competition and the number of firms in a market are duopolies more competitive than atomistic markets this paper uses a variant of the standard search model to examine market equilibrium and the consequences for market equilibrium of an increase in the number of firms if marginal search costs increase with the number of searches then the demand curve facing any firm will be kinked with the elasticity of demand with respect to price decreases being less than with respect to price increases prices may not change in response to changes in marginal costs as the number of firms increases the maximum price that is consistent with equilibrium increases to the monopoly price but the minimum price decreases on the other hand if marginal search costs decrease with the number of searches equilibrium if it exists is characterized by a

on the effects of downstream entry we study the effects of entry in a downstream market where firms e g compaq and ibm cvs and safeway buy an input e g microprocessor grocery items from an upstream supplier e g intel procter gamble and sell their output to consumers we show demand conditions where contrary to conventional wisdom entry of a new downstream firm lowers the downstream market output and increases the consumer price thus consumers may be better off with fewer sellers in such markets we also show that this entry may cause the profit of each incumbent downstream firm to i remain unchanged ii decrease or iii even increase also for a class of widely used demand conditions the supplier s optimal price is shown invariant to the entry exit of its downstream buyer firms we classify all possible effects of downstream entry in terms of fundamental market demand conditions

a folk theorem for repeated games with unequal discounting we introduce a dynamic non equivalent utilities dneu condition and the notion of dynamic player specific punishments for a general repeated game with unequal discounting both naturally generalizing the stationary counterparts in abreu et al 1994 we show that if the dneu condition i e no pair of players have equivalent utility functions in the repeated game is satisfied then any feasible and strictly sequentially individually rational payoff sequence allows dynamic player specific punishments using this result we prove a folk theorem for unequal discounting repeated games that satisfy the dneu condition

equilibrium price dispersion with sequential search abstract the paper studies equilibrium pricing in a product market for an indivisible good where buyers search for sellers buyers search sequentially for sellers but do not meet every seller with the same probability specifically a fraction of the buyers meetings lead to one particular large seller while the remaining meetings lead to one of a continuum of small sellers in this environment the small sellers would like to set a price that makes the buyers indifferent between purchasing the good and searching for another seller the large seller would like to price the small sellers out of the market by posting a price that is low enough to induce buyers not to purchase from the small sellers these incentives give rise to a game of cat and mouse whose only equilibrium involves mixed strategies for both the large and the small sellers the fact that the small sellers play mixed strategies implies that there is price dispersion the fact that the large seller plays mixed strategies implies that prices and allocations vary over time we show that the fraction of the gains from trade accruing to the buyers is positive and nonmonotonic in the degree of market power of the large seller as long as the large seller has some positive but incomplete market power the fraction of the gains from trade accruing to the buyers depends in a natural way on the extent of search frictions

long run competition in capacity short run competition in price and the cournot model in this article we investigate the nature of equilibrium in markets in which firms choose the scale of operation before they make pricing decisions we analyze a duopoly model in which firms choose their capacities before engaging in bertrand like price competition we demonstrate that the cournot outcome is unlikely to emerge in such markets and that the equilibrium tends to be more competitive than the cournot model would predict in addition our results indicate a tendency toward asymmetric firm sizes and price dispersion that results from the mixed strategies firms use in equilibrium

interest rates and currency prices in a two country world abstract this paper is a theoretical study of the determination of prices interest rates and currency exchange rates set in an infinitely lived two country world which is subject both to stochastic endowment shocks and to monetary instability formulas are obtained for pricing all equity claims nominally denominated bonds and currencies and these formulas are related to earlier closely related results in the theories of money finance international trade

do consumers search for the highest price oligopoly equilibrium and monopoly optimum in differentiated products markets we develop a model of search among substitutes for the best combination of commodity variant and price in which the structure of search costs is manipulable by the suppliers of these variants e g by joining an existing market or opening a new one we analyze the subgame perfect equilibria arising in a multistage game involving specialized firms choice of entry variant and price and we compare them to a multiproduct monopolist s optimal choice we show that equilibrium prices increase in the number of substitutes sold in one market and that in the situation considered here monopoly increases welfare

an evolutionary model of bertrand oligopoly we analyze the long run outcome of markets in which boundedly rational firms with a decreasing returns to scale technology compete in prices the behavior of these firms is based on limitation of success and experimentation in this framework we introduce a new approach to model boundedly rational behavior based on the idea of behavioral principles i e formal descriptions even with the simplest ones the result is that the prices announced are a strict refinement of the set of nash equilibria with more sophisticated behavioral principles the long run outcome corresponds to the concept of central prices wich are also nash equilibria introduced here this is a robust and clear cut prediction wich under quadratic costs and arbitrary demand essentially coincides with the walrasian equilibrium

lag length selection and tests of granger causality between money and income one of the most widely accepred relationships in macroeconomics is the positive relationship between the rate of growth of the money supply and the rate of growth of income a diversity of opinion arises however with the attempt to identify a causal relationship between these variables while friedman and schwartz 1963 initiated the empirical investigation of money income causality sims 1972 made the most significant contribution to this literature with a practical application of the criterion developed by granger 1969 for identifying a causal relationship since the appearance of sims s approach and an alternative one advanced by sargent 1976 many researchers have applied these techniques to the investigation of the causal relationship between money and income l with two exceptions hsiao 1981 and mcmillin and fackler 1984 these researchers have arbitrarily chosen the lengths of their distributed lags the purpose of this paper is to test for granger causality between money and income this paper differs from previous work in that considerably more attention is focused on the effect of the lag specification on the test results in particular we investigate the extent to which rules of thumb arbitrary lag specifications and

in search of the exchange risk premium a six currency test assuming mean variance optimization abstract a number of authors examining deviations of actual rates of currency depreciation from forward discounts have claimed to find evidence of risk premiums if these deviations are indeed partly due to risk premiums rather than being entirely due to expectational errors then they should be systematically related to those variables on which risk premiums are thought to depend finance theory tells us that if investors optimize with respect to mean and variance the risk premium depends in a specific way on 1 the supplies of assets denominated in the various currencies 2 the variance covariance matrix of the rates of return and 3 the coefficient of risk aversion the null hypothesis of this paper is that the coefficient of risk aversion is zero countries assets are perfect substitutes and risk premiums are nonexistent the alternative hypothesis is that rates of return are systematically related to asset supplies by a macroeconomic portfolio balance function the maximum likelihood technique used dominates previous attempts to find such a relationship in that the parameters of the portfolio balance function are constrained to depend on the variance covariance matrix as the finance theory says they should on the other hand the technique also dominates previous applications of the finance theory in that the expected returns are allowed to vary over time as the macroeconomic portfolio balance theory says they should the paper s finding is a statistical inability to reject the null hypothesis for a portfolio of six currencies although this could be due to low power in the test

imitation by price and quantity setting firms in a differentiated market abstract we study the evolution of imitation behaviour in a differentiated market where firms are located equidistantly on a salop circle firms choose price and quantity simultaneously leaving open the possibility for non market clearing outcomes the strategy of the most successful firm is imitated behaviour in the stochastically stable outcome depends on the level of market differentiation and corresponds exactly with the nash equilibrium outcome of the underlying stage game for high level of differentiation firms end up at the monopoly outcome for intermediate level of differentiation they gravitate to a mutually non aggressive outcome where price is higher than the monopoly price for low level of differentiation firms price at a mark up above the marginal cost market clearing always results endogenously

bargaining in standing committees with an endogenous default committee voting has mostly been investigated from the perspective of the standard baron ferejohn model of bargaining over the division of a pie in which bargaining ends as soon as the committee reaches an agreement in standing committees however existing agreements can be amended this article studies an extension of the baron ferejohn framework to a model with an evolving default that reflects this important feature of policymaking in standing committees in each of an infinite number of periods the ongoing default can be amended to a new policy which is in turn the default for the next period the model provides a number of quite different predictions i from a positive perspective the key distinction turns on whether the quota is less than unanimity in that case patient enough players waste substantial shares of the pie each period and the size principle fails in some pure strategy markov perfect equilibria in contrast the unique markov perfect equilibrium payoffs in a unanimity committee coincide with those in the corresponding baron ferejohn framework ii if players have heterogeneous discount factors then a large class of subgame perfect equilibria including all markov perfect equilibria are inefficient

repeated games with differential time preferences when players have identical time preferences the set of feasible repeated game payoffs coincides with the convex hull of the underlying stage game payoffs moreover all feasible and individually rational payoffs can be sustained by equilibria if the players are sufficiently patient neither of these facts generalizes to the case of different time preferences first players can mutually benefit from trading payoffs across time hence the set of feasible repeated game payoffs is typically larger than the convex hull of the underlying stage game payoffs second it is not usually the case that every trade plan that guarantees individually rational payoffs can be sustained by an equilibrium no matter how patient the players are this paper provides a simple characterization of the sets of nash and of subgame perfect equilibrium payoffs in two player repeated games

survival at the center the stability of minimum differentiation abstract we model a hotelling market with multidimensional product differentiation in an evolutionary framework both evolutionary stability in the sense of schaffer 1989 and stochastic stability following kandori et al 1993 young 1993 are analyzed it is shown that firms move towards the center in product space i e a principle of minimum differentiation on all dimensions of the product space applies

currency prices terms of trade and interest rates a general equilibrium asset pricing cash in advance approach currency prices terms of trade and interest rates a general equilibrium asset pricing cash in advance approach

imitators and optimizers in cournot oligopoly we analyze a symmetric n firm cournot oligopoly with a heterogeneous popu lation of optimizers and imitators imitators mimic the output decision of the most successful firms of the previous round a la vega redondo 1997 optimizers play a myopic best response to the opponents previous output firms are allowed to make mistakes and deviate from the decision rules with a small probability apply ing stochastic stability analysis we find that the long run distribution converges to a recurrent set of states in which imitators are better o than are optimizers this finding appears to be robust even when optimizers are more sophisticated it suggests that imitators drive optimizers out of the market contradicting a funda mental conjecture by friedman 1953

imitation and price competition in a differentiated market abstract we study the stable market outcome that evolves in a spatially differentiated market when price competing firms choose actions by imitation of the most profitable firm we compare and contrast the stable outcomes under two imitation procedures one where each firm immediately imitates the most profitable firm and the other when a firm imitates another firm only if it is more profitable while being sufficiently similar in context of the market segment it operates in or sufficiently close in either case the symmetric pure strategy nash equilibrium is always a stable outcome however when imitation of the most profitable firm is immediate and market differentiation is moderate states with prices lower than the nash equilibrium are also stable in contrast when imitation of the most profitable firm is more gradual and market differentiation is below a threshold states with prices above the nash equilibrium are also stable thus while competitive evolutionary pressure in this imitation based model does result in the nash equilibrium always being stable other outcomes may be stable as well interestingly the states that are stable under gradual imitation give the firms a higher profit than the stable states under immediate imitation

risk uncertainty and exchange rates this paper is motivated by two facts failure of log linear empirical exchange rate models of the 1970 s and the observed variability of risk premiums in the forward market rational maximizing models predict that changes in conditional variances of monetary policies government spendings and income growths affect risk premiums and induce conditional volatility of exchange rates i examine theoretically how changes in these exogenous conditional variances affect the level of the current exchange rate and attempt to quantify the extent that this channel explains exchange rate volatility using autoregressive conditional heteroscedastic models

price increasing competition in a discrete choice model of product differentiation the symmetric duopoly price may be lower than equal to or higher than the single product monopoly price whereas the market share effect encourages a duopolist to charge less than the monopoly price because a duopolist serves fewer consumers the price sensitivity effect motivates a higher price when more consumer choice steepens the firm s demand curve the joint distribution of consumer values for the two conceivable products determines the relative strength of these effects the analysis provides precise conditions for price increasing competition and reveals that it is unexceptional from a theoretical perspective

autoregressive modelling and money income causality detection abstract a step wise procedure based on granger s concept of causality and abaike s final prediction error criterion is suggested as a practical means to identify the order of lags of each variable in a multivariate autoregressive process the model seems useful because it can serve as a reduced form formulation to avoid imposing often spurious or false restrictions of the model it also provides a reasonably powerful test of causality the idea is applied to u s postwar money and income data it is found that between m1 and gnp a bivariate feedback model fits the data best between m2 and gnp a one way causal model from money to income performs better diagnostic checks applied to our model seem to indicate the adequacy of our approach

on the dispensability of public randomization in discounted repeated games abstract we show that any feasible individually rational payoffs of an infinitely repeated game can arise as subgame perfect equilibrium payoffs if the discount factor is close enough to one even if mixed strategies are not observable and public randomizations are not available

money and asset prices in a cash in advance economy an asset pricing model with money introduced via a cash in advance constraint is presented the monetary velocity is variable hence money demand does not obey the trivial quantity equation the effects of disturbances in output and money growth on real balances the price level and interest rates are examined monetary policy has effects on real asset prices the fisher relation and the premium on nominal bonds are discussed the precise role of the timing of information and transactions for properties of price levels and interest rates are clarified

the evolution of walrasian behavior consider an evolutionary context where a given number of quantity setting oligopolists tend to mimic successful behavior occasionally experimenting with some small probability in this context it is shown that the unique long run outcome of the process has all firms playing walrasian i e choosing an output that maximizes profits when taking the market clearing price as given

nash and perfect equilibria of discounted repeated games abstract the perfect folk theorem for discounted repeated games establishes that the sets of nash and subgame perfect equilibrium payoffs are equal in the limit as the discount factor tends to one we provide conditions under which the two sets coincide before the limit is reached that is we show how to compute such that the nash and perfect equilibrium payoffs of the discounted game are identical for all

opec the seven sisters and oil market dominance an evolutionary game theory and agent based modeling approach abstract a methodological toolkit comprised of evolutionary game theory and agent based modeling is used to study opec and the seven sisters as they struggled for control over global petroleum markets during the 1960s and 1970s an evolutionary game theory model incorporates heterogeneous populations energy specific variables and behavioral considerations to capture the fundamentals of the applied problem an agent based model is used to provide detailed results and demonstrate the importance of the natural resource to the outcome of the model

extreme equilibria in the negotiation model with different time preferences abstract we study a negotiation model with a disagreement game between offers and counteroffers when players have different time preferences delay can be pareto efficient thereby violates the presumption of the hicks paradox we show that all equilibria are characterized by the extreme equilibria making unacceptable offers supports extreme equilibria and significantly alters the backward induction technique to find the extreme equilibrium payoffs a player s worst equilibrium payoff is characterized by a minmax problem involving efficient equilibrium payoffs that are above the bargaining frontier which is possible when players have sufficiently different time preferences

valuating payoff streams under unequal discount factors abstract we study repeated prize allocation when the discount factors of the agents are unequal the feasible set of payoffs behaves badly the pareto frontier is everywhere discontinuous and there is an open subset of high discount factors under which the feasible set is totally disconnected

evolution to equilibrium in an asymmetric oligopoly with differentiated goods abstract we present results on finite population evolutionarily stable strategies esss and stochastically stable states for a model of evolution with an imitative rule of strategy choice in an asymmetric oligopoly with differentiated goods and two groups of firms one group of low cost firms and one of high cost firms the firms play price setting and quantity setting oligopoly games under linear demand functions we will show that the stochastically stable state in a price setting oligopoly and that in a quantity setting oligopoly coincide

stochastic adaptation in finite games played by heterogeneous populations we analyze stochastic adaptation in finite n player games played by heterogeneous populations containing best repliers better repliers and imitators individuals select strategies by applying a

imitators and optimizers in a changing environment abstract we analyze the repeated interaction between an imitating and a myopically optimizing player in an otherwise symmetric environment of changing marginal payoff focusing on finite irreducible environments and the case of strategic substitutes we unfold a trade off between the degree of interaction and the size of environmental shocks the optimizer outperforms the imitator if interaction is weak or shocks are large as to the case of duopoly this translates into small cross price elasticities or large shocks in marginal cost and or the maximum willingness to pay in these cases a changing environment creates selection pressure against imitative behavior

macroeconomic uncertainty and the risk premium in the foreign exchange market abstract in modeling the risk premium in the foreign exchange market i assume that money and production follow a joint stochastic process with bivariate garch innovations my formulation is based on lucas asset pricing model and implies that the risk premium in the foreign exchange market is due to time varying volatilities in macroeconomic variables testing the model for three currencies shows the time varying risk premium to be significant in explaining the deviation of the forward foreign exchange rate from the future spot rate diagnostic testing of the model partially supports the market efficiency hypothesis after accounting for the time varying risk premium jel f31 1997 elsevier science ltd

conditional variance and the risk premium in the foreign exchange market abstract we investigate the existence of a risk premium in the foreign exchange market based on the conditional variance of market forecast errors the forecast errors are assumed to follow the arch process introduced by engle 1982 estimation and diagnostic testing of the model are discussed and results are presented for the currencies of the united kingdom france germany japan and switzerland