Path Dependence and Learning from Neighbors

We study the long-run properties of a class of locally interactive learning systems. A finite set of players at fixed locations play a two-by-two symmetric normal form game with strategic complementarities, with one of their “neighbors” selected at random. Because of the endogenous nature of experimentation, or “noise,” the systems we study exhibit a high degree of path dependence. Different actions of a pure coordination game may survive in the long-run at different locations of the system. A reinterpretation of our results shows that the local nature of search may be a robust reason for price dispersion in a search model,Journal of Economic LiteratureClassification Numbers: C72, D83.     

Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games

Most learning models assume players are adaptive (i.e., they respond only to their own previous experience and ignore others' payoff information) and behavior is not sensitive to the way in which players are matched. Empirical evidence suggests otherwise. In this paper, we extend our adaptive experience-weighted attraction (EWA) learning model to capture sophisticated learning and strategic teaching in repeated games. The generalized model assumes there is a mixture of adaptive learners and sophisticated players. An adaptive learner adjusts his behavior the EWA way. A sophisticated player rationally best-responds to her forecasts of all other behaviors. A sophisticated player can be either myopic or farsighted. A farsighted player develops multiple-period rather than single-period forecasts of others' behaviors and chooses to “teach” the other players by choosing a strategy scenario that gives her the highest discounted net present value. We estimate the model using data from p-beauty contests and repeated trust games with incomplete information. The generalized model is better than the adaptive EWA model in describing and predicting behavior. Including teaching also allows an empirical learning-based approach to reputation formation which predicts better than a quantal-response extension of the standard type-based approach. Journal of Economic Literature Classification Numbers: C72, C91.     

The Nash-threats folk theorem with communication and approximate common knowledge in two player games

We show that the use of communications to coordinate equilibria generates a Nash-threats folk theorem in two-player games with “almost public” information. The results generalize to the n-person case. However, the two-person case is more difficult because it is not possible to sustain equilibria by comparing the reports of different players, and using these “third parties” to effectively enforce contracts.     

Rejuveniles and growth

Rejuveniles are “people who cultivate tastes and mind-sets traditionally associated with those younger than themselves” [Noxon, C., 2006. Rejuvenile. Crown Publishers]. In this paper, we study a standard AK growth model of overlapping generations populated by rejuveniles. For our purposes, rejuveniles are old agents who derive utility from “keeping up” their consumption with that of the current young. We find that such cross-generational keeping up is capable of generating interesting equilibrium growth dynamics, including growth cycles. No such growth dynamics is possible either in the baseline model, one where no such generational consumption externality exists, or for almost any other form of keeping up. Steady-state growth in a world with rejuveniles may be higher than that obtained in the baseline model.     

On Learning to Cooperate

This paper shows that experimentation can have the effect of inducing outcomes that are “far” from Nash in a learning model similar to that studied by D. Fudenberg and D. K. Levine (1993, Econometrica61, 547-573). The game under consideration is a version of a finitely repeated prisoner's dilemma, and the average length of players' lifetimes is arbitrarily large, but fixed. If the number of stages in the prisoner's dilemma is sufficiently large, then experimentation induces cooperation within the society on an arbitrarily large scale, even though the beliefs of almost all players are eventually within an arbitrary η>0 of being correct at all of the information sets in the game. Journal of Economic Literature Classification Numbers: C72.     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.     

Law enforcement and transition

We present a simple model to analyze law enforcement problems in transition economies. Law enforcement implies coordination problems and multiplicity of equilibria due to a law abidance and a fiscal externality. We analyze two institutional mechanisms for solving the coordination problem. A first mechanism, which we call “dualism”, follows the scenario of Chinese transition where the government keeps direct control over economic resources and where a liberalized non-state sector follows market rules. The second mechanism we put forward is accession to the European Union. We show that accession to the European Union, even without external borrowing, provides a mechanism to eliminate the “bad” equilibrium, provided the “accessing” country is small enough relative to the European Union. Interestingly, we show that accession without conditionality is better than with conditionality because conditionality creates a coordination problem of its own that partly annihilates the positive effects of expected accession.     

Can sustainable consumption be learned? A model of cultural evolution

This paper shows how sustainable consumption patterns can spread within a population via processes of social learning even though a strong individual learning bias may favor environmentally harmful products. We present a model depicting how the biased transmission of different behaviors via individual and social learning influences agents' consumption behavior. The underlying learning biases can be traced back to evolved cognitive dispositions. Challenging the vision of a permanent transition toward sustainability, we argue that “green” consumption patterns are not self-reinforcing and cannot be “locked in” permanently.     

Generational Explanation of Long-Term “Billow-Like” Dynamics of Societal Processes

An increasing amount of empirical evidence has accumulated showing the existence of several kinds of recurrent long-term societal processes. Particular attention was given to the 50–60 year billows, usually related to economical and technological processes (Kondratieff cycles). These studies generated a large set of different theories—intrinsic to the economy and the technology—that tried to explain the recurrent process origin. Since the last century, several scholars have identified even longer societal billows usually related to long-term political processes (Hegemonic and Ferrari cycles). The paradigm of long-term societal processes was not always accepted because of the lack of a consistent theoretical framework that could account for it. In this article we introduce a partially formalized version of that framework which contains only one, to be determined constant, namely: a generational time lag. We show that this time constant is equal to the life lapse of human beings in which they are mainly motivated to interact with their contextual, social, and “habital” processes. We call the constant τ, Societal Historical Generation (SHG) and conclude, using theoretical and empirical arguments, that its length is 39 ± 4 years. A mathematical model of the societal temporal diffusion of those motivational concerns, in agreement with all the empirically determined characteristics of the long-term billow-like processes, is presented. The solutions for the first three oscillatory modes have the following “billow-lengths”: 156 ± 16; 31 ± 3; 17 ± 2 years (with k > 0) and 52 ± 5; 22 ± 2; 14 ± 1 years (with k < 0). The basis of this model has anthropo-psycho-epigenetic human roots that allow the emergence of collective societal behavior patterns with the appearance of long-term billows in economical and political indicators. An interpretation and discussion of the main characteristics of the societal moods as well as other research lines to test the model are presented.     

Testing threats in repeated games

Under most game-theoretic solution concepts, equilibrium beliefs are justified by off-equilibrium events. I propose an equilibrium concept for infinitely repeated games, called “Nash Equilibrium with Tests” (NEWT), according to which players can only justify their equilibrium beliefs with events that take place on the equilibrium path itself. In NEWT, players test every threat that rationalizes a future non-myopic action that they take. The tests are an integral part of equilibrium behavior. Characterization of equilibrium outcomes departs from the classical “folk theorems”. The concept provides new insights into the impact of self-enforcement norms, such as reciprocity, on long-run cooperation.     

Does truth win when teams reason strategically?

We study behavior in the race game with the aim of assessing whether teams can create synergies. The race game has the advantage that the optimal strategy depends neither on beliefs about other players nor on distributional or efficiency concerns. Our results reveal that teams not only outperform individuals but that they can also beat the “truth-wins” benchmark. In particular, varying the length of the race game we find that the team advantage increases with the complexity of the game.     

On the folk theorem with one-dimensional payoffs and different discount factors

Proving the folk theorem in a game with three or more players usually requires imposing restrictions on the dimensionality of the stage-game payoffs. Fudenberg and Maskin (1986) assume full dimensionality of payoffs, while Abreu et al. (1994) assume the weaker NEU condition (“nonequivalent utilities”). In this note, we consider a class of n-player games where each player receives the same stage-game payoff, either zero or one. The stage-game payoffs therefore constitute a one-dimensional set, violating NEU. We show that if all players have different discount factors, then for discount factors sufficiently close to one, any strictly individually rational payoff profile can be obtained as the outcome of a subgame-perfect equilibrium with public correlation.     

Friedman's Money Supply Rule vs. Optimal Interest Rate Policy

Using New Keynesian models, we compare Friedman's k‐percent money supply rule to optimal interest rate setting, with respect to determinacy, stability under learning and optimality. First we review the recent literature: open‐loop interest rate rules are subject to indeterminacy and instability problems, but a properly chosen expectations‐based rule yields determinacy and stability under learning, and implements optimal policy. We show that Friedman's rule also can generate equilibria that are determinate and stable under learning. However, computing the mean quadratic welfare loss, we find for calibrated models that Friedman's rule performs poorly when compared to the optimal interest rate rule.     

Crime and punishment in the “American Dream”

We observe that countries where belief in the “American dream”(i.e., effort pays) prevails also set harsher punishment for criminals. We know that beliefs are also correlated with several features of the economic system (taxation, social insurance, etc). Our objective is to study the joint determination of these three features (beliefs, punitiveness and economic system) in a way that replicates the observed empirical patterns. We present a model where beliefs determine the types of contracts that firms offer and whether workers exert effort. Some workers become criminals, depending on their luck in the labor market, the expected punishment, and an individual shock that we call “meanness”. It is this meanness level that a penal system based on “retribution” tries to detect when deciding the severity of the punishment. We find that when initial beliefs differ, two equilibria can emerge out of identical fundamentals. In the “American” (as opposed to the “French”) equilibrium, belief in the “American dream” is commonplace, workers exert effort, there are high powered contracts (and income is unequally distributed) and punishments are harsh. Economists who believe that deterrence (rather than retribution) shapes punishment can interpret the meanness parameter as pessimism about future economic opportunities and verify that two similar equilibria emerge.     

Clever agents in adaptive learning

Saez-Marti and Weibull (J. Econom. Theory 86 (1999) 268) investigate the consequences of letting some agents play a myopic best reply to the myopic best reply in Young's (J. Econom. Theory 59 (1993) 145) bargaining model, which is how they introduce “cleverness” of players. I analyze such clever agents in general finite two-player games and show Young's (Individual Strategy and Social Structure, Princeton University Press, Princeton, NJ, 1998) prediction to be robust: adaptive learning with clever agents does select the same minimal curb set as in the absence of clever agents, if their population share is less than one. However, the long-run strategy distribution in such a curb set may vary with the share of clever agents.     

The evolution of conventions under incomplete information

Summary. We formulate an evolutionary learning process with trembles for static games of incomplete information. For many games, if the amount of trembling is small, play will be in accordance with the games (strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Often the process will select a specific equilibrium. We study an extension to incomplete information of the prototype conflict known as Chicken and find that the equilibrium selection by evolutionary learning may well be in favor of inefficient Bayesian equilibria where some types of players fail to coordinate.Received: 17 March 2003, Revised: 3 December 2003, JEL Classification Numbers: C72.     

Differentiating ambiguity and ambiguity attitude

The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modelled formally in the context of a general decision model. We introduce a relation derived from the DM's preferences, called “unambiguous preference”, and show that it can be represented by a set of probabilities. We provide such set with a simple differential characterization, and argue that it is a behavioral representation of the “ambiguity” that the DM may perceive. Given such revealed ambiguity, we provide a representation of ambiguity attitudes. We also characterize axiomatically a special case of our decision model, the “α-maxmin” expected utility model.     

Misery loves company: Social regret and social interaction effects in choices under risk and uncertainty

Extensive field evidence shows individuals? decisions in settings involving uncertainty depend on their peers? decisions. One hypothesized cause of peer group effects is social interaction effects: an individual?s utility from an action is enhanced by others taking the same action. We employ a series of controlled laboratory experiments to study the causes of peer effects in choice under uncertainty. We find strong peer group effects in the laboratory. Our design allows us to rule out social learning, social norms, group affiliation, and complementarities as possible causes for the observed peer group effects, leaving social interaction effects as the likely cause. We use a combination of theory and empirical analysis to show that preferences including “social regret” are more consistent with the data than preferences including a taste for conformity. We observe spillover effects, as observing another?s choice of one risky gamble makes all risky gambles more likely to be chosen.     

Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining

We did experiments in a three-round bargaining game where the (perfect) equilibrium offer was $1.25 and an equal split was $2.50. The average offer was $2.11. Patterns of information search (measured with a computerized information display) show limited lookahead rather than backward induction. Equilibrium theories which adjust for social utilities (reflecting inequality-aversion or reciprocity) cannot explain the results because they predict subjects will make equilibrium offers to “robot” players, but offers to robots are only a little lower. When trained subjects (who quickly learned to do backward induction) bargained with untrained subjects, offers ended up halfway between equilibrium and $2.11. Journal of Economic Literature Classification Numbers: C7, C9.     

Operators for the adjudication of conflicting claims

We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A “rule” associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study “operators” on the space, that is, mappings that associate to each rule another one. Duality, claims truncation, and attribution of minimal rights are the operators we consider. We first establish a number of results linking them. Then, we determine which properties of rules are preserved under each of these operators, and which are not.