long term competition in a dynamic game the cold fish war this article presents a model of credible voluntary collective agreements in a dynamic game these agreements are implicit in collections of history dependent threat strategies i consider the strategies in a game of resource exploitation credibility is represented by perfect equilibrium voluntarism requires at least that all behavior be supported by the threat of collapse of the agreement which would return the players to the memoryless equilibrium collective rationality requires that the agreement be robust to the possibility of mutually beneficial renegotiation i analyze the set of agreements meeting each of these restrictions

differential games with nonconvexities and positive spillovers abstract this paper deals with differential games characterized by nonconvexities and increasing returns the objective function of the players is convex in the control variables and nonconvex in the state variables we employ the open loop nash equilibrium solution concept this framework enables us to handle games characterized by positive spillovers and strategic complementarities e g capital accumulation differential games with learning by doing where the knowledge available to a firm is given by the knowledge accumulated by the economy as a whole

capital accumulation games with a non concave production function abstract we consider an economy with a single capital stock that two agents strategically exploit by choosing a consumption profile over an infinite time horizon we analyze two different games and their corresponding equilibria in one game firms are able to pre commit and choose simple time functions as their strategies in the other game agents are assumed to employ markov strategies it turns out that in the case of pre commitment there exists a threshold level of the capital stock such that if the initial stock is above this threshold equilibrium consumption converges to the efficient steady state while if the initial condition is below it the capital stock converges to zero in case of the markov equilibrium there exists a unique interior steady state that is globally stable

reputation and imperfect information abstract a common observation in the informal literature of economics and elsewhere is that is multistage games players may seek early in the game to acquire a reputation for being tough or benevolent or something else but this phenomenon is not observed in some formal game theoretic analyses of finite games such as selten s finitely repeated chain store game or in the finitely repeated prisoners dilemma we reexamine selten s model adding to it a small amount of imperfect or incomplete information about players payoffs and we find that this addition is sufficient to give rise to the reputation effect that one intuitively expects

a dynamic model of conflict and appropriation abstract this paper presents an extension of a static model of economic conflict analyzed by hirshleifer 1991 1995 and skaperdas 1992 to an infinite horizon differential game our aim is to highlight the strategic role of appropriation among a smaller group of agents in an intertemporal context the model yields the conclusion that there exists a unique linear nonlinear markov perfect equilibrium strategy even when strategies are defined over the entire state space we demonstrate that partial cooperation can be seen as a long run response to conflict moreover a decrease in the effectiveness of appropriation the depreciation rate of a common pool stock the rate of time preferences or an increase in the degree of noise improves the degree of partial cooperation and thus welfare in an anarchic society

some unpleasant properties of loglinearized solutions when the nominal rate is zero does fiscal policy have large and qualitatively different effects on the economy when the nominal interest rate is zero an emerging consensus in the new keynesian nk literature is that the answer to this question is yes evidence presented here suggests that the nk model s implications for fiscal policy at the zero bound may not be all that different from its implications for policy away from it for a range of empirically relevant parameterizations employment increases when the labor tax rate is cut and the government purchase multiplier is less than 1 05

occbin a toolkit for solving dynamic models with occasionally binding constraints easily abstract the toolkit adapts a first order perturbation approach and applies it in a piecewise fashion to solve dynamic models with occasionally binding constraints our examples include a real business cycle model with a constraint on the level of investment and a new keynesian model subject to the zero lower bound on nominal interest rates compared with a high quality numerical solution the piecewise linear perturbation method can adequately capture key properties of the models we consider a key advantage of the piecewise linear perturbation method is its applicability to models with a large number of state variables

inflation and output in new keynesian models with a transient interest rate peg a familiar result in the canonical dynamic new keynesian dnk model is that policymakers constrained by the zero bound can improve outcomes by promising to keep rates low after the zero bound is not binding we examine a general class of interest rate pegs in a variety of dnk models standard versions of the model produce counterintuitive reversals where the effect of the interest rate peg can switch from highly expansionary to highly contractionary for modest changes in the length of the interest rate peg this unusual behavior does not arise in sticky information models of the phillips curve

estimating dsge models with zero interest rate policy we propose estimating dsge models in which the central bank fixes the policy rate for an extended period of time and apply our approach to estimate expected durations of the federal reserve s zero interest rate policy since 2009 we find a large increase in expected duration in 2011 with the move to calendar based guidance and a decrease in 2013 with the taper tantrum these changes are identified by the influence of expected duration on output inflation and interest rates at longer maturities the structural model measures the severity of the zero lower bound constraint and the effects of unconventional policy

network effects aftermarkets and the coase conjecture a dynamic markovian approach this paper investigates the expansion of the network of a monopolist firm that produces a durable good and is also involved in the corresponding aftermarket we characterize the markov perfect equilibrium of the continuous time dynamic game played by the monopolist and the forward looking consumers under the assumption that consumers benefit from the subsequent expansion of the network the paper contributes to the theoretical discussion on the validity of the coase conjecture analyzing whether coase s prediction that the monopolist serves the market in a twinkling of an eye remains valid in our setup we conclude that the equilibrium network development may actually be gradual contradicting coase s conjecture we find that a necessary condition for such a result is the existence of aftermarket network effects that accrue at least partly to the monopolist firm

solving linear rational expectations models with predictable structural changes abstract standard solution methods for linear stochastic models with rational expectations presuppose a time invariant structure consequently credible announcements that entail future changes of the structure cannot be handled by standard solution methods this paper develops the solution for linear stochastic rational expectations models in the face of a finite sequence of anticipated structural changes these events encompass anticipated changes to the structural parameters and also anticipated additive shocks we apply the solution to some examples of practical relevance to monetary policy

comparative dynamics in a productive asset oligopoly abstract we build a subgame perfect nash equilibrium of a common property productive asset oligopoly and analyze separately the impact of a change in the implicit growth rate of the asset and a change in the number of firms exploiting the asset we show that the steady state level of asset can be a decreasing function of the asset s implicit growth rate this phenomenon arises when the initial stock of asset is below a certain threshold in the short run we show that firms exploitation rate can be a decreasing function of the implicit growth rate we study the impact of a change in the number of firms that share access to the asset reducing the number of firms can result in the long run in higher industry production in the short run it can result in an increase of the industry s exploitation and a decrease of the level of the asset s stock

e stability vis a vis determinacy in regime switching models abstract this paper examines e stability determinacy and indeterminacy in a general class of regime switching models with lagged endogenous variables using determinacy conditions from cho 2016 2020 our first result extends mccallum 2007 to models with time varying parameters the unique mean square stable equilibrium is e stable if agents have current information and one period ahead decision rules further we address the existence of e stable non fundamental equilibria and find that iteratively e stable equilibria of indeterminate switching models can exist finally we show that indeterminate new keynesian models with persistent recurring interest rate peg regimes admit iteratively e stable equilibria in special cases the iterative e stability condition coincides with the long run taylor principle

stackelberg versus cournot a differential game approach abstract we propose an infinite horizon differential oligopoly game where at each point in time m stackelberg leaders and n m stackelberg followers exploit a common pool renewable resource and sell their harvest in the marketplace at a price that depends on total harvest we derive a feedback generalized stackelberg nash cournot equilibrium a generalization of the feedback stackelberg equilibrium nesting feedback stackelberg and feedback cournot as special cases we proceed with a comparison between the feedback stackelberg and the feedback cournot equilibria and find a number of interesting results in contrast with static oligopoly theory as to the relative efficiency of the two equilibria we show that the cournot equilibrium can be more efficient than the stackelberg equilibrium this holds true in the short run at the steady state and in terms of discounted welfare

on the multiplicity of efficiency inducing tax rules abstract we derive corrective tax rules for a monopoly whose production processes generate emissions that add to a stock of pollution which evolves over time in our model the monopolist maximizes the discounted sum of its instantaneous profits and the government designs a tax rule that corrects for both the externalities associated with pollution and the market power of the monopolist we show that there exists a continuum of time independent tax rules that guide the monopolist to achieve the socially optimum production path

evaluating the macroeconomic effects of the ecb s unconventional monetary policies we quantify the macroeconomic effects of the european central bank s unconventional monetary policies using a dynamic stochastic general equilibrium model which includes a set of shadow interest rates extracted from the yield curve these shadow rates provide unconstrained measures of the overall stance of monetary policy counterfactual analyses show that without unconventional measures the euro area would have suffered i a substantial loss of output since the great recession and ii a period of deflation from mid 2015 to early 2017 specifically year on year inflation and gdp growth would have been on average about 0 61 and 1 09 below their actual levels over the period 2014q1 17q2 respectively

carbon capture and storage and transboundary pollution a differential game approach abstract we study the strategic behavior of two countries facing transboundary co2 pollution under a differential game setting in our model the reduction of co2 concentration occurs through the carbon capture and storage process rather than through the adoption of cleaner technologies furthermore we first provide the explicit short run dynamics for this dynamic game with symmetric open loop and a special markovian nash strategy then we compare these strategies at the games steady states and along some balanced growth paths our results show that if the initial level of co2 is relatively high state dependent emissions reductions can lead to higher overall environmental quality hence feedback strategy leads to less social waste

dynamic resource management under the risk of regime shifts abstract this paper provides a framework through which a dynamic resource management problem with potential regime shifts can be analyzed both in a strategic environment and from a social planner s perspective based on a fairly general model a condition for a precautionary policy is discussed by applying the framework to a common property resource problem with a linear production technology we illustrate how the qualitative as well as quantitative nature of equilibrium is altered due to the possibility of regime shifts in particular when the risk is endogenously affected by the players behavior potential regime shifts can facilitate the precautionary management of resources as long as the resource stock is in good shape as the stock of resource becomes scarce however the precautionary effect vanishes and more aggressive resource exploitation emerges the impacts of irreversibility on the equilibrium behavior are highlighted it is also shown that there can exist a resource depletion trap in which a regime shift once it happens triggers a continuous decline of resource stock no matter which regime materializes in the subsequent periods

policy effectiveness in spatial resource wars a two region model abstract we develop a spatial resource model in continuous time in which two agents strategically exploit a mobile resource in a two region setup to counteract the overexploitation of the resource the tragedy of commons that occurs when players are free to choose where to harvest the regulator can establish a series of spatially structured policies we compare the equilibria in the case of a common resource with those that emerge when the regulator either creates a natural reserve or assigns territorial user rights to the players we show that when technological and preference parameters dictate a low harvesting effort the policies are ineffective in promoting the conservation of the resource and in addition they lead to a lower payoff for at least one of the players conversely in a context of higher harvesting effort the intervention can help to safeguard the resource preventing extinction while also improving the welfare of both players

monetary policy expectations at the zero lower bound we show that conventional dynamic term structure models dtsms estimated on recent u s data severely violate the zero lower bound zlb on nominal interest rates and deliver poor forecasts of future short rates in contrast shadow rate dtsms account for the zlb by construction capture the resulting distributional asymmetry of future short rates and achieve good forecast performance these models provide more accurate estimates of the most likely path for future monetary policy including the timing of policy liftoff from the zlb and the pace of subsequent policy tightening we also demonstrate the benefits of including macroeconomic factors in a shadow rate dtsm when yields are constrained near the zlb

investment shocks and business cycles abstract the origins of business cycles are still controversial among macroeconomists this paper contributes to this debate by studying the driving forces of fluctuations in an estimated new neoclassical synthesis model of the u s economy in this model most of the variability of output and hours at business cycle frequencies is due to shocks to the marginal efficiency of investment imperfect competition and to a lesser extent technological frictions are the key to their transmission although labor supply shocks explain a large fraction of the fluctuations in hours at very low frequencies they are irrelevant over the business cycle this finding is important because the microfoundations of these disturbances are widely regarded as unappealing

duopoly can be more anti competitive than monopoly abstract we prove two results on feedback equilibria under dynamic renewable resource duopoly the linear feedback output is smallest which sharply contrasts to the existing literature where it is largest moreover prices in two feedback equilibria are higher than under monopoly

non linear strategies in a linear quadratic differential game abstract we study non linear markov perfect equilibria in a two agent linear quadratic differential game in contrast to the literature owing to tsutsui and mino 1990 nonlinear strategies in dynamic duopolistic competition with sticky prices journal of economic theory 52 136 161 we do not associate endogenous subsets of the state space with candidate solutions instead we use the catching up optimality criterion to address the possibility of infinitely valued value functions applying sufficiency conditions for existence based on those in dockner et al 2000 differential games in economics and management science cambridge university press cambridge yields the familiar linear mpe and a condition under which a continuum of non linear mpes exists these include as their limit a previously unreported piecewise linear mpe the condition relaxes with increasing patience allowing more efficient steady states thus suggesting a folk theorem for differential games as the lower state and control bounds go to the non linear strategies are eliminated

climate contracts a game of emissions investments negotiations and renegotiations the paper presents a dynamic game where players can contribute to a public bad invest in technologies and write incomplete contracts despite the n 1 stocks in the model the analysis is tractable and the symmetric markov perfect equilibrium unique the framework helps to analyze emissions investments and international environmental agreements if only the emission levels are contractible then investments are suboptimally small if the contract is short term or close to its expiration date to encourage investments the optimal contract is more ambitious if it is short term and it is tougher to satisfy close to its expiration date and for countries with small investment costs if renegotiation is possible such an incomplete contract implements the rst best the results have important lessons for how to design a climate treaty

nonlinear adventures at the zero lower bound abstract in this paper we argue for the importance of explicitly considering nonlinearities in analyzing the behavior of the new keynesian model with a zero lower bound zlb of the nominal interest rate to show this we report how the decision rules and the equilibrium dynamics of the model are substantially affected by the nonlinear features brought about by the zlb we also illustrate a tension between the length of a spell at the zlb and the drop in consumption there

feedback equilibria in a dynamic renewable resource oligopoly pre emption voracity and exhaustion abstract we revisit a recent literature on productive asset exploitation describing a differential oligopoly game of resource extraction under static linear feedback and nonlinear feedback strategies where we explicitly allow for the possibility of resource exhaustion we show that i feedback rules entail resource exhaustion for a finite number of firms and ii feedback strategies are more aggressive than static ones as long as the resource stock is large enough in accordance with the acquired view based on the traditional pre emption argument associated with feedback information

optimal monetary policy at the zero interest rate bound what should a central bank do when faced with a weak aggregate demand even after reducing the short term nominal interest rate to zero to address this question we solve a central bank s intertemporal loss minimization problem in which the non negativity constraint on nominal interest rates is explicitly considered we find that the optimal path is characterized by policy inertia in the sense that a zero interest rate policy should be continued for a while even after the natural rate of interest returns to a positive level by making such a commitment the central bank is able to achieve higher expected inflation lower long term nominal interest rates and a weaker domestic currency in the adverse periods when the natural rate of interest significantly deviates from a steady state level

consumer surplus enhancing cooperation in a natural resource oligopoly abstract in this study we use a differential game to illustrate that cooperation among oligopolists selling a common pool renewable resource may lead not only to higher industrial output consumer surplus and resource stock in the stationary equilibrium but also a greater discounted sum of consumer surplus a priori this finding is not straightforward an increase in the coefficient of cooperation causes industry output to first decrease and then increase over time thus making consumers worse off in the short run and better off in the long run this study establishes the conditions under which the long run effects outweigh the short run effects of cooperation leading to an increase in the discounted sum of consumer surplus our analysis suggests that in some cases conservation cartels should be promoted on the basis of not only resource conservation but also efficiency

a structural decomposition of the us yield curve abstract by expanding the macro part of macro finance models historical fluctuations in us bond yields turn out to be largely consistent with the rational expectations hypothesis we estimate a medium scale macro finance dsge model of the term structure to establish this our finding contrasts with existing macro finance models and suggests that their small scale or non structural perspective on the macroeconomy mutes expectations thereby underestimating the expectations hypothesis potential out of sample forecasts are competitive with more flexible term structure models given the empirical validation we interpret various episodes through the lens of the model and investigate which structural shocks cause the yield curve to contain information about future growth

reputation and equilibrium selection in games with a patient player a single long run player plays a simultaneous move stage game against a sequence of opponents who play only once but observe all previous play let the stackelberg strategy be the pure strategy to which the long run player would most like to commit himself if there is positive prior probability that the long run player will always play the stackelberg strategy then his payoff in any nash equilibrium exceeds a bound that converges to the stackelberg payoff as his discount factor approaches one when the stage game is not simultaneous move this result must be modified to account for the possibility that distinct strategies of the long run player are observationally equivalent

existence and properties of equilibria for a dynamic game on productive assets abstract we consider a model in which two agents share access to the same stock of a productive asset and study the implications of non cooperative consumption behavior over time under standard assumptions on the production function we construct infinitely many nash equilibria all of which consist of stationary markovian strategies these equilibria result in overconsumption so that the uniquely determined long run asset stock is too low as compared to the cooperative solution however in the limit as the discount rate becomes sufficiently small the stead states generated by the markovian nash equilibria converge to the efficient steady state journal of economic literatureclassification numbers c73 o41 q22

on the markovian efficiency of bertrand and cournot equilibria we characterize and compare closed loop feedback price and quantity strategies within a full fledged dynamic model of oligopolistic competition in which production requires exploitation of a renewable productive asset unlike previous papers on the strategic exploitation of productive assets we allow for imperfect product substitutability which enables us to deal with price competition we show that the traditional result that the bertrand equilibrium is more efficient than the cournot equilibrium does not necessarily hold in a markovian environment either in the short run or at the stationary equilibrium or using the discounted sum of welfare as a criterion for relative efficiency

oligopoly extraction of a common property natural resource the importance of the period of commitment in dynamic games the theory of noncooperative dynamic games has provided an extremely powerful framework for studying many of the classic questions in industrial organization for example questions about resource extraction advertising research and development investment in new capacity and barriers to entry where interactions over time among few firms are involved however an important methodological issue arises when economic competition over time is modeled as a dynamic game the issue is the appropriate formulation of the players strategy spaces

competition on many fronts a stackelberg signaling equilibrium an economic agent the incumbent is operating in many environments at the same time these may be locations markets or specific activities he is informed of the particular conditions relevant to each situation his action in each case is observable by another agent the entrant who does not have the private information because the incumbent is in operation in many environments simultaneously the entrant has the ability to discern the exact statistical relationship between the incumbent s action and information and we assume that he cannot commit not to draw this inference at each location the entrant must choose one of two actions which we call attack or no attack this paper concerns the interplay between these sets of decisions we characterize the optimal actions of the incumbent under the assumption that he can commit to his decisions and thus that he will behave as a stackelberg leader by manipulating the inferences drawn by the entrant the solution obtained is compared with and contrasted to the bayesian perfect equilibria of a game where both players move simultaneously that game is a more appropriate model of the no commitment case thus the value of the possibility of commitment and manipulation of the entrant s beliefs is assessed some applications are discussed

unilateral production restrictions in a dynamic duopoly abstract this paper examines a dynamic game of exploitation of a productive asset by a duopoly a closed loop nash equilibrium of the game is constructed and used to analyze the effects of a unilateral production restriction surprisingly such unilateral action may result in a decrease of the long run asset s stock we also exhibit production restrictions that can result simultaneously in an increase of the asset s stock and the long run profits of the firm that is being imposed the production restriction moreover a unilateral decrease of the production of one firm can induce its rival to also decrease its production

oligopoly exploitation of a private property productive asset abstract in this paper we build a closed loop nash equilibrium of a private property productive asset oligopoly we compare and contrast private with common property in terms of exploitation rates and social welfare and provide a comparative dynamic analysis with respect to the number of firms in the industry contrary to previous studies on oligopolistic exploitation of productive assets before exploitation begins the resource is parcelled out each firm privately owns and manages the assigned parcel over the entire planning horizon compared with the common property regime we find a new set of results both in the short and in the long run as for social welfare we provide conditions on the implicit growth rate and the initial asset stock under which the socially optimal allocation of the resource implies a natural monopoly