the dynamic relationship between the federal funds rate and the treasury bill rate an empirical investigation this article examines the dynamic relationship between two key us money market interest rates the federal funds rate and the 3 month treasury bill rate using daily data over the period from 1974 99 we find a long run relationship between these two rates that is remarkably stable across monetary policy regimes of interest rate and monetary aggregate targeting employing a non linear asymmetric vector equilibrium correction model which is novel in this context we find that most of the adjustment toward the long run equilibrium occurs through the federal funds rate in turn there is strong evidence for the existence of significant asymmetries and non linearities in interest rate dynamics that have implications for the conventional view of interest rate behaviour

comparison shopping as a simultaneous move game this paper analyzes simultaneous move models of comparison shopping it shows that the equilibria in wilde schwartz 1979 can be rationalized as symmetric mixed strategies in an appropriately defined game in which information acquisition costs are endogenous it also shown that in the simultaneous move version of salop stiglitz 1977 nonexistence of equilibrium is not a problem in fact a variety of forms of equilibria emerge in that model pure strategy mixed strategy and blends of the two copyright 1992 by royal economic society

the stability of price dispersion under seller and consumer learning in many markets it is possible to find rival sellers charging different prices for the same good earlier research has attempted to explain this phenomenon by demonstrating the existence of dispersed price equilibria when consumers must make use of costly search to discover prices we ask whether such equilibria can be learned when sellers adjust prices adaptively in response to current market conditions with consumer behavior fixed convergence to a dispersed price equilibrium is possible in some cases however once consumer learning is introduced the monopoly outcome first found by diamond journal of economic theory3 1971 156 68 is the only stable equilibrium

market share dynamics in a duopoly model with word of mouth communication abstract we analyze dynamic price competition in a homogeneous goods duopoly where consumers exchange information via word of mouth communication a fraction of consumers who do not learn any new information remain locked in at their previous supplier in each period we analyze markov perfect equilibria in which firms use mixed pricing strategies market share dynamics are driven by the endogenous price dispersion depending on the parameters we obtain different classes of dynamics when firms are impatient there is a tendency towards equal market shares when firms are patient there are extended intervals of market dominance interrupted by sudden changes in the leadership position

costly buyer search in laboratory markets with seller advertising in this experiment sellers simultaneously choose prices and advertising strategies buyers either purchase at an advertised price or search sequentially for other prices in the unique symmetric equilibrium sellers charge a high unadvertised price or advertise a price chosen from a lower interval increases in search or advertising costs raise equilibrium prices and affect equilibrium advertising intensity empirical results are consistent with most comparative static predictions sellers however price much lower and advertise more intensely than predicted consequently market outcomes more closely resemble a perfect information bertrand like equilibrium than the imperfect information mixed strategy equilibrium with significant seller market power

on the learning and stability of mixed strategy nash equilibria in games of strategic substitutes abstract this paper analyzes the learning and stability of mixed strategy nash equilibria in games of strategic substitutes gss complementing recent work done in the case of strategic complements gsc mixed strategies in gss are of particular interest because it is well known that such games need not exhibit pure strategy nash equilibria first we establish bounds on the strategy space which indicate where randomizing behavior may occur in equilibrium second we show that mixed strategy nash equilibria are generally unstable under a wide variety of learning rules multiple examples are given

a note on best response dynamics we investigate the relationship between the continuous time best response dynamic its perturbed version and evolutionary dynamics in relation to mixed strategy equilibria we find that as the level of noise approaches zero the perturbed best response dynamic has the same qualitative properties as a broad class of evolutionary dynamics that is stability properties of equilibria are robust across learning dynamics of quite different origins and motivations journal of economic literature classification numbers c72 d83

revisiting dynamic duopoly with consumer switching costs abstract the degree of collusiveness of a market with consumer switching costs is analyzed in an infinite horizon model of duopolistic competition in contrast with previous analyses we assume that firms compete for the demand for a homogeneous good by setting prices simultaneously in each period this problem is formulated as a simple stochastic game and a symmetric stationary markovian perfect equilibrium with distinctive economic features is studied we show that switching costs unambiguously relax price competition in equilibrium but that on the contrary they may make tacit collusion more difficult to sustain journal of economic literature classification numbers c73 d43 l13

equilibrium price distributions equilibrium price distributions for a homogeneous product consistent with individual incentives are investigated they arise in informationally imperfect markets in which the only primitive datum is the distribution of search costs it is shown that single multi and continuous price distributions are all viable long run phenomena depending on the nature of search costs a method for computing equilibrium price distributions is also provided jevons law of one price has long been an accepted dictum in economic theory in a classroom presentation it still serves sometimes implicitly as a major premise in many micro models of market interaction much of the descriptive theory as well as welfare analysis hinges on this assumption yet one s day to day experience reveals that price differentials are a viable phenomenon and that looking for lower prices may very well be a rewarding activity the prospects of eventually hitting a bargain and the resulting price reduction would more than compensate for the cost incurred during the search process moreover the existence of price dispersions appear to be an empirically stable phenomenon snapshots of markets for relatively homogeneous products reveal substantial and recurring price differentials stigler 1961 and pratt wise and zeckhauser 1979 for example report some evidence supporting this claim an important article by stigler 1961 focused economists attention on the crucial role played by the informational structure of markets it gave rise to the study of the

adaptive learning models of consumer behavior abstract in a model of dynamic duopoly optimal price policies are characterized assuming consumers learn adaptively about the relative quality of the two products a contrast is made between belief based and reinforcement learning under reinforcement learning consumers can become locked into the habit of purchasing inferior goods such lock in permits the existence of multiple history dependent asymmetric steady states in which one firm dominates in contrast belief based learning rules must lead asymptotically to correct beliefs about the relative quality of the two brands and so in this case there is a unique steady state

search market equilibrium bilateral heterogeneity and repeat purchases abstract we develop a general model of search market equilibrium with heterogeneous buyers and sellers this framework unifies previous models with one sided heterogeneity and clarifies many of their special properties it easily accounts for price dispersion active search and the matching of buyer and seller types it also extends to repeat purchases once we embed it into a dynamic game with incomplete information we formalize the inferences and strategies underlying equilibria where firms charge constant prices and customers patronize them loyally we establish a general correspondence between such equilibria and single purchase markets journal of economic literature classification numbers d83 l13

learning in games with unstable equilibria we propose a new concept for the analysis of games the tasp which gives a precise prediction about non equilibrium play in games whose nash equilibria are mixed and are unstable under fictitious play like learning we show that when players learn using weighted stochastic fictitious play and so place greater weight on recent experience the time average of play often converges in these unstable games even while mixed strategies and beliefs continue to cycle this time average the tasp is related to the cycle identified by shapley l s shapley some topics in two person games in m dresher et al eds advances in game theory princeton university press princeton 1964 the tasp can be close to or quite distinct from nash equilibrium

instability of endogenous price dispersion equilibria a simulation models of price posting by firms and search by consumers such as burdett and judd 1983 often feature equilibria with endogenous price dispersion however such equilibria are strategically fragile in order to investigate how robust they are in the absence of an external coordination mechanism i simulate various protocols firms may use to update their prices despite firms being myopic some protocols yield results close to the benchmark model if firms rush to update before observing competitors actions profits are higher on average but volatile and cyclical with cost dispersion prices become more stable as they are more closely tied to costs all results are robust to moderate menu costs

on the dynamic stability of a price dispersion model using gradient dynamics abstract this paper studies the evolutionary stability of a unique nash equilibrium in a price dispersion model burdett and judd 1983 using gradient dynamics the numerical solution to the partial differential equation that governs the evolution of prices shows that the stationary equilibrium is not a nash equilibrium and that it differs from the cyclical behavior predicted by another family of dynamics such as replicator and logit in a continuous action space

an experimental study of price dispersion abstract we report an experiment examining a simple clearinghouse model that generates price dispersion according to this model price dispersion arises because of consumer heterogeneity some consumers are informed and simply buy from the firm offering the lowest price while the remaining consumers are captive and shop based on considerations other than price in our experiment we observe substantial and persistent price dispersion we find that as predicted an increase in the fraction of informed consumers leads to more competitive pricing for all consumers we also find as predicted that when more firms enter the market prices to informed consumers become more competitive while prices to captive customers become less competitive thus our experiment provides strong support for the model s comparative static predictions about how changes in market structure affect pricing

the dynamics of price dispersion or edgeworth variations abstract hypotheses on the dynamics of dispersed prices are extracted from computer simulations and theory and are tested using laboratory data as predicted in some variations of the edgeworth hypothesis the data exhibit a significant cycle relative to the unique stationary distribution the empirical distribution of posted prices has excess mass in an interval that declines until it approaches the lower boundary of the stationary distribution then jumps upward and the downward cycle resumes the amplitude of the cycle seems fairly constant over the longer experimental sessions a hybrid of gradient dynamics and logit dynamics seems to best reproduce the observed dynamics

buyer search and price dispersion a laboratory study we study markets with costly buyer search in which sellers simultaneously post prices buyers costlessly observe one or with probability 1 q two of the posted prices and can accept one or pay to search again the experiment varies q the search cost and the number of buyers equilibrium theory predicts a unified very low high price for q 0 q 1 and predicts specific distributions of dispersed prices for q 1 3 and 2 3 actual prices conform closely to the predictions in some treatments buyers reservation prices are biased away from the extremes however and sellers prices have positive autocorrelation and cross sectional correlation

the dynamic instability of dispersed price equilibria abstract we adopt an evolutionary framework to explain price dispersion as a time varying phenomenon by developing a finite strategy analogue of the burdett and judd 1983 price dispersion model we show that all dispersed price equilibria are unstable under the class of perturbed best response dynamics instead numerical simulations using the logit dynamic show that price dispersion manifests itself as a limit cycle we verify that limit cycles persist even when the finite strategy model approaches the original continuous strategy model for a particularly simple case of the model we prove the existence of a limit cycle

strategic complementarities and search market equilibrium abstract in this paper we apply supermodular game theory to the equilibrium search literature with sequential search we identify necessary and sufficient conditions for the pricing game to exhibit strategic complementarities and prove existence of equilibrium we then show that price dispersion is inherently incompatible with strategic complementarities in the sense that the diamond paradox obtains when firms are identical and is robust within the class of search cost densities that are small near zero and support strategic complementarities we also show that a major criticism of the literature that agents act as if they know the distribution of prices can be justified in the sense of convergent best response dynamics

learning mixed equilibria we study learning processes for finite strategic form games in which players use the history of past play to forecast play in the current period in a generalization of fictitious play we assume only that players asymptotically choose best responses to the historical frequencies of opponents past play this implies that if the stage game strategies converge the limit is a nash equilibrium in the basic model plays seems unlikely to converge to a mixed strategy equilibrium but such convergence is natural when the stage game is perturbed in the manner of harsanyi s purification theorem journal of economic literature classification number c72