Better-reply dynamics and global convergence to Nash equilibrium in aggregative games

We consider n-person games with quasi-concave payoffs that depend on a player's own action and the sum of all players' actions. We show that a discrete-time, stochastic process in which players move towards better replies—the better-reply dynamics—converges globally to a Nash equilibrium if actions are either strategic substitutes or strategic complements for all players around each Nash equilibrium that is asymptotically stable under a deterministic, adjusted best-reply dynamics. We present an example of a 2-person game with a unique equilibrium where the derivatives of the best-reply functions have different signs and the better-reply dynamics does not converge.     

Existence of a Pareto-optimal equilibrium in nearly-stationary overlapping-generations economies

Summary In overlapping-generations models of fiat money, the existence of a Pareto-optimal equilibrium — which defines an optimal quantity of money — is more general than well-known counter-examples suggest. Those examples, having no optimal equilibrium just because there are small variations in households' tastes and endowments across generations, are not typical. On the contrary: For an open-dense, full-measure subset of smooth stationary economies and an open-dense subset of continuous stationary economies, introducing small variations in tastes and endowments across generations preserves the existence of an optimal equilibrium. Put simply, optimal equilibria generically exist for nearly-stationary economies.I thank Scott Freeman, Katsuhiko Kawai, and two referees for proofreading this text; all lead to clarifications.     

Trade prices and supply in the UK economy

Current account imbalances are a major source of instability in the world monetary and trading system. Measures to correct these imbalances have largely involved adjustments to exchange rates. In the international trade literature, when the current account is in deficit, the Marshall-Lerner condition is sufficient for a successful devaluation. However, this partial equilibrium condition — apart from being based on the assumption that supply elasticities are infinite — abstracts from how the domestic economy responds to the change in relative prices. In this paper we develop a model of price and output determination in an open economy with imperpectly competitive markets, and draw a distinction between goods which are exported and those which are supplied to the domestic market. This means that we have to determine jointly both export prices and the domestic price of house sales. We show that as long as there is no money illusion in the labour market a fall in the nominal exchange rate raises domestic and export prices proportionally and leaves trade volumes unaffected. However, shifts in domestic absorption relative to overseas demand — by changing relative prices — cause shifts in the relative supply of exports and domestically sold goods and affect the trade balance. Thus fiscal and monetary measures directed towards reducing domestic absorption are more likely to be successful in correcting current account imbalances than exchange rate depreciation.     

Averting economic collapse and the solipsism bias

We study the behavior of experimental subjects who have to make a sequence of risky investment decisions in the presence of network externalities. Subjects follow a simple heuristic—investing after positive experiences and reducing their propensity to invest after a failure. This result contrasts with the theoretical findings of Jeitschko and Taylor [Jeitschko, T.D., Taylor, C., 2001. Local discouragement and global collapse: A theory of coordination avalanches. Amer. Econ. Rev. 91 (1), 208–224] in which even agents who have only good experiences eventually stop investing because they account for the fact that others with worse experiences will quit. This can trigger sudden economic collapse—a coordination avalanche—even in the most efficient Bayesian equilibrium. In the experiment, subjects follow their own experiences and disregard the possible bad experiences of others—thus exhibiting behavior that we term “solipsism bias.” Solipsism results in sustained investment activity and thus averts complete collapse.     

Central bank instruments, fiscal policy regimes, and the requirements for equilibrium determinacy

This paper examines the role of the monetary instrument choice for local equilibrium determinacy under sticky prices and different fiscal policy regimes. Corresponding to Benhabib et al.'s results for interest rate feedback rules [Benhabib, J., Schmitt-Grohé, S., Uribe, M., 2001. Monetary policy and multiple equilibria. American Economic Review 91, 167–185], the money growth rate should not rise by more than one for one with inflation when the primary surplus is raised with public debt. Under an exogenous primary surplus, money supply should be accommodating—such that real balances grow with inflation—to ensure local equilibrium determinacy. When the central bank links the supply of money to government bonds by controlling the bond-to-money ratio, an inflation stabilizing policy can be implemented for both fiscal policy regimes. Local determinacy is then ensured when the bond-to-money ratio is not extremely sensitive to inflation, or when interest payments on public debt are entirely tax financed, i.e., the budget is balanced.     

Ex post implementation

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and—in economic environments—sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto condition that is sufficient. Ex post monotonicity is satisfied in all single crossing environments with strict ex post incentive constraints.We show by means of two classic examples that ex post monotonicity does not imply nor is it implied by Maskin monotonicity. The single unit auction with interdependent valuations is shown to satisfy ex post monotonicity but not Maskin monotonicity. We further describe a Pareto correspondence that fails ex post monotonicity but satisfies Maskin monotonicity.     

Trading networks with price-setting agents

In a wide range of markets, individual buyers and sellers trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and sellers have access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient allocation of goods. Finally, we analyze trader profits in terms of the graph structure — roughly, a trader can command a positive profit if and only if it has an “essential” connection in the network, thus providing a graph-theoretic basis for quantifying the amount of competition among traders.     

The new long-term trend in the price of natural gas

A significant negative trend in the long-term price of natural gas at the wellhead is revealed from simulations with a partial equilibrium model of the industry in the United States. The model framework consists of a simultaneous equations system for production from reserves and for demands for production in the residential, commercial and industrial sectors. We utilize a wide range of historical data to calibrate the model and then develop two sets of scenarios for future prices, one based on further industry development under current regulation, and the other based on deregulation and development of an open market for gas services. The key variables — price of natural gas, level of production and inground gas reserves — for the next 10 years improve for the consumer whether or not there is deregulation but the second scenario leaves the consumer better off sooner.     

Trade mechanism selection in markets with frictions

We endogenize the trade mechanism in a search economy with many homogeneous sellers and many heterogeneous buyers of unobservable type. We study how heterogeneity and the traders' continuation values—which are endogenous—influence the sellers' choice of trade mechanism. Sellers trade off the probability of an immediate sale against the surplus expected from it, choosing whether to trade with everyone and how quickly. In equilibrium sellers may simply target one buyer type via non-negotiable offers (price posting), or may price discriminate (haggling). We also study when haggling generates trading delays. A price setting externality arises because of a strategic complementarity in the sellers' pricing choices.     

The structure of consumer preferences,Federal Republic of Germany, 1950–1973

Summary The objective of this paper is to analyze the structure of consumer preferences and changes in preferences over time. Consumer preferences are represented by an indirect translog utility function with time-varying preferences that is quadratic in the logarithms of its arguments. We consider a system of demand functions associated with parameter restrictions consistent with the theory. We characterize groupwise separability and groupwise homotheticity of preferences and derive for each set of restrictions on preferences parametric restrictions on the corresponding system of demand functions. Empirical results of the tests, based on time series data for FRG consumption expenditures on three commodity groups — durables, non-durables, and energy — are presented.     

Expectations,substitution, and scrapping in a putty-clay model

The paper presents a framework for analyzing the effect of changing expectations about future prices on a firm's choice of technique, and on its anticipated scrapping of capital equipment. Assuming a putty-clay technology, particular attention is paid to the way in which the scrapping age depends on the degree of ex ante input substitution. Numerical illustrations — based on data for Norwegian manufacturing for the years 1964–1983, an ex ante technology represented by a Generalized Leontief cost function in materials, energy, labor, and capital, and an ARMA representation of the price expectation mechanism — are presented. The results indicate that the price changes in this period may have had a substantial impact on planned scrapping, and on the chosen production techniques.     

A theory of sequential reciprocity

Many experimental studies indicate that people are motivated by reciprocity. Rabin [Amer. Econ. Rev. 83 (1993) 1281] develops techniques for incorporating such concerns into game theory and economics. His theory is developed for normal form games, and he abstracts from information about the sequential structure of a strategic situation. We develop a theory of reciprocity for extensive games in which the sequential structure of a strategic situation is made explicit, and propose a new solution concept—sequential reciprocity equilibrium—for which we prove an equilibrium existence result. The model is applied in several examples, and it is shown that it captures very well the intuitive meaning of reciprocity as well as certain qualitative features of experimental evidence.     

Gender Equality and Long-Run Growth

This research suggests that long-run economic and demographic development in Europe can be better understood when related to long-term trends in gender equality, dating back to the spread of Christianity. We set up a growth model where gaps in female-to-male human capital arise at equilibrium through a coordination process. An economy which over a long stretch of time re-coordinates on continuously more equal equilibria—as one could argue happened in Europe—exhibits growth patterns qualitatively similar to that of Europe.     

Free entry and stability in a cournot model

In a Cournot model for a single homogeneous good, we study simultaneously two stability properties of a Cournot equilibrium: the stability of a continuous quantity adjustment process with a fixed number of firms and the stability relative to entry. Under usual assumptions, we show that these two properties are consistent—i.e., there exists an equilibrium that is stable in both senses—and determine quite sharply the number of active firms.     

The Transition from Stagnation to Growth: An Adaptive Learning Approach

This article develops the first model in which, consistentwith the empirical evidence, the transition from stagnation toeconomic growth is a very long endogenous process. The modelhas one steady state with a low and stagnant level of incomeper capita and another steady state with a high and growing levelof income per capita. Both of these steady states are locallystable under the perfect foresight assumption. We relax the perfectforesight assumption and introduce adaptive learning into thisenvironment. Learning acts as an equilibrium selection criterionand provides an interesting transition dynamic between steadystates. We find that for sufficiently low initial values of humancapital—values that would tend to characterize preindustrialeconomies—the system under learning spends a long periodof time (an epoch) in the neighborhood of the low-income steadystate before finally transitioning to a neighborhood of the high-incomesteady state. We argue that this type of transition dynamic providesa good characterization of the economic growth and developmentpatterns that have been observed across countries.     

Residence-and source-based taxation of capital income in an overlapping generations model

By using an intertemporal equilibrium model with overlapping generations, this paper explores how residence-and source-based taxes on capital income affect the external current account in small open economies. These taxes influence the saving-investment balance not only through their incentive effects on rates of return but also through their impact on the intergenerational distribution of resources. This paper, in its examination of these effects — both intertemporal substitution and intergenerational distribution — identifies the net effect of the various impacts.The author would like to thank Dieter Bös and an anonymous referee for helpful comments on an earlier draft.     

Globally evolutionarily stable portfolio rules

The paper examines a dynamic model of a financial market with endogenous asset prices determined by short-run equilibrium of supply and demand. Assets pay dividends that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify globally evolutionarily stable strategies, allowing an investor to “survive,” i.e., to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this property—an analogue of the famous Kelly rule of “betting your beliefs.” A game theoretic interpretation of this result is given.     

Is error learning behaviour stabilizing?

It is very commonly admitted that error-learning behaviour in general improves the stability of dynamical economic evolutions. We show here, in the context of Temporary General Equilibrium Theory, that such an intuition is not true, in the sense that “most often,” for a large class of models, learning does not assuredly leads to more stable dynamics. The presentation of the problem then allows for a discussion of the type of hypothesis—very high levels of information or very careful behaviours—which can invalidate such a conclusion.     

p-Best response set and the robustness of equilibria to incomplete information

In this paper, we use p-best response sets—a set-valued extension of p-dominance—in order to provide a new sufficient condition for the robustness of equilibria to incomplete information: if there exists a set S which is a p-best response set with , and there exists a unique correlated equilibrium μ^* whose support is in S then μ^* is a robust Nash equilibrium.