Adaptive learning in models with lagged variables

In this work I study the stability of the dynamics generated by adaptivelearning processes in intertemporal economies with lagged variables. Iprove that determinacy of the steady state is a necessary condition for the convergence of the learning dynamics and I show that the reciprocal is not true characterizing the economies where convergence holds. In the case of existence of cycles I show that there is not, in general, a relationship between determinacy and convergence of the learning process to the cycle. I also analyze the expectational stability of these equilibria.

Recursive contracts

We obtain a recursive formulation for a general class of contractingproblems involving incentive constraints. Under these constraints,the corresponding maximization (sup) problems fails to have arecursive solution. Our approach consists of studying the Lagrangian.We show that, under standard assumptions, the solution to theLagrangian is characterized by a recursive saddle point (infsup)functional equation, analogous to Bellman's equation. Our approachapplies to a large class of contractual problems. As examples, westudy the optimal policy in a model with intertemporal participationconstraints (which arise in models of default) and intertemporalcompetitive constraints (which arise in Ramsey equilibria).

Financial intermediation and equity investment with costly monitoring

This paper studies the efficiency of equilibria in a productive OLG economy where the process of financial intermediation is characterized by costly state verification. Both competitive equilibria and Constrained Pareto Optimal allocations are characterized. It is shown that market outcomes can be socially inefficient, even when a weaker notion than Pareto optimality is considered.

A simple adaptive procedure leading to correlated equilibrium

We propose a simple adaptive procedure for playing a game. In thisprocedure, players depart from their current play with probabilities thatare proportional to measures of regret for not having used other strategies(these measures are updated every period). It is shown that our adaptiveprocedure guaranties that with probability one, the sample distributionsof play converge to the set of correlated equilibria of the game. Tocompute these regret measures, a player needs to know his payoff functionand the history of play. We also offer a variation where every playerknows only his own realized payoff history (but not his payoff function).

The effect of intergroup competition on group coordination: An experimental study

We report an experiment on the effect of intergroup competition on group coordination in the minimal-effort game (Van Huyck et al., 1990). The competition was between two 7-person groups. Each player in each group independently chose an integer from 1 to 7. The group with the higher minimum won the competition and each of its members was paid according to the game s original payoff matrix. Members of the losing group were paid nothing. In case of a tie, each player was paid half the payoff in the original matrix. This treatment was contrasted with two control treatments where each of the two groups played an independent coordination game, either with or without information about the minimum chosen by the outgroup. Although the intergroup competition does not change the set of strict equilibria, we found that it improved collective rationality by moving group members in the direction of higher-payoff equilibria. Merely providing group members with information about the minimal-effort level in the other group was not sufficient to generate this effect.

Free entry does not imply zero profits

Traditional economic wisdom says that free entry in a market will drive profits down to zero. This conclusion is usually drawn under the assumption of perfect information. We assumethat a priori there exists imperfect information about theprofitability of the market, but that potential entrants maylearn the demand curve perfectly at negligible cost byengaging in market research. Even if in equilibrium firmslearn the demand perfectly, profits may be strictly positivebecause of insufficient entry. The mere fact that it will notbecome common knowledge that every entrant has perfectinformation about demand causes this surprising result. Belief means doubt. Knowing means certainty. Introduction to the Kabalah.

Valuation bubbles and sequential bubbles

Price bubbles in an Arrow-Debreu valuation equilibrium in infinite-timeeconomy are a manifestation of lack of countable additivity of valuationof assets. In contrast, known examples of price bubbles in sequentialequilibrium in infinite time cannot be attributed to the lack of countableadditivity of valuation. In this paper we develop a theory of valuation ofassets in sequential markets (with no uncertainty) and study the nature ofprice bubbles in light of this theory. We consider an operator, calledpayoff pricing functional, that maps a sequence of payoffs to the minimumcost of an asset holding strategy that generates it. We show that thepayoff pricing functional is linear and countably additive on the set ofpositive payoffs if and only if there is no Ponzi scheme, and providedthat there is no restriction on long positions in the assets. In the knownexamples of equilibrium price bubbles in sequential markets valuation islinear and countably additive. The presence of a price bubble indicatesthat the asset's dividends can be purchased in sequential markers at acost lower than the asset's price. We also present examples of equilibriumprice bubbles in which valuation is nonlinear but not countably additive.

Wage structures and family economies in the Catalan textile industry in an age of nascent capitalism

This paper deals with changes in managerial practices in Catalonia in anage of nascent capitalism (1830-1925) and adaptive family strategies inorder to face the absence of state welfare. During the 19 t h Century andin the absence of recorded labor contracts, human resources of the firmwere organized by means of implicit contracts and informal labor markets.With the advent of scientific organization of labor, wage per hour workedbegan to be recorded. This is why in the 1920s the perfect competitionmodel applies to our case. On the other hand, in the same period, and inthe absence of state welfare, ideas stemming from cooperative game theoryapply to the pattern of household income formation. Kin related networkswere used to improve the living standards of the household. In thisparticular direction we also show that there was a demonstration effectby means of which migrant s living standards were higher than those ofnatives.

The survival of the welfare state

This paper provides an analytical characterization of Markov perfectequilibria in a politico-economic model with repeated voting, whereagents vote over distortionary income redistribution. The key featureof the theory is that the future constituency of redistributive policiesdepends positively on the current level of redistribution, since thisaffects both private investments and the future distribution of voters.Agents vote rationally and fullly anticipate the effects of their politicalchoice on both private incentives and future voting outcomes. The modelfeatures multiple equilibria. In "pro-welfare" equilibria, both welfarestate policies and their effects on distribution persist forever. In"anti-welfare equilibria", even a majority of beneficiaries ofredistributive policies vote strategically so as to induce the formationof a future majority that will vote for zero redistribution.

The evolution of conventions under incomplete information

We formulate an evolutionary learning process in the spirit ofYoung (1993a) for games of incomplete information. The process involves trembles. For many games, if the amount of trembling is small, play will be in accordance with the games' (semi-strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Further, often play will most of the time be in accordance with exactly one Bayesian equilibrium. This gives a selection among the Bayesian equilibria. For two specific games of economic interest wecharacterize this selection. The first is an extension to incomplete information of the prototype strategic conflict known as Chicken. The second is an incomplete information bilateral monopoly, which is also an extension to incompleteinformation of Nash's demand game, or a simple version ofthe so-called sealed bid double auction. For both gamesselection by evolutionary learning is in favor of Bayesianequilibria where some types of players fail to coordinate, such that the outcome is inefficient.

Circulation of private notes during a currency shortage

This paper provides a search theoretical model that captures two phenomena that have characterized several episodes of monetary history: currency shortages and the circulation of privately issued notes. As usual in these models, the media of exchange are determined as part of the equilibrium. We characterize all the different equilibria and specify the conditions under which there is a currency shortage and/or privately issued notes are used as means of payment. There is multiplicity of equilibria for the entire parameter space, but there always exist an equilibrium in which notes circulate, either alone or together with coins. Hence, credit is a self-fulfilling phenomenon that depends on the beliefs of agents about the acceptability and future repayment of notes. The degree of circulation of coins depends on two crucial parameters, the intrinsic utility of holding coins and the extent with which it is possible to find exchange opportunities in the market.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implementsocial choice functions in the traditional sense. Will agents actually playthe equilibrium assumed by the analysis? As an example, we study theconvergence and stability properties of Sj\"ostr\"om's (1994) mechanism, onthe assumption that boundedly rational players find their way to equilibriumusing monotonic learning dynamics and also with fictitious play. Thismechanism implements most social choice functions in economic environmentsusing as a solution concept the iterated elimination of weakly dominatedstrategies (only one round of deletion of weakly dominated strategies isneeded). There are, however, many sets of Nash equilibria whose payoffs maybe very different from those desired by the social choice function. Withmonotonic dynamics we show that many equilibria in all the sets ofequilibria we describe are the limit points of trajectories that havecompletely mixed initial conditions. The initial conditions that lead tothese equilibria need not be very close to the limiting point. Furthermore,even if the dynamics converge to the ``right'' set of equilibria, it stillcan converge to quite a poor outcome in welfare terms. With fictitious play,if the agents have completely mixed prior beliefs, beliefs and play convergeto the outcome the planner wants to implement.

Correspondence analysis of raw data

Correspondence analysis has found extensive use in ecology, archeology, linguisticsand the social sciences as a method for visualizing the patterns of association in a table offrequencies or nonnegative ratio-scale data. Inherent to the method is the expression of the datain each row or each column relative to their respective totals, and it is these sets of relativevalues (called profiles) that are visualized. This relativization of the data makes perfect sensewhen the margins of the table represent samples from sub-populations of inherently differentsizes. But in some ecological applications sampling is performed on equal areas or equalvolumes so that the absolute levels of the observed occurrences may be of relevance, in whichcase relativization may not be required. In this paper we define the correspondence analysis ofthe raw unrelativized data and discuss its properties, comparing this new method to regularcorrespondence analysis and to a related variant of non-symmetric correspondence analysis.

Corporate finance and the monetary transmission mechanism

This paper analyzes the transmission mechanisms of monetarypolicy in a general equilibrium model of securities marketsand banking with asymmetric information. Banks' optimal asset/liability policy is such that in equilibrium capital adequacy constraints are always binding. Asymmetric information about banks' net worth adds a cost to outside equity capital, which limits the extent to which banks can relax their capital constraint. In this context monetarypolicy does not affect bank lending through changes in bank liquidity. Rather, it has the effect of changing theaggregate composition of financing by firms. The model also produces multiple equilibria, one of which displays all the features of a "credit crunch". Thus, monetary policy can also have large effects when it induces a shift from one equilibrium to the other.