an approach to asset pricing under incomplete and diverse perceptions we model a dynamic competitive market where in every period risk neutral traders trade a one period bond against an infinitely lived asset with limited short selling of the long term asset traders lack structural knowledge and use different incomplete theories all of which give statistically correct beliefs about next period s market price of the long term asset the more theories there are in the market the higher is the equilibrium price of the long term asset investors with more complete theories do not necessarily earn higher returns than those with less complete ones who can earn above the risk free rate we provide two necessary conditions for a trader to earn above the risk free rate

nash equilibrium when players account for the complexity of their forecasts abstract nash equilibrium is often interpreted as a steady state in which each player holds the correct expectations about the other players behavior and acts rationally this paper investigates the robustness of this interpretation when there are small costs associated with complicated forecasts the model consists of a two person strategic game in which each player chooses a finite machine to implement a strategy in an infinitely repeated 2 2 game with discounting i analyze the model using a solution concept called nash equilibrium with stable forecasts esf my main results concern the structure of equilibrium machine pairs they provide necessary and sufficient conditions on the form of equilibrium strategies and plays in contrast to the folk theorem these structural properties place severe restrictions on the set of equilibrium paths and payoffs for example only sequences of the one shot nash equilibrium can be generated by any esf of the repeated game of chicken

an r d race with knowledge accumulation i develop a model of an r d race with knowledge accumulation my model does not inherit the memorylessness property of the exponential distribution that troubles existing models of r d races hence firms knowledge stocks are no longer irrelevant to their behavior during the r d race and knowledge accumulation has strategic implications in this more general setting i obtain results that stand in marked contrast to the previous literature in particular under some conditions the firm that is behind in the race engages in catch up behavior this pattern of strategic interactions action reaction is consistent with empirical research copyright 2003 by the rand corporation

correlation neglect in belief formation many information structures generate correlated rather than mutually independent signals the news media being a prime example this article provides experimental evidence that many people neglect the resulting double counting problem in the updating process in consequence beliefs are too sensitive to the ubiquitous telling and re telling of stories and exhibit excessive swings we identify substantial and systematic heterogeneity in the presence of the bias and investigate the underlying mechanisms the evidence points to the paramount importance of complexity in combination with people s problems in identifying and thinking through the correlation even though most participants in principle have the computational skills that are necessary to develop rational beliefs many approach the problem in a wrong way when the environment is moderately complex thus experimentally nudging people s focus towards the correlation and the underlying independent signals has large effects on beliefs

bayesian networks and boundedly rational expectations i present a framework for analyzing decision makers with an imperfect understanding of their environment s correlation structure the decision maker faces an objective multivariate probability distribution his own action is one of the random variables he is characterized by a directed acyclic graph over the set of variables his subjective belief filters the objective distribution through his graph via the factorization formula for bayesian networks this belief distortion implies that the decision maker s long run behavior may affect his perception of the consequences of his actions accordingly i define a personal equilibrium notion of optimal choices i show how recent models of boundedly rational expectations as well as new ones e g reverse causality can be subsumed into this framework as special cases some general properties of the bayesian network representation of subjective beliefs are presented as well as a missing data foundation

the variable rate of growth effect in the life cycle saving model the rate of growth in real gnp g affects the aggregate saving rate positively in life cycle saving models this rate of growth effect is invariably estimated as the coefficient of g in the saving function we show that other determinants of the saving rate influence the rate of growth effect in other words the rate of growth effect is not constant specifically the real rate of return on financial assets and the population dependency ratio determine the timing of saving over the life cycle and hence alter the rate of growth effect the dependency ratio also has an effect on the saving rate which is independent of g because it together with the foreign saving rate determines the level of saving over the life cycle

inflation and savings international evidence on inflation induced income losses the fall in the average propensity to consume a p c in the i970s in most industrialised countries has been the subject of much debate it has been ascribed to a wide variety of causes most important it has been widely interpreted as a typical example of a situation in which economic forecasting has failed simply because it did not take into account the psychological effects of rapid changes in the economic environment given the inability of economists to predict sudden changes in consumer expectations these would naturally set severe limits to the usefulness of economic forecasting this paper takes a different approach to the problem it contends that the true fall in the a p c has been considerably lower than indicated by the statistics the argument runs roughly as follows the increase in the rate of inflation has led to a net transfer of real resources away from the personal sector this transfer was due to the fall in the real value of net monetary assets held by the personal sector and issued by the public and business sectors of the economy consumers considered this fall as negative income and adjusted their expenditure accordingly the definition of personal sector disposable income used in the national accounts statistics does not include such a correction in inflationary periods this leads to a large overestimate of true personal sector disposable income given this overestimate of the denominator it is hardly surprising that measured c y should fall when the rate of inflation rises the simplicity of this theory indicates that it can quite easily be subjected to empirical testing the tests proposed in this paper are based on a novel specification of the consumption function developed by davidson et al i978 henceforth dhsy this function has a solid theoretical foundation good statistical properties and allows both shortand long run phenomena to be easily incorporated in an acceptable manner simple theoretical considerations indicate roughly how one should go about measuring true income this corrected measure of income can be incorporated into the consumption function to be estimated in such a way that the coefficient of the correction term is endogenously determined in the regression the statistical properties of the resulting regressions are the evidence leading to a rejection or tentative acceptance of the theory

coarse thinking and persuasion we present a model of uninformative persuasion in which individuals think coarsely they group situations into categories and apply the same model of inference to all situations within a category coarse thinking exhibits two features that persuaders take advantage of i transference whereby individuals transfer the informational content of a given message from situations in a category where it is useful to those where it is not and ii framing whereby objectively useless information influences individuals choice of category the model sheds light on uninformative advertising and product branding as well as on some otherwise anomalous evidence on mutual fund advertising

correlation misperception in choice we present a decision theoretic analysis of an agent s understanding of the interdependencies in her choices we provide the foundations for a simple and flexible model that allows the misperception of correlated risks we introduce a framework in which the decision maker chooses a portfolio of assets among which she may misperceive the joint returns and present simple axioms equivalent to a representation in which she attaches a probability to each possible joint distribution over returns and then maximizes subjective expected utility using her possibly misspecified beliefs

modeling the economic interaction of agents with diverse abilities to recognize equilibrium patterns we model differences among agents in their ability to recognize temporal patterns of prices using the concept of debruijn sequences in two dynamic models of markets we demonstrate the existence of equilibria in which prices fluctuate in a pattern that is independent of the fundamentals and that can be recognized only by the more competent agents jel c7 d4 s477

the interest elasticity of savings in developing countries the existing evidence abstract this paper presents a critical analysis of some of the most recent empirical work on the interest elasticity of savings in developing economies supported by a set of empirical results the paper argues that a the real interest elasticity of savings is not easily detected using the existing empirical models which generally yield insignificant interest rate parameters in the seventies b the existing models suffer from serious defects that make if very difficult to interpret the estimated parameters

inflation and savings testing deaton s hypothesis a money illusion savings function in which unanticipated inflation affects the savings ratio positively is tested this is strongly supported by finnish data goodness of fit statistics are quite high and the coefficient estimates are of the expected sign and are highly significant standard stability tests of both the brown durbin evans type and of the vpr type are generally rather favourable finally cross country evidence from ten oecd countries gives further support for the suggested specification

can agents with causal misperceptions be systematically fooled using data on house sales and inventories this paper shows that housing market dynamics are driven mainly by listings and less so by transaction speed thus the decision to move house is key to understanding the housing market the paper builds a model where moving house is essentially an investment in match quality implying that moving depends on macroeconomic developments and housing market conditions the endogeneity of moving means there is a cleansing effect those at the bottom of the match quality distribution move first which generates overshooting in aggregate variables the model is applied to the 1995 2004 housingmarket boom

escaping nash inflation an ordinary differential equation ode gives the mean dynamics that govern the convergence to self confirming equilibria of self referential systems under discounted least squares learning another ode governs escape dynamics that recurrently propel away from a self confirming equilibrium in a model with a unique self confirming equilibrium the escape dynamics make the government discover too strong a version of the natural rate hypothesis the escape route dynamics cause recurrent outcomes close to the ramsey commitment inflation rate in a model with an adaptive government

a dynamic game of r and d patent protection and competitive behavior a theory of dynamic optimal resource allocation to r and d in an n firm industry is developed using differential games this technique represents a synthesis of the analytic methods previously applied to the problem static game theory and optimal control the use of particular functional forms allows the computation and detailed discussion of the nash equilibrium in investment rules this paper addresses the problem of resource allocation to research and development among the important issues that a firm engaging in r and d must evaluate are uncertainty regarding the feasibility and profitability of a particular innovation the possibility of a protracted development period the possibility that a rival firm may innovate first capturing either a patent or a significant share of the new market the possibility that a rival firm may imitate the innovation and appropriate some of the profits in the new market in what follows we will develop a theory of optimal resource allocation to research and development which incorporates the aspects of r and d enumerated above we will use a dynamic game theoretic analysis determining the nash equilibrium strategies for n identical firms the availability of perfect patent protection is shown to accelerate development of the innovation and the effect of increasing rivalry is addressed the impact of increasing rivalry on nash equilibrium investment in r and d depends upon the degree of appropriability of rewards if patent protection is perfect then increasing the number of nash rivals results in increased r and d effort however when imitation is rewarded the opposite may be true finally some notions of competitive and perfectly competitive equilibrium are examined in the context of the model developed below

revisiting games of incomplete information with analogy based expectations this paper studies the effects of analogy based expectations in static two player games of incomplete information players are assumed to be boundedly rational in the way they forecast their opponent s state contingent strategy they bundle states into analogy classes and play best responses to their opponent s average strategy in those analogy classes we provide general properties of analogy based expectation equilibria and apply the model to a variety of well known games we characterize conditions on the analogy partitions for successful coordination in coordination games under incomplete information rubinstein a 1989 the electronic mail game strategic behavior under almost common knowledge amer econ rev 79 385 391 we show how analogy grouping of the receiver may facilitate information transmission in crawford and sobel s cheap talk games crawford v p sobel j 1982 strategic information transmission econometrica 50 1431 1451 and we show how analogy grouping may give rise to betting in zero sum betting games such as those studied to illustrate the no trade theorem

the macroeconomic impact of development aid a critical survey the early literature explained aid s macroeconomic impact in the context of the dual gap model showing a clear link between aid and growth many now believe that the empirical evidence shows there to be no such relationship this paper critically reviews the different theoretical perspectives the dual gap model the savings debate recipient fiscal response and aid as dutch disease and the empirical debates on aid savings and growth the basis for denying a relationship between aid and growth is shown to be weak though more recent areas of research offer promising directions for future work

self confirming equilibrium rium path of play thus if a self confirming equilibrium occurs repeatedly no player ever observes play that contradicts his beliefs even though beliefs about play at off path information sets need not be correct we characterize the ways in which self confirming equilibria and nash equilibria can differ and provide conditions under which self con firming equilibria correspond to standard solution concepts nash equilibrium and its refinements describe a situation in which i each player s strategy is a best response to his beliefs about the play of his opponents and ii each player s beliefs about the opponents play are exactly correct we propose a new equilibrium concept self confirming equilibrium that weakens condition ii by requiring only that players beliefs are correct along the equilibrium path of play thus each player may have incorrect beliefs about how his opponents would play in contingencies that do not arise when play follows the equilibrium and moreover the beliefs of different players may be wrong in different ways the concept of self confirming equilibrium is motivated by the idea that noncooperative equilibria should be interpreted as the outcome of a learning process in which players revise their beliefs using their observations of previous play suppose that each time the game is played the players observe the actions chosen by their opponents but that players do not observe the actions their opponents would have played at the information sets that were not reached along the path of play then if a self confirming equilibrium occurs repeatedly no player ever observes play that contradicts his beliefs so the equilibrium is self confirming in the weak sense of not being inconsistent with the evidence by analogy with the literature on the bandit problem e g rothschild 1974 one might expect that a non nash self confirming equilibrium can be the outcome of plausible learning processes this point was made by fudenberg and

venture capital financed investments in intellectual capital abstract the paper considers a new company in the it industry founded by a management team and partially financed by venture capital among the questions that the paper addresses are how much venture capital should be acquired to help finance the development of the firm how should a wish to grow with the aim of making a breakthrough in the it area be balanced against the stockholders wish to consume the problem is studied as an optimal control problem with a random time horizon and we derive a series of prescriptions for investment and financial decisions

learning to play games in extensive form by valuation abstract game theoretic models of learning which are based on the strategic form of the game cannot explain learning in games with large extensive form we study learning in such games by using valuation of moves a valuation for a player is a numeric assessment of her moves that purports to reflect their desirability we consider a myopic player who chooses moves with the highest valuation each time the game is played the player revises her valuation by assigning the payoff obtained in the play to each of the moves she has made we show for a repeated win lose game that if the player has a winning strategy in the stage game there is almost surely a time after which she always wins when a player has more than two payoffs a more elaborate learning procedure is required we consider one that associates with each move the average payoff in the rounds in which this move was made when all players adopt this learning procedure with some perturbations then with probability 1 there is a time after which strategies that are close to subgame perfect equilibrium are played a single player who adopts this procedure can guarantee only her individually rational payoff

analysing disequilibrium interest rate systems in developing countries abstract under equilibrium conditions monetary policy measures to raise institutional interest rates are contractionary when interest rates are held below their free market equilibrium levels however an increase can be expansionary higher institutional interest rates may deter savings in the form of unproductive inflation hedges and encourage savings in the form of financial claims issued to finance productive investment in most developing countries money is the predominant financial repository of savings and bank loans are a major source of investible funds hence attention is focused here on models which analyse the effects of binding interest rate ceilings on financial intermediation empirical evidence reported in this paper is consistent with the view that binding institutional interest rate ceilings can have a substantial growth reducing impact

perceptrons play the repeated prisoner s dilemma abstract we examine the implications of bounded rationality in repeated games by modeling the repeated game strategies as perceptrons f rosenblatt principles of neurodynamics spartan books and m minsky and s a papert perceptions an introduction to computational geometry mit press cambridge ma 1988 in the prisoners dilemma game if the cooperation outcome is pareto efficient then we can establish the folk theorem by perceptrons with single associative units minksy and papert whose computational capability barely exceeds what we would expect from players capable of fictitious plays e g l shapley some topics in two person games adv game theory5 1964 1 28 journal of economic literature classification number c72

games with procedurally rational players the authors study interactive situations in which players are boundedly rational each player rather than optimizing given a belief about the other players behavior as in the theory of nash equilibrium uses the following choice procedure she first associates one consequence with each of her actions by sampling literally or virtually each of her actions once then she chooses the action that has the best consequence the authors define a notion of equilibrium for such situations and study its properties copyright 1998 by american economic association

behavioral equilibrium in economies with adverse selection i propose a new solution concept behavioral equilibrium to study environments with players who are naive in the sense that they fail to account for the informational content of other players actions a behavioral equilibrium requires that i players have no incentives to deviate given their beliefs about the consequences of deviating ii these beliefs are consistent with the information obtained from the actual equilibrium play of all players and iii when processing this information naive players fail to account for the correlation between other players actions and their own payouncertainty i apply the framework to certain adverse selection settings and show that contrary to the received literature the adverse selection problem is exacerbated when naive players fail to account for selection more generally the main distinguishing feature of the framework is that in equilibrium beliefs about both fundamentals and strategies are jointly restricted consequently whether a bias may arise or not is determined endogenously in equilibrium jel c72 d82 a large literature presents evidence that psychological and cognitive biases aect people s be havior this evidence raises some questions what are the eects of these biases and can they persist at all in economic settings where people strategically interact with each other and have the opportunity to learn from their experience 1 in this paper i introduce a game theoretic equilibrium framework to study these questions in the context of a particular bias people s failure to take into account the informational content of other people s actions i apply the framework to a class of games that arises naturally in adverse selection settings and then show that the adverse selection

what you see is all there is news reports and communication are inherently constrained by space time and attention as a result news sources often condition the decision of whether to share a piece of information on the similarity between the signal and the prior belief of the audience which generates a sample selection problem this article experimentally studies how people form beliefs in these contexts in particular the mechanisms behind errors in statistical reasoning i document that a substantial fraction of experimental participants follows a simple what you see is all there is heuristic according to which participants exclusively consider information that is right in front of them and directly use the sample mean to estimate the population mean a series of treatments aimed at identifying mechanisms suggests that for many participants unobserved signals do not even come to mind i provide causal evidence that the frequency of such incorrect mental models is a function of the computational complexity of the decision problem these results point to the context dependence of what comes to mind and the resulting errors in belief updating

on some estimates of an asian savings function abstract recent empirical studies have led many economists to argue that a number of countries in asia could stimulate savings if they permitted higher rates of interest and accepted less foreign aid this paper critically examines the econometric basis of these claims for this purpose the model specifications found in past work are encompassed within a more general model so that they may be replicated and tested as restricted forms

on price recognition and computational complexity in a monopolistic model a single seller of an indivisible good operates in a market with many consumers who differ in their ability to process information the consumers constraints are modeled in two submodels the first in terms of the limits on the number of sets in the partition of the price space and the second in terms of the limits on the complexity of the operation he can use to process a price offer for the construction of the second submodel the tool of a perceptron is borrowed from the parallel computation literature assuming a negative correlation between the seller s cost of supply of the good and the consumer s ability to process information i demonstrate that the heterogeneity of consumer s abilities can be used by the seller to profitably discriminate among them