Bubbles, collateral and monetary equilibrium

Consider an economy where infinite-lived agents trade assets collateralized by durable goods. We obtain results that rule out bubbles when the additional endowments of durable goods are uniformly bounded away from zero, regardless of whether the asset’s net supply is positive or zero. However, bubbles may occur, even for state-price processes that generate finite present value of aggregate wealth. First, under complete markets, if the net supply is being endogenously reduced to zero as a result of collateral repossession. Secondly, under incomplete markets, for a persistent positive net supply, under the general conditions guaranteeing existence of equilibrium. Examples of monetary equilibria are provided.

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

Affiliation, equilibrium existence and the revenue ranking of auctions

We consider private value auctions where bidders’ types are dependent, a case usually treated by assuming affiliation. We show that affiliation is a restrictive assumption in three senses: topological, measure-theoretic and statistical (affiliation is a very restrictive characterization of positive dependence). We also show that affiliation’s main implications do not generalize for alternative definitions of positive dependence. From this, we propose new approaches to the problems of pure strategy equilibrium existence in first-price auctions (PSEE) and the characterization of the revenue ranking of auctions. For equilibrium existence, we slightly restrict the set of distributions considered, without loss of economic generality, and offer a complete characterization of PSEE. For revenue ranking, we obtain a characterization of the expected revenue differences between second and first price auctions with general dependence of types.