dynamic oligopoly with incomplete information we consider learning and signalling in a dynamic cournot oligopoly where firms have private information about their production costs and only observe the market price which is subject to unobservable demand shocks an equilibrium is markov if play depends on the history only through the firms beliefs about costs and calendar time we characterize symmetric linear markov equilibria as solutions to a boundary value problem in every such equilibrium given a long enough horizon play converges to the static complete information outcome for the realized costs but each firm only learns its competitors average cost the weights assigned to costs and beliefs under the equilibrium strategies are non monotone over time we explain this by decomposing incentives into signalling and learning and discuss implications for prices quantities and welfare

efficient mechanisms for bilateral trading we consider bargaining problems between one buyer and one seller for a single object the seller s valuation and the buyer s valuation for the object are assumed to be independent random variables and each individual s valuation is unknown to the other we characterize the set of allocation mechanisms that are bayesian incentive compatible and individually rational and show the general impossibility of ex post efficient mechanisms without outside subsidies for a wide class of problems we show how to compute mechanisms that maximize expected total gains from trade and mechanisms that can maximize a broker s expected profit journal of economic literature classification number 026

cooperation dynamics in repeated games of adverse selection abstract we study cooperation dynamics in repeated games with markovian private information after any history signaling reveals information that helps players coordinate their future actions but also makes the problem of coordinating current actions harder in equilibrium players may play aggressive or uncooperative actions that signal private information and partners tolerate a certain number of such actions we discuss several applications of our results we explain the cycles of cooperation and conflict observed in trench warfare during world war i show that price leadership and unilateral price cuts can be part of an optimal signaling equilibrium in a repeated bertrand game with incomplete information and show that communication between cartel members may be socially efficient in a repeated cournot game finally we show that the welfare losses disappear as the persistence of the process of types increases and the interest rate goes to zero

a theory of contracts with limited enforcement we present a theory of contracts under costly enforcement in the context of a dynamic relationship between an uninformed buyer and a seller who is privately informed on his persistent cost at the outset public enforcement relies on remedies for breach private enforcement comes from severing relationships we first characterize aggregate enforcement constraints ensuring that trading partners do not breach contracts unduly whether a long term contract is enforceable does not depend on the distribution of penalties for breach between the buyer and the seller while under complete information the optimal contract would remain stationary non stationarity might arise under asymmetric information enforcement constraints are time dependent and easier to satisfy as time passes indeed a high cost seller may be tempted to trade high volumes at high prices at the beginning of the relationship before breaching the contract later on yet such take the money and run strategy becomes less attractive as time passes and can be prevented with backloaded payments the optimal contract thus goes through two different phases first quantities and prices increase at the inception of the relationship later on the contract looks more stationary the public and private sides of enforcement plays different roles in determining the length of the earlier phase of contracting long run screening distortions encapsulate the quality of enforcement offering de facto a link between the quality of the legal system and contractual performances

default settlement and signalling lending resumption in a reputational model of sovereign debt this paper develops a simple model of sovereign debt in which defaulting nations are excluded from capital markets and regain access by making partial repayments this implication of the model is consistent with the historical evidence that defaulting countries return to international loan markets soon after a settlement but after varying periods of exclusion copyright 1995 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

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

on communication and collusion we study the role of communication within a cartel our analysis is carried out in stigler s 1964 model of repeated oligopoly with secret price cuts firms observe neither the prices nor the sales of their rivals for a xed discount factor we identify conditions under which there are equilibria with cheap talk that result in near perfect collusion whereas all equilibria without such communication are bounded away from this outcome in our model communication improves monitoring and leads to higher prices and pro ts jel classi cation c73 d43

bargaining and reputation the paper develops a reputation based theory of bargaining the idea is to investigate and highlight the influence of bargaining postures on bargaining outcomes a complete information bargaining model a la rubinstein is amended to accommodate irrational types who are obstinate and indeed for tractability assumed to be completely inflexible in their offers and demands a strong independence of procedures result is derived after initial postures have been adopted the bargaining outcome is independent of the fine details of the bargaining protocol so long as both players have the opportunity to make offers frequently the latter analysis yields a unique continuous time limit with a war of attrition structure in the continuous time game equilibrium is unique and entails delay consequently inefficiency the equilibrium outcome reflects the combined influence of the rates of time preference of the players and the ex ante probabilities of different irrational types as the probability of irrationality goes to zero delay and inefficiency disappear furthermore if there is a rich set of types for both agents the limit equilibrium payoffs are inversely proportional to their rates of time preference

collusion and price rigidity we consider an in nitely repeated bertrand game in which prices are publicly observed and each rm receives a privately observed i i d cost shock in each period we focus on symmetric perfect public equilibria sppe wherein any punishments are borne equally by all rms we identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each rm is strictly increasing in its cost level such fully sorting schemes offer efficiency bene ts as they ensure that the lowest cost rm makes the current sale but they also imply an informational cost distorted pricing and or equilibrium path price wars since a higher cost rm must be deterred from mimicking a lower cost rm by charging a lower price a rigid pricing scheme where a rm s collusive price is independent of its current cost position sacri ces efficiency bene ts but also diminishes the informational cost for a wide range of settings the optimal symmetric collusive scheme requires i the absence of equilibrium path price wars and ii a rigid price if rms are sufficiently impatient however the rigid pricing scheme cannot be enforced and the collusive price of lower cost rms may be distorted downward in order to diminish the incentive to cheat when the model is modi ed to include i i d public demand shocks the downward pricing distortion that accompanies a rm s lower cost realization may occur only when current demand is high

collusion with almost no information we analyze noncooperative collusion in an infinitely repeated bertrand game where each of the n firms receives a privately observed i i d cost shock in each period and firms only and privately observe whether they have won the unit mass of consumers no other information is available and no communication is allowed we prove that there exist equilibria in private strategies approximating first best profits when firms are sufficiently patient in particular productive efficiency obtains in the limit

tacit collusion in repeated auctions abstract this paper considers the question of tacit collusion in repeated auctions with independent private values and with limited public monitoring mcafee and mcmillan show that the extent of collusion is tied to the availability of transfers monetary transfers allow cartels to extract full surplus a folk theorem proved by fudenberg et al econometrica 62 1994 997 1039 shows that transfers of future payoffs are almost as good if players are patient and communicate before auctions we ask how the scope of collusion is affected if players dispense with explicit communication and their monitoring is limited collusion better than bid rotation is still feasible but full surplus cannot be extracted this constraint becomes less severe with more players and large cartels can become asymptotically efficient even with very limited monitoring

optimal multiperiod contracts and the gain from enduring relationships under private information informational asymmetries can play a key role in explaining the existence and nature of multiperiod contracts in an illustrative risk sharing model even relatively short two period contracts can be mutually beneficial if there is private information though one period contracts suffice otherwise further contracts which are pareto optimal relative to the environment and the information structure are defined and partially characterized an example illustrates how otherwise inefficient intertemporal tie ins can be used optimally to mitigate incentive problems the obvious borrowing lending schemes are not private information pareto optimal in these period by period actions are not sufficiently constrained discounting affects the form of the optimal contract but none of these qualitative conclusions

relational incentive contracts standard incentive theory models provide a rich framework for studying informational problems but assume that contracts can be perfectly enforced this paper studies the design of self enforced relational contracts i show that optimal contracts often can take a simple stationary form but that self enforcement restricts promised compensation and affects incentive provision with hidden information it may be optimal for an agent to supply the same inefficient effort regardless of cost conditions with moral hazard optimal contracts involve just two levels of compensation this is true even if performance measures are subjective in which case optimal contracts terminate following poor performance jel c73 d82 l14

truthful equilibria in dynamic bayesian games this paper characterizes an equilibrium payoff subset for markovian games with private information as discounting vanishes monitoring might be imperfect transitions depend on actions types correlated or not values private or interdependent it focuses on equilibria in which players report their information truthfully this characterization generalizes those for repeated games and reduces to a collection of one shot bayesian games with transfers with independent private values the restriction to truthful equilibria is shown to be without loss except for individual rationality in the case of correlated types results from static mechanism design can be applied resulting in a folk theorem

the folk theorem with imperfect public information the authors study repeated games in which players observe a public outcome that imperfectly signals the actions played they provide conditions guaranteeing that any feasible individually rational payoff vector of the stage game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting the central condition requires that there exist action profiles with the property that for any two players no two deviations one by either player give rise to the same probability distribution over public outcomes the results apply to principal agent partnership oligopoly and mechanism design models and to one shot games with transferable utilities copyright 1994 by the econometric society

self enforcing voting in international organizations some international organizations are governed by unanimity rule some others by a majority system still others have moved from one system to the other over time the existing voting models have a difficult time explaining the observed variation in governance mode and in particular the widespread occurrence of the unanimity system we present a model whose main departure from standard voting models is that there is no external enforcement mechanism each country is sovereign and cannot be forced to follow the collective decision or in other words the voting system must be self enforcing the model yields unanimity as the optimal system for a wide range of parameters and delivers rich predictions on the variation in the mode of governance both across organizations and over time we thank james anderson matt jackson francois maniquet guido tabellini and jean tirole for very helpful comments arnaud costinot provided excellent research assistance we also bene

a sequential concession game with asymmetric information the essence of the situation to be studied here is this two players are involved in a conflict that can be resolved in only two possible ways each player favors a different outcome during the bargaining phase which lasts until some finite time to each player has the option to concede if none concedes the game ends at time t in a way that is known to one of the players from the beginning of the game the other player is uncertain about the outcome time is valuable but each player prefers to receive his favored outcome at m than to concede immediately thus the game analyzed here is characterized by the asymmetric information about the outcome at the end point i e at time to whereas one player is perfectly informed about the possible outcome the other is compelled to deduce the information from the actions of his informed opponent the latter in turn can try to exploit his initial advantage by manipulating the flow of information for example the informed player may adopt a tough stance in order to create the impression that he is not afraid of forcing the resolution of the conflict at to and thereby builds his reputation at the same time the uninformed player by not conceding can test the opponent s resolve this brief description suggests that the problem analyzed here is a variant of the game of attrition 2 however our problem differs from the standard game of attrition in two respects first we formulate the game in discrete time which has important analytic consequences these are fully developed in hendricks and wilson 1985 second and more important perhaps we study

an efficient dynamic mechanism this paper constructs an efficient budget balanced bayesian incentive compatible mechanism for a general dynamic environment with quasilinear payoffs in which agents observe private information and decisions are made over countably many periods first under the assumption of private values other agents private information does not directly affect an agent s payoffs we construct an efficient ex post incentive compatible mechanism which is not budget balanced second under the assumption of independent types the distribution of each agent s private information is not directly affected by other agents private information we show how the budget can be balanced without compromising agents incentives finally we show that the mechanism can be made self enforcing when agents are sufficiently patient and the induced stochastic process over types is an ergodic finite markov chain publication abstract

efficiency in games with markovian private information we study repeated bayesian games with communication and observable actions in which the players privately known payoffs evolve according to an irreducible markov chain whose transitions are independent across players our main result implies that generically any pareto efficient payoff vector above a stationary minmax value can be approximated arbitrarily closely in a perfect bayesian equilibrium as the discount factor goes to 1 as an intermediate step we construct an approximately efficient dynamic mechanism for long finite horizons without assuming transferable utility publication abstract

overcoming incentive constraints by linking decisions consider a bayesian collective decision problem in which the preferences of agents are private information we provide a general demonstration that the utility costs associated with incentive constraints become negligible when the decision problem is linked with a large number of independent copies of itself this is established by defining a mechanism in which agents must budget their representations of preferences so that the frequency of preferences across problems mirrors the underlying distribution of preferences and then arguing that agents incentives are to satisfy their budget by being as truthful as possible we also show that all equilibria of the linking mechanisms converge to the target utility levels the mechanisms do not require transferable utility or interpersonal comparisons of utility and are immune to manipulations by coalitions

predation reputation and entry deterrence abstract economists often argue that predatory practices are irrational since there exist cheaper or more certain means to gain or maintain a monopoly our gametheoretic equilibrium analysis suggests that if a firm is threatened by several potential entrants then predation may be rational against early entrants even if it is costly when viewed in isolation because it yields a reputation which deters other entrants asymmetric information plays a crucial role in our analysis since it provides the rationale for entrants to base their expectations of the firm s future behavior on its past actions the analysis also suggests methods to treat general reputational phenomena

games of perfect information predatory pricing and the chain store paradox the thesis of this paper is that finite noncooperative games possessing both complete and perfect information ought to be treated like one player decision problems that is players ought to assign at every move subjective probabilities to every subsequent choice in the game and ought to make decisions via backward induction this view is in contrast with the gametheoretic approach of nash equilibrium after expanding on this view for games in the abstract in sections 2 and 3 attention is turned in section 4 to an example due to reinhard selten called the chain store paradox which possesses the flavor of a situation involving a predatory pricing monopolist it is argued that for the chain store game the decision analytic approach leads under certain assumptions to more realistic outcomes than the standard nash equilibrium approach

dynamic games with hidden actions and hidden states abstract we consider a class of dynamic games in which each player s actions are unobservable to the other players and each player s actions can influence a state variable that is unobservable to the other players we develop an algorithm that solves for the subset of sequential equilibria in which equilibrium strategies depend on private information only through the privately observed state journal of economic literature classification numbers c63 c73

collusion enforcement with private information and private monitoring abstract this paper shows that a cartel that observes neither costs prices nor sales may still enforce a collusive agreement by tying each firm s continuation profit to the truncated current profits of the other firms the mechanism applies to both price and quantity competition and the main features are broadly consistent with common cartel practice identified by harrington and skrzypacz 24

public trust and government betrayal abstract this study presents a simple model of government reputation in which government type cannot be directly observed by households with the variation that government type rather than being permanent follows an exogenous markov process this formulation captures three characteristics of bad policy outcomes governments which betray public trust do so erratically public trust is regained only gradually after a betrayal and governments with recent betrayals betray with higher probability than other governments

who wants a good reputation we examine a market in which long lived firms face a short term incentive to exert low effort but could earn higher profits if it were possible to commit to high effort there are two types of firms inept firms who can only exert low effort and competent firms who have a choice between high and low effort there is occasional exit and competent and inept potential entrants compete for the right to inherit the departing firm s reputation consumers receive noisy signals of effort choice and so competent firms choose high effort in an attempt to distinguish themselves from inept firms a competent firm is most likely to enter the market by purchasing an average reputation in the hopes of building it into a good reputation than either a very low reputation or a very high reputation inept firms in contrast find it more profitable to either buy high reputations and deplete them or buy low reputations

collusion with persistent cost shocks we consider a dynamic bertrand game in which prices are publicly observed and each firm receives a privately observed cost shock in each period although cost shocks are independent across firms within a firm costs follow a first order markov process we analyze the set of collusive equilibria available to firms emphasizing the best collusive scheme for the firms at the start of the game in general there is a trade off between productive efficiency whereby the low cost firm serves the market in a given period and high prices we show that when costs are perfectly correlated over time within a firm if the distribution of costs is log concave and firms are sufficiently patient then the optimal collusive scheme entails price rigidity firms set the same price and share the market equally regardless of their respective costs when serial correlation of costs is imperfect partial productive efficiency is optimal for the case of two cost types first best collusion is possible if the firms are patient relative to the persistence of cost shocks but not otherwise we present numerical examples of first best collusive schemes

dynamic insurance with private information and balanced budgets this paper studies a dynamic insurance problem with bilateral asymmetric information and balanced budgets there are two infinitely lived agents in our model both risk averse and each has an i i d random endowment stream which is unobservable to the other in each period each agent must have a non negative consumption and together they must consume the entire aggregate endowment dynamic incentive compatibility in the nash sense is defined we give sufficient and necessary conditions for the existence of a constrained efficient contract we show that a constrained efficient contract can be characterized in a bellman equation we demonstrate that the long run distribution of expected utilities of each agent is not degenerate we also develop an algorithm for computing the efficient contract and in a numerical example we find that the consumption processes of the agents form stationary markov chains

full extraction of the surplus in bayesian and dominant strategy auctions we consider auctions for a single indivisible object in the case where the bidders have information about each other which is not available to the seller we show that the seller can use this information to his own benefit and we completely characterize the environ ments in which a well chosen auction gives him the same expected payoff as that obtainable were he able to sell the object with full information about each bidder s willingness to pay we provide this characterization for auctions in which the bidders have dominant strate gies and for those where the relevant equilibrium concept is bayesian nash in both set ups the existence of these auctions hinges on the possibility of constructing lotteries with the correct properties we consider the situation in which an agent the seller possesses one indivisible unit of a good to which he attaches no value but the good has value to a number of potential buyers and its transfer to one of them would increase social welfare in particular the transfer to the buyer with the highest valuation maximizes social welfare in this paper we completely characterize environments in which the seller can design an auction that will enable him to capture for himself the full increase in social welfare induced by the transfer of the good to the bidder with the highest willingness to pay if the seller had full information about the reservation prices of potential buyers his optimal selling strategy would be very simple he would announce a price equal or very close to the highest reservation value the optimal strategy for the bidder with the highest evaluation would be to accept the offer note that we are treating a situation in which the seller can commit himself to a price as a result of the exchange the utility of the seller increases by the full amount of the increase in social welfare and he has been able to fully extract the surplus in many circumstances however a seller has only imperfect knowledge of the buyers willingnesses to pay in this case he must find some mechanism or auction which will enable him to maximize his benefit from the sale of the object the auction literature starts with this observation and shows how the seller can by an astute choice of auction extract the largest possible fraction of the surplus in general the literature has shown that this proportion is strictly less than one in some circumstances the bidders will have information about each other which is not available to the seller for instance in auctions for petroleum drilling rights bidders know the results of geological tests which they have

optimal dynamic information provision abstract we study a dynamic model of information provision a state of nature evolves according to a markov chain an advisor with commitment power decides how much information to provide to an uninformed decision maker so as to influence his short term decisions we deal with a stylized class of situations in which the decision maker has a risky action and a safe action and the payoff to the advisor only depends on the action chosen by the decision maker the greedy disclosure policy is the policy which at each stage minimizes the amount of information being disclosed in that stage under the constraint that it maximizes the current payoff of the advisor we prove that the greedy policy is optimal in many cases but not always