Besides some convexity, continuity, and nondegeneracy hypotheses, the crucial axioms are: anonymity (i.e., the names of traders are irrelevant to the market) and aggregation (i.e., the net trade received by a trader depends only on his own action and the mean action of all traders). It is also shown that the same axioms do not guarantee efficiency if there is only a finite number of traders. Some examples are discussed and a notion of strict noncooperative equilibrium for anonymous games is introduced.     

Is gold an efficient store of value?

Summary. Gold and tobacco have both been used as commodity money. One difference between the two is that gold yields utility, on account of its beauty, without diminishing its quantity. Tobacco yields utility when it is consumed. If this were the only difference, Received: January 2, 2001; revised version: February 22, 2002 Correspondence to: J. Geanakoplos     

The inflationary bias of real uncertainty and the harmonic Fisher equation

Summary. We argue that real uncertainty itself causes long-run nominal inflation. Consider an infinite horizon cash-in-advance economy with a representative agent and real uncertainty, modeled by independent, identically distributed endowments. Suppose the central bank fixes the nominal rate of interest. We show that the equilibrium long-run rate of inflation is strictly higher, on almost every path of endowment realizations, than it would be if the endowments were constant.Indeed, we present an explicit formula for the long-run rate of inflation, based on the famous Fisher equation. The Fisher equation says the short-run rate of inflation should equal the nominal rate of interest less the real rate of interest. The long-run Fisher equation for our stochastic economy is similar, but with the rate of inflation replaced by the harmonic mean of the growth rate of money.Received: 25 February 2005, Revised: 26 May 2005, JEL Classification Numbers: C7, C73, D81, E41, E58.An earlier version of this paper “Inflationary Bias in a Simple Stochastic Economy,” as a 2001 Cowles Foundation Discussion Paper No. 1333.     

Some dynamics of a strategic market game with a large number of agents

This paper is designed to combine the game-theoretic investigation of the static or equilibrium properties of large strategic market games together with the investigation of some very simple dynamics, which nevertheless are sufficient to show differences between two related games, one with only trade and one in which both borrowing from an outside bank and trade take place. The role of banking reserves emerges as relevant and sensitive to the transient state dynamics.Several 100,000 player games are simulated and the behavior is compared with the analytical prediction for the games with a continuum of agents.The dynamics considered here is so simple that it does not show adaptive learning. A natural extension calls for updating via a learning program such as a genetic algorithm.