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 specified a priori.
Keywords: Capital asset pricing model, incomplete markets, asset prices, CAPM, general equilibrium model
Decision theory and game theory are extended to allow for information processing errors. This extended theory is then used to reexamine market speculation and consensus, both when all actions (opinions) are common knowledge and when they may not be. Five axioms of information processing are shown to be especially important to speculation and consensus. They are called nondelusion, knowing that you know, nested, balanced, and positively balanced. We show that it is necessary and sufficient that each agent’s information processing errors be nondeluded and (1) balanced so that the agents cannot agree to disagree, (2) positively balanced so that it cannot be common knowledge that they are speculating, and (3) KTYK and nested so that agents cannot speculate in equilibrium. Each condition is strictly weaker than the next one, and the last is strictly weaker than partition information.
Keywords: Game theory, decision theory, speculation, consensus, information, common knowledge
We enlarge the standard model of general equilibrium with incomplete market (GEI), to incorporate liquidity constraints as well as the possibility of bankruptcy and default. A new equilibrium results, which we abbreviate GELBI (general equilibrium with liquidity, bankruptcy and incomplete markets). When the supply of bank money and bankruptcy/default penalties are taken sufficiently high (the high regime), GEI occur as GELBI. But outside the high regime many new phenomena appear: money is (almost) never neutral, it has positive value and its optimum quantity is often finite; bankruptcy and default not only occur in equilibrium but can have welfare improving consequences for everyone; there is no real indeterminacy even with financial assets.
History has seen many examples of the lone man — like Christ, Luther, Gandhi, or Hitler — who without initial wealth or position, succeeds in changing the behavior of an entire society, for good or for ill. Whence comes this power. No doubt such leaders have possessed extraordinary ability, and have formulated original ideas with great appeal which others could readily follow. But there is another striking similarity among these leaders; namely their single-minded devotion to their, ideals, and their uncompromising attitude toward those who opposed them, no matter what the personal cost. There is hardly any need to document this facet of their personalities, so widely is it known. But we cannot help recalling Gandhi’s threat to starve himself to death if the fighting between Hindus and Muslims did not stop. Indeed the whole-hearted commitment of these leaders to their ideals was often reflected in their followers’ commitment to them. The purpose of this paper is to show how significant is the power to make commitments, perhaps in the name of some ideal.
We study the “generalized correlated equilibria” of a game when players make information processing errors. It is shown that the assumption of information processing errors is equivalent to that of “subjectivity” (i.e., differences between the players’ priors). Hence a bounded rationality justification of subjective priors is provided. We also describe the set of distributions on actions induced by generalized correlated equilibria with common priors.
Consider a group of people who are asked to offer their opinions on some issue. “Business confidence” surveys are an example: groups of businessmen are often asked for their predictions of economic indicators such as growth or inflation rates. Each member of the group makes a prediction based on his or her private information, and the average prediction is then publicly announced. If the members of the group are then allowed to revise their opinions, based on whatever information they glean from the public announcement, is there any tendency for the opinions in the group to converge on a common, consensus opinion? In this note we show that under certain conditions the answer to this question is yes.
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.
Overlapping generations models with or without production or a portfolio demand for money display a fundamental indeterminacy. Expectations matter; and they are not, in the short run, constrained by the hypotheses of agent optimization, rational expectations, and market clearing. No short run policy analysis is possible without some explicit understanding of how agents expect the economy to respond to the policy. In this framework of perfect foresight and market clearing prices, it is possible to make Keynesian assumptions about the rigidity of money wages and the exogeneity of “animal spirits” of investors, to use the standard IS-LM apparatus, and to derive Keynesian conclusions about the short run effectiveness of policy. Alternatively, starting from difference but no less rational expectations, one can derive the “new classical” neutrality propositions.
This study is an effort to give a simple measure of the local size of the equilibrium set of OLG economies in which there may be more than one good and more than one consumer per period, and in which the generations may differ across time.
In this paper we propose a pseudo-Nash equilibrium for N-person games in which very simply we allow play in the last period to be arbitrary, but otherwise it must conform to the (perfect) Nash optimality criterion.