the solution to the tullock rent seeking game when r 2 mixed strategy equilibria and mean dissipation rates in tullock s rent seeking model the probability a player wins the game depends on expenditures raised to the power r we show that a symmetric mixed strategy nash equilibrium exists when r 2 and that overdissipation of rents does not arise in any nash equilibrium we derive a tight lower bound on the level of rent dissipation that arises in a symmetric equilibrium when the strategy space is discrete and show that full rent dissipation occurs when the strategy space is continuous our results are shown to be consistent with recent experimental evidence on the dissipation of rents

the chaotic duopolists revisited the adjustment process of three oligopolists is studied under cournot and stackelberg action it is demonstrated that with an iso elastic demand function and constant marginal costs the system can result in periodic or in chaotic behaviour in particular the case with two identical and one different oligopolists is focused which turns into a virtual duopoly though displaying a wider set of bifurcations than can occur in genuine duopoly

global analysis of an expectations augmented evolutionary dynamics we consider a deterministic evolutionary model where players form expectations about future play players are not fully rational and have expectations that change over time in response to current payoffs and feedback from the past we provide a complete characterization of the qualitative dynamics so induced for a two strategy population game and relate our findings to standard evolutionary dynamics and equilibrium selection when agents have rational forward looking expectations

farsighted coalitional stability abstract i define the largest consistent set a solution concept which applies to situations in which coalitions freely form but cannot make binding contracts act publicly and are fully farsighted in that a coalition considers the possibility that once it acts another coalition might react a third coalition might in turn react and so on without limit i establish weak nonemptiness conditions and apply it to strategic and coalitional form games and majority rule voting i argue that it improves on the von neumann morgenstern stable set as it is usually defined but is consistent with a generalization of the stable set as in the theory of social situations journal of economic literature classification numbers c70 c71

improved methods for predicting property prices in hazard prone dynamic markets property prices are affected by changing market conditions incomes and preferences of people price trends in natural hazard zones may shift significantly and abruptly after a disaster signalling structural systemic changes in property markets it challenges accurate market assessments of property prices and capital at risk after major disasters a rigorous prediction of property prices in this case should ideally be done based only on the most recent sales which are likely to form a rather small dataset hedonic analysis has been long used to understand how various factors contribute to the housing price formation yet the robustness of its assessment is undermined when the analysis needs to be performed on relatively small samples the purpose of this study is to suggest a model that can be widely applicable and quickly calibrated in a changing environment we systematically study four statistical models starting from a typical standard hedonic function and gradually changing its functional specification by reducing the hedonic analysis to some basic property characteristics and applying kriging to control for neighbourhood effects across different sample sizes we find that the latter performs consistently better in the out of sample predictions than other traditional price prediction methods we present the specific improvements to the traditional spatial hedonic model that enhance the model s prediction accuracy the improved model can be used to monitor price changes in risk prone areas accounting for changes in flood risk and at the same time controlling for autonomous market responses to flood risk

dynamic complexity in duopoly games abstract we discuss the occurrence of periodic and chaotic phenomena in infinite horizon duopoly games where firms maximize their discounted sum of profits and use markov perfect equilibrium strategies in the alternating case their corresponding actions are then constrained orbits of a map similar to a cournot t tonnement we show that any behavior is possible for small discount factors and that one obtains the cournot t tonnement as the discount factor goes to zero in the simultaneous case we show by mean of an example that many cournot t tonnements can be viewed as markov perfect equilibria of an infinite horizon game and that one obtains the nash equilibrium of the static game as the discount parameter goes to zero we are thus led to study in detail the dynamical properties of a cournot t tonnement

the existence of equilibrium in discontinuous economic games ii applications in part i of this study we established two existence theorems for mixed strategy equilibrium in games with discontinuous payoff functions see theorems 4 4 and 5 5 in dasgupta and maskin 1986 hereafter d m 1986 in this second part we use the second of these two theorems to prove the existence of mixed strategy equilibrium in some wellknown discontinuous economic games that fail to have pure strategy equilibria the models we analyse are the bertrand edgeworth example of price setting duopolists with capacity constraints see section 2 2 price competition among firms producing differentiated products hotelling 1929 and d aspremont gabszewicz and thisse 1979 see section 2 3 spatial competition eaton and lipsey 1975 and shaked 1975 see section 3 and models of market dependent information rothschild and stiglitz 1976 and wilson 1977 section 4 the paper concludes section 5 with a classification of these models

analysis of global bifurcations in a market share attraction model in this paper we demonstrate how the global dynamics of an economic model can be analyzed in particular as an application we consider a market share attraction model widely used in the analysis of interbrand competition in marketing theory we analyze the local and global dynamic properties of the resulting two dimensional noninvertible dynamical system in discrete time the main result of this paper is given by the study of some global bifurcations that change the structure of the attractors and their basins these bifurcations are investigated by the use of critical curves a powerful tool for the analysis of the global properties of noninvertible two dimensional maps 2000 elsevier science b v all rights reserved jel classixcation e32 m30

do people play nash equilibrium lessons from evolutionary game theory evolutionary game theory provides an answer to two of the central questions in economic modeling when is it reasonable to assume that people are rational and when is it reasonable to assume that behavior is part of a nash equilibrium and if it is reasonable which equilibrium the traditional answers are not compelling and much of evolutionary modeling is motivated by the need for a better answer evolutionary game theory suggests that in a range of settings agents do eventually play a nash equilibrium moreover evolutionary modeling has shed light on the relative plausibility of different nash equilibria

complicated endogenous business cycles under gross substitutability abstract in this paper we investigate the global behaviour of the output equilibrium time paths in a two dimensional overlapping generations model with productive investment and capital accumulation where agents behave rationally and markets are competitive we show that equilibrium time paths can converge to complicated chaotic attractors as well as periodic attractors when the substitution effect dominates the income effect everywhere the occurrence of complicated equilibrium paths is guaranteed by homoclinic intersections of the stable and unstable manifolds of the autarkic steady state journal of economic literature classificiation number e32

selection dynamics asymptotic stability and adaptive behavior selection dynamics are often used to distinguish stable and unstable equilibria this is particularly useful when multiple equilibria prevent a priori comparative static analysis this paper reports an experiment designed to compare the accuracy of the myopic best response dynamic and an inertial selection dynamic the inertial selection dynamic makes more accurate predictions about the observed mutual best response outcomes

investment confidence corporate debt and income fluctuations in this paper we present a macroeconomic model with new keynesian features which endogenously generates dynamic paths of income and the stock of corporate debt of a cyclic and chaotic nature from the market clearing condition on goods and money markets we derive the dynamic paths of income and corporate debt whose stability properties depend upon the propensity to invest out of the flow of internally generated funds which in turn is a positive function of income if it is relatively low the dynamic paths on income and corporate debt converge to their steady state long run values when the propensity to invest is neither too low nor too high the system can exhibit either bounded cycles or chaotic dynamics finally if it exceeds a critical upper value an explosive growth of debt occurs and a financial crisis is likely to ensue

games for cautious players the equilibrium in secure strategies abstract a non cooperative solution the equilibrium in secure strategies einss is defined as an extension of the nash equilibrium in pure strategies and is meant to solve games where players are cautious i e looking for secure positions and avoiding threats this concept abstracts and unifies ad hoc solutions already formulated in various applied economic games that have been discussed extensively in the literature a general existence theorem is provided and then applied to the price setting game in the hotelling location model to tullock s rent seeking contests and to bertrand edgeworth duopoly finally competition in the insurance market game is re examined and the rothschild stiglitz wilson contract is shown to be an einss even when the nash equilibrium breaks down

the existence of equilibrium in discontinuous economic games i theory the article presents information about the existence of equilibrium in discontinuous economic games in this paper and its sequel presents study the existence of nash equilibrium in games where agents payoff functions are discontinuous the enquiry is motivated by a number of recent studies that have uncovered serious existence problems in seemingly innocuous economic games in the sequel to this paper authors have explained the utility function in the economic games referred to earlier are neither continuous nor quasi concave however they demonstrate that the payoff functions in mildly modified versions of these constructs exhibit two weaker forms of continuity which together with the requirement of quasi concavity suffice for the existence of an equilibrium from this one may conclude that at least in the modified versions of these models discontinuities in the payoff functions are not the real source of the problem rather it is the failure of the payoff functions to the quasi concave which is responsible for the non existence of equilibrium these observations bear on the existence of nash equilibrium in pure strategies

solution of the hotelling s game in secure strategies abstract we show that the price setting subgame in the classic hotelling s model 1929 with the linear transport costs has the unique equilibrium solution for all location pairs under the assumption that duopolists secure themselves against being driven out of the market by undercutting in contrast to the modified zero conjectural variation approach of eaton and lipsey 1978 we assume that the players consider the threat of pressing out of the market as a real possibility we employ the concept of equilibrium in secure strategies einss as the generalization of the nash equilibrium the einss coincides with the nash equilibrium when nash equilibrium exists and postulates the incentive of players to maximize their profit under the condition of security against the actions of other players

the stability of the cournot oligopoly model a reassessment abstract the stability properties of the cournot oligopoly model are examined for the continuous adjustment process sufficient conditions for instability are established which are shown to be of significance when the number of firms n is small local and global stability are shown under appropriate conditions which for global stability include the restriction n 5 the proof of global stability corrects a well known proof by f hahn rev econ stud 29 1962 329 331 results for the discrete time adjustment process are reported and the restrictiveness of the model s assumptions are discussed

learning to play cournot duopoly strategies abstract the paper reports results from experiments designed to determine whether subjects can learn to play cournot duopoly strategies and whether their out of equilibrium play is consistent with the predictions of learning models the experiments include duopolies with constant and with decreasing marginal costs and with theoretically stable and unstable equilibria after a few periods subjects do play stable interior equilibria but they do not play stable boundary equilibria nor unstable interior equilibria subjects out of equilibrium play is inconsistent with the predictions of the learning models

holding idle capacity to deter entry in this journal dixit i980 carefully analysed the extent to which an established firm facing a prospective entrant might make an investment in capacity beyond that which is optimal for its pre entry output in his model both the established firm and prospective entrants understand that a quantity setting nash equilibrium would be established in any post entry game dixit showed that spence i977 had studied an imperfect equilibrium that is an equilibrium that depended upon a threat that was not credible to obtain his result that firms might hold excess capacity to deter entry in a perfect equilibrium a firm would not wish to install capacity that would be left idle if entry did not occur dixit s conclusion however depends on his assumption that each firm s marginal revenue is always decreasing in the other s output this is quite a restrictive assumption for example it is never satisfied in the relevant range for economists second favourite demand curve constant elasticity demand the basic point is unchanged if the firms anticipate price competition with differentiated products rather thanquantity competition in any post entry game under quite plausible conditions rational firms facing rational potential entrants may install capacity that will certainly be left idle we are thus able to rehabilitate spence s original proposition in a perfect equilibrium setting

changes in implicit flood risk premiums empirical evidence from the housing market abstract hedonic valuation models have shown that sales prices can capitalize property risk factors such as flood zone properties facing lower risk sell at a premium all else being equal previous research has indicated that price differentials reflecting risk of flooding become much larger in the wake of a storm we re examine these findings for pitt county north carolina using multiple storm events within a difference in differences framework and we compare flood zone price differentials for a more recent sample of property sales prior to hurricane fran in 1996 we detect no market risk premium for the presence in a flood zone but we find significant price differentials after major flooding events amounting to a 5 7 decrease after hurricane fran and 8 8 decrease after hurricane floyd results from a separate model that examines more recent data covering a period without significant storm related flood impacts indicate a significant risk premium ranging between 6 0 and 20 2 for homes sold in the flood zone but this effect is diminishing over time essentially disappearing about 5 or 6 years after hurricane floyd the lack of a persistent effect suggests that buyers and sellers risk perceptions may change with the prevalence of hazard events and that homebuyers are unaware of flood risks and insurance requirements when bidding on properties

indeterminacy of equilibria in a hyperinflationary world experimental evidence the authors design and study an olg experimental economy where the government finances a fixed real deficit through seigniorage the economy has continua of nonstationary rational expectations equilibria and two stationary rational expectations equilibria the authors do not observe nonstationary rational expectations paths observed paths tend to converge close to or somewhat below the low inflation stationary state the adaptive learning hypothesis is consistent with the data in selecting the low inflation stationary state rational expectations equilibrium as a long run stationary equilibrium nevertheless simple adaptive learning models do not capture the market uncertainty or the biases observed in the data copyright 1993 by the econometric society

on the existence of pure and mixed strategy nash equilibria in discontinuous games a game is better reply secure if for every nonequilibrium strategy x and every payoff vector limit u resulting from strategies approaching x some player i has a strategy yielding a payoff strictly above u i even if the others deviate slightly from x if strategy spaces are compact and convex payoffs are quasiconcave in the owner s strategy and the game is better reply secure then a pure strategy nash equilibrium exists better reply security holds in many economic games it also permits new results on the existence of symmetric and mixed strategy nash equilibria

flooding risk and housing values an economic assessment of environmental hazard abstract climate change the boom and bust cycles of rivers and altered water resource management practice have caused significant changes in the spatial distribution of the risk of flooding hedonic pricing studies predominantly for the us have assessed the spatial incidence of risk and the associated implicit price of flood risk using these implicit price estimates and their associated standard errors we perform a meta analysis and find that an increase in the probability of flood risk of 0 01 in a year is associated to a difference in transaction price of an otherwise similar house of 0 6 the actual occurrence of a flooding event or increased stringency in disclosure rules causes ex ante prices to differ from ex post prices but these effects are small the marginal willingness to pay for reduced risk exposure has increased over time and it is slightly lower for areas with a higher per capita income we show that obfuscating amenity effects and risk exposure associated with proximity to water causes systematic bias in the implicit price of flood risk

equilibrium selection in a nonlinear duopoly game with adaptive expectations abstract we analyze a nonlinear discrete time cournot duopoly game where players have adaptive expectations the evolution of expected outputs over time is generated by the iteration of a noninvertible two dimensional map the long run behavior is characterized by multistability that is the presence of coexisting stable consistent beliefs which correspond to nash equilibria in the quantity space hence a problem of equilibrium selection arises and the long run outcome strongly depends on the choice of the players initial beliefs we analyze the basins of attraction and their qualitative changes as the model parameters vary we illustrate that the basins might be nonconnected sets and reveal the mechanism which is responsible for this often neglected kind of complexity the analysis of the global bifurcations which cause qualitative changes in the topological structure of the basins is carried out by the method of critical curves

on the consistency of backward looking expectations the case of the cobweb in dynamic models of economic fluctuations backward looking expectations with systematic forecasting errors are inconsistent with rational behaviour in non linear dynamic models exhibiting seemingly unpredictable chaotic fluctuations however simple habitual rule of thumb backward looking expectation rules may yield non zero but nevertheless non systematic forecasting errors in a chaotic model expectational forecasting errors may have zero autocorrelations at all lags even for rational agents patterns in these forecasting errors may be very difficult to detect especially in the presence of small noise backward looking expectations are then not necessarily inconsistent with rational behaviour we investigate whether simple expectation schemes such as naive or adaptive expectations can be consistent with rational behaviour in the simplest of all non linear dynamic economic models the non linear cobweb model

cournot competition organization and learning abstract we model firms output decisions in a repeated duopoly framework focusing on three interrelated issues 1 the role of learning in the adjustment process toward equilibrium 2 the role of organizational structure in the firm s decision making and 3 the role of changing environmental conditions on learning and output decisions we characterize the firm as a type of artificial neural network which must estimate its optimal output decision based on signals it receives from the economic environment which influences the demand function via simulation analysis we show 1 how organizations learn to estimate the optimal output over time as a function of the environmental dynamics 2 which networks are optimal for each level of environmental complexity and 3 the equilibrium industry structure