A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Monotone equilibria in Bayesian games of strategic complementarities

For Bayesian games of strategic complementarities, we provide a constructive proof of the existence of a greatest and a least Bayesian Nash equilibrium, each one in strategies that are monotone in type. Our main assumptions, besides strategic complementarities, are that each player's payoff displays increasing differences in own action and the profile of types and that each player's interim beliefs are increasing in type with respect to first-order stochastic dominance (e.g., types are affiliated). The result holds for general action and type spaces (single-, multi-, or infinite-dimensional; continuous or discrete) and no prior is assumed. We also provide the following comparative statics result: the greatest and least equilibria are higher if there is a first-order stochastic dominant shift in the interim beliefs. We apply this result to strategic information revelation in games of voluntary disclosure.     

Bayesian learning and convergence to Nash equilibria without common priors

Summary. Consider an infinitely repeated game where each player is characterized by a “type” which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria. Received: March 3, 1995; revised version: February 17, 1997     

European unification: a new proposal

My contribution presents a possibility to unify Europe based on newly emerging political units focused on solving problems rather than on historically given nation states. These Endogenous Political Entities (EPE), as they shall be called, are better suited to reach the goals of European unification as they strengthen the fundamental European values of variety and freedom. I make three propositions: to base the unification of Europe on nation states is unfortunate as the latter are responsible for the political disaster of the two World Wars; the unification must proceed in a problem-oriented manner. The constitution of Europe must allow and promote EPE to emerge specifically to deal with particular problems; the new political units can be introduced in marginal steps. Over time, a flexible and dynamic net of political entities will arise taking care of the large economic, social and cultural diversity in Europe.     

Reinterpreting social pacts: Theory and evidence

We investigate the empirical determinants of social pacts over the 1970–2004 period. We adopt a political economy approach, showing that governments are more likely to sign a pact when the cost of a conflict with trade unions is relatively larger. Such a cost depends on macroeconomic variables and on measures of social conflict and union strength. These findings are remarkably stable across sub-periods, in apparent contrast with previous contributions that emphasised differences between first- and second-generation pacts. Our interpretation is that pacts were different across periods because the policy issues changed, but the incentives to seek union consensus did not.     

Semiparametric Bayesian estimation of mixed count regression models

This paper develops semiparametric Bayesian estimation approach for Poisson regression models with unobserved heterogeneity of unknown density. This approach is computationally efficient and allows automatic adaptation of the approximating density to data during estimation. Simulations show the estimator performs well.     

Common priors under incomplete information: a unification

Summary. While the meaningfulness of the common prior assumption (CPA) under incomplete information has been established recently by various authors, its epistemic rationale has not yet been adequately clarified. To do so, we provide a characterization of the CPA in terms of a new condition called “Mutual Calibration”, and argue that it constitutes a more transparent and more primitive formalization of the Harsanyi Doctrine than the existing characterizations. Our analysis unifies the understanding of the CPA under incomplete information and clarifies the role of higher-order expectations and of the difference between situations with only two and those with at least three agents. In the concluding section, the analysis is applied to the problem of defining Bayesian consistency of the intertemporal beliefs of a single-agent with imperfect memory. The CPA yields a notion of “Bayesian updating without a prior”. Received: March 24, 2000; revised version: April 27, 2000     

Stationarity and structural breaks — evidence from classical and Bayesian approaches

The purpose of this paper is to analyze and compare the results of applying classical and Bayesian methods to testing for a unit root in time series with a single endogenous structural break. We utilize a data set of macroeconomic time series for the Mexican economy similar to the Nelson–Plosser one. Under both approaches, we make use of innovational outlier models allowing for an unknown break in the trend function. Classical inference relies on bootstrapped critical values, in order to make inference comparable to the finite sample Bayesian one. Results from both approaches are discussed and compared.     

On the existence of pure strategy Nash equilibria in two person discrete games

We construct a generalized two-person discrete strategy static game of complete information where continuity, convexity and compactness cannot be invoked to show the existence of pure strategy Nash equilibrium. We show that, when best responses are unique from both sides, a condition of Minimal Acyclicity is necessary and sufficient for the existence of pure strategy Nash equilibria.     

Capital in the Twenty-First Century: Reinterpreting the fundamental contradiction of capitalism

At a theoretical level this article discusses Piketty’s hypothesis that the distribution of income and wealth tends to become more concentrated over time when the rate of return on capital is greater than the growth rate of real output. We develop a post Keynesian model of growth and distribution showing that once capital is differentiated from wealth, the increase in income and wealth concentration actually occurs when the rate of valorization of financial and real estate assets is greater than the growth rate of real output, and that this situation may be triggered by financial liberalization.     

Existence of perfect equilibria: a direct proof

We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game.     

A Ricardian excursion to Bermuda: an estimation of mixed strategy equilibrium

While there is a rich theoretical literature on mixed strategy equilibria, there has long been doubt with regard to the actual prevalence of scuh equilibria. The objective of this paper is to empirically demonstrate a mixed strategy equilibrum in a model of Ricardian rent generation. The oligopolistic resort hotel industry in Bermuda is used as the illustrative case.     

Computing equilibria: a computational complexity perspective

Computational complexity is the subfield of computer science that rigorously studies the intrinsic difficulty of computational problems. This survey explains how complexity theory defines “hard problems”; applies these concepts to several equilibrium computation problems; and discusses implications for computation, games, and behavior. We assume minimal prior background in computer science.     

Reinterpreting the performance of immigrant wages from panel data

Immigrants differ from the native born in terms of unobserved factors, such as motivation, and observed factors, including those related to the interruption of labour market activity and earning capacity, which may bias estimates of immigrant integration. Using panel data from the Survey of Labour and Income Dynamics, we show that using potential experience, rather than actual experience, exaggerates estimates of the disruption and recovery caused by immigration. More importantly, we find support for omitted variables bias, arising from unobserved fixed effects. Instrumental variable estimates for both pooled and separate samples of immigrant and native born men demonstrate a wage disadvantage for immigrants upon entry that persists through their lifetime. Standard estimates of a modest wage advantage for the children of immigrants also suffer from omitted variables bias arising from unobservables. Contrary to most of the literature to date, our instrumental variable estimates which allow for unobservable fixed effects suggest that immigrants never catch up to otherwise comparable native born workers, but their children do just as well. We would like to thank Statistics Canada for permitting access to the data and solving associated technical problems, the Prairier Centre for Research on Immigration and Integration for financial assistance, and Peter Schnabl for excellent research assistance. An earlier version of this paper was presented to the 10th International Conference on Panel Data in Berlin, July 5–6, 2002. The authors take sole responsibility for errors, omissions and interpretation of the data.     

Payoff equivalence between Bayesian and ex post individually rational dominant strategy mechanisms

Summary. An efficient, interim individually rational, ex post budget balanced Bayesian mechanism is shown to be payoff equivalent to an ex post individually rational and ex ante budget balanced dominant strategy mechanism. This result simplifies the search for mechanisms that implement efficient allocation rules by pointing to a class of Groves mechanisms. It eliminates the strict requirement of common knowledge of priors and can be applied to many problems of incomplete information. Received: October 22 1996; revised version: November 25, 1997     

Bayesian averaging of classical estimates in forecasting macroeconomic indicators with application of business survey data

In this paper, we develop a methodology for forecasting key macroeconomic indicators, based on business survey data. We estimate a large set of models, using an autoregressive specification, with regressors selected from business and household survey data. Our methodology is based on the Bayesian averaging of classical estimates method. Additionally, we examine the impact of deterministic and stochastic seasonality of the business survey time series on the outcome of the forecasting process. We propose an intuitive procedure for incorporating both types of seasonality into the forecasting process. After estimating the specified models, we check the accuracy of the forecasts.     

Oligopoly equilibria in exchange economies: a limit theorem

In a pure exchange economy, agents have the possibility of behaving strategically by putting only a part of their initial endowments on the market. An oligopoly equilibrium is defined to be a Nash equilibrium of the game in which agents choose simultaneously quantities to be put on the market. It is proved that under standard hypotheses, the oligopoly equilibrium leads to the competitive equilibrium when the economy is replicated an infinite number of times. Received: May 26, 1999; revised version: April 3, 2000     

Germany before and after unification: A structural VAR analysis

Recent theoretical research in business cycle modelling has aimed at putting forward a unified framework for studying both short-term cycles and long-term growth. Empirical research based on structural vector-autoregression has established that the same factors which drive long-run growth also explain a large proportion of the movements of key macro variables at business cycle frequencies. The present paper aims at applying this approach to study the determinants of the post-unification downturn in Germany. The results suggest that German business cycles were not all alike. Whilst adverse supply shocks clearly matter before unification, it is primarily adverse aggregate demand shocks and a too tight monetary policy which dominate the German post-unification decline in output growth rates.