stable equilibrium in beliefs in extensive games with perfect information abstract the purpose of this paper is to present a new solution concept of stable equilibrium in beliefs seb by assuming it is common knowledge that players are uncertainty averse in the sense of gilboa and schmeidler 1989 journal of mathematical economics 18 141 153 by making use of an appealing criterion of stability an seb is defined as a strategy profile supported by a stable belief system it is shown that all sebs constitute a unique stable belief system and an seb satisfies subgame perfectness moreover it is shown that the notion of seb refines that of subgame perfect equilibrium in terms of path of play finally following aumann 1995 games and economic behavior 8 6 19 this paper establishes some epistemic foundation for the notion of seb

coase versus pacman who eats whom in the durable goods monopoly in standard durable goods monopoly models both the set of buyers and the set of prices are assumed to be continua if the set of buyers is finite the perfectly discriminating monopoly outcome is a unique subgame perfect equilibrium when the seller is sufficiently patient introducing instead a smallest unit of account yields the coasian outcome as a generically unique subgame perfect equilibrium for patient enough buyers a folk theorem is obtained if both sets are finite these results reflect a strategic disadvantage of having to make moves with a large impact on other players payoffs the analysis is extended to durable goods oligopoly

durable goods monopolists durable goods monopolists face special problems because the sale of their products creates a secondhand market not controlled by the monopolist to the extent the monopolist is able to rent his product rather than sell it or to make binding promises about his future production such problems are ameliorated given the inability to do the above the monopolist is led to producing goods less durable than those produced by either competitive firms or monopolist returns a reverse averch johnson result that monopolist sellers may invest less in fixed costs including plant modernization and research and development than would the renters is shown it is also shown that even though sellers have less monopoly power than renters and nondurable goods monopolists it is possible that the seller will cause a greater deadweight loss than the other types of monopolies

dynamically consistent beliefs must be bayesian abstract experimental evidence such as the ellsberg paradox contradicts the savage model of decision making under uncertainty since the representation of beliefs underlying preferces by a single probability measure leaves no room for the degree of imprecision in information to affect decisions proceeding axiomatically this paper shows that the existence of a bayesain prior is implied even if savage s sure thing principle is deleted if preferences i are based on beliefs and ii admit dynamically consistent updating in response to new information the result raises questions about the appeal of models of preference that feature a separation of tastes and beliefs journal of economic literature classification number d81

uncertainty aversion and rationality in games of perfect information abstract this paper shows how uncertainty aversion can resolve ties in extensive games of perfect information and thereby refine subgame perfection in such games this is done by assuming that a players are rational with multi prior expected utility functions of gilboa and schmeidler 1989 journal of economic theory 48 221 237 and b a player s plan of the game corresponds to set valued acts at each of his decision nodes the so called strategy system in contrast to single valued act as specified in the traditional notion of strategy profile the effects of pre communication channels among players are studied and are reflected in each of the three proposed solutions finally existence of equilibria are established for each proposed solution concept as well as comparisons with other existing solutions

dynamic adverse selection and the supply size in this paper we examine the problem of dynamic adverse selection in a stylized market where the quality of goods is a seller s private information while the realized distribution of qualities is public information we obtain that full trade occurs in every dynamic competitive equilibrium moreover we show that if prices can be conditioned on the supply size then a dynamic competitive equilibrium always exists while it fails to exist if prices cannot be conditioned on the supply size and the frequency of exchanges is high enough we conclude that the possibility to condition prices on the supply size allows us to reach efficiency in the limit for exchanges becoming more and more frequent while otherwise the welfare loss due to delays of exchanges remains bounded away from zero

foundations of dynamic monopoly and the coase conjecture subgame perfect equilibria are characterized for a market in which the seller quotes a price each period assume zero costs positive interest rate continuum of buyers and some technical conditions if buyers valuations are positive then equilibrium is unique buyers strategies are stationary and the price sequence is determinant along the equilibrium path but possibly randomized elsewhere otherwise a continuum of stationary equilibria can exist but at most one with analytic strategies coase s conjecture is verified for stationary strategies reducing the period length drives all prices to zero or the least valuation connections to bargaining models are described journal qf economic literature classification

no lease is short enough to solve the time inconsistency problem the author provides a model of endogenous lease duration determination in the context of the durable goods monopolist problem he shows that infinitely many leases per finite unit of time are required to solve completely the time inconsistency problem thus suggesting that leasing may not provide a practical solution the author also provides a warning regarding the results that can be derived by exogenously setting lease durations equal to one period by resolving a paradoxical result in the literature copyright 1994 by blackwell publishing ltd

the intertemporal consequences of unauthorized reproduction of intellectual property in an intertemporal framework the harm to firms from unauthorized reproduction of their products may be significantly greater than that predicted by most static models copying by some consumers reduces the appropriable surplus from all consumers including those consumers lacking any propensity to copy somewhat paradoxically however the commitment value of copies may also imply that profits are higher with copying than without copying it is therefore suggested that firms may prefer differential copyright enforcement and that the commitment value of copies may offer a strategic explanation for free giveaways of abridged versions of intellectual property and vertical product differentiation more generally

extracting rents with forward contracts abstract we consider a risk neutral final goods producer operating with a concave production function we show that when faced with the possibility of quantity rationing in the spot market for an input the producer will always pay a premium to purchase some units of that input in a forward market a monopolistic supplier of the input can therefore earn additional rents by offering to sell units in both a forward market and a spot market effectively price discriminating along a producer s demand curve for the input we thus provide a model of forward contracting in which prices are set sequentially there is no risk aversion and customers purchase positive quantities in both the forward and the spot market

credible signals of the release of new versions i introduction many products are marketed some time after they have been developed for instance a new smartphone may be developed and tested well before it is available for purchase a new car might be prototyped and driven months before it comes to the market indeed a firm will often have several products concurrently in a development pipeline consumers may know a product is in that pipeline without knowing its progress towards the market because the outcome of such development and testing is not visible to outsiders the firm knows whether it can market a product before consumers do consumers are uninformed about when and if the new product will be marketed to them economists have long recognized that the present demand for durable goods depends on future prospects such as the future price or the introduction of an improved version 1 the existence of such an improved version is often the seller s private information if consumers anticipate a new version some will defer purchases until the new version is available and the seller will face low demand for the present version disclosing the new version is not in a monopoly seller s interest a seller whose good does not have a new version would also like to communicate that fact to consumers while a firm with a successful product innovation can credibly disclose the new version with relative ease a firm that has failed to develop a new product could have great difficulty convincing consumers that the product has no new version in such situations it is important to examine whether prices can inform consumers whether a new version will be marketed in the near future in a recent paper choi et al 2010 developed a model with a risky product development process in which reputation effects allow cheap talk announcements to signal successful product development to consumers an announcement induces consumers to delay or divert purchases to the announcer s coming product which increases the announcer s profit and can improve welfare 2 in their model the announcer and her non innovative rivals supply the original good competitively because of this an announcement does not reduce profit on the current version this paper will focus on markets where the seller has substantial market power before innovating so announcing a successful product development has a cost in terms of current revenue further because we attend to prices as signals this model may also apply to markets where a long run relationship between consumers and firms may not be sustainable another objective of this paper is to examine the welfare effects of mandatory disclosure a government policy mandating disclosure of any new version is an alternative means of informing consumers 3 as long as firms are not willing to lie to the government such a policy would credibly communicate whether a new version of a durable is coming mandatory disclosure would bring about full information as consumers are informed about any improved future version before observing the price of the current version in this paper we explore a two period model of a durable good monopoly in which consumers are initially uninformed about whether there will be a new version of the current good the monopoly seller is privately informed if he will be able to market an improved version in the second period in the first period consumers must decide whether to purchase the good now or wait for an upgraded version they may be able to infer from the price of the current version whether the seller will bring a new version to the market it is important to see first whether prices can serve as signals and second how welfare compares between any signaling outcome and a full information benchmark corresponding to mandatory disclosure we will show that there is a unique equilibrium supported by intuitive beliefs in this equilibrium the seller s private information about an improved version is completely revealed to consumers

rationalizable strategic behavior the notion of equilibrium proposed by nash 19 has come to play a dominant role in economic applications of noncooperative games while analyses of nash equilibria have unquestionably contributed to our understanding of economic behavior it would be unreasonably optimistic to maintain that nash solved the problem of noncooperative strategic choice there is a small literature beginning with ellsberg 6 and a much larger oral tradition which argues that nash behavior is neither a necessary consequence of rationality nor a reasonable empirical proposition in this paper i take the view that although there may be various reasons why an agent might select a nash strategy the notion of an equilibrium has little intrinsic appeal within a strategic context when an agent reaches a decision in ignorance of the strategies adopted by other players rationality consists of making a choice which is justifiable by an internally consistent system of beliefs rather than one which is optimal post hoc this point of view is not original indeed most serious justifications of the nash hypothesis embrace such an approach arguing that agents will expect the game to yield a nash outcome and consequently will choose their equilibrium strategies nevertheless when we think in terms of maximizing utility subject to expectations rather than realizations it becomes clear that the nash hypothesis far from being a consequence of rationality arises from certain restrictions on agents expectations which may or may not be plausible depending upon the game being played we are then quite naturally led to ask are there any restrictions of individuals expectations and hence choices which are required by rationality alone rather than by subjective plausibility this paper is concerned with defining justifying characterizing and refining a criterion for rational strategic choice which i label rationalizability

rationalizable strategic behavior and the problem of perfection this paper explores the fundamental problem of what can be inferred about the outcome of a noncooperative game from the rationality of the players and from the information they possess the answer is summarized in a solution concept called rationalizability strategy profiles that are rationalizable are not always nash equilibria conversely the information in an extensive form game often allows certain unreasonable nash equilibria to be excluded from the set of rationalizable profiles a stronger form of rationalizability is appropriate if players are known to be not merely rational but also cautious what constitutes rational behavior in a noncooperative strategic situation this paper explores the issue in the context of a wide class of finite noncooperative games in extensive form the traditional answer relies heavily upon the idea of nash equilibrium nash 17 the position developed here however is that as a criterion for judging a profile of strategies to be reasonable choices for players in a game the nash equilibrium property is neither necessary nor sufficient some nash equilibria are intuitively unreasonable and not all reasonable strategy profiles are nash equilibria the fact that a nash equilibrium can be intuitively unattractive is well known the equilibrium may be imperfect introduced into the literature by selten 20 the idea of imperfect equilibria has prompted game theorists to search for a narrower definition of equilibrium while this research some of which will be discussed here has been extremely instructive it remains inconclusive theorists often agree about what should happen in particular games but to capture this intuition in a general solution concept has proved to be very difficult if this paper is successful it should make some progress in that direction the other side of the coin has received less scrutiny can all non nash profiles really be excluded on logical grounds i believe not the standard justifications for considering only nash profiles are circular in nature or make gratuitous assumptions about players decision criteria or beliefs the following discussion of these points is extremely brief due to space constraints more detailed arguments may be found in pearce 18

cheap talk games may have unique informative equilibrium outcomes abstract we demonstrate that cheap talk games can have unique informative equilibrium outcomes by providing an example of an infinite action bayesian game which absent cheap talk does not possess an equilibrium

monopoly extraction of a durable non renewable resource failure of the coase conjecture the author studies a perfect information rational expectations markov equilibrium for the situation where a monopolist extracts a nonrenewable resource that is converted to a durable good even if short run extraction costs are constant the coase conjectur e fails provided that the depreciation rate of the durable good is positive copyright 1993 by the london school of economics and political science

durable goods monopoly with limited choice of commitment strategy when should the monopolist precommit consider a firm a monopolist offering a unique product to a fixed number of potential customers suppose that no consumer desires more than one unit of the good within a given period or across periods that is there is no value to repeat purchases in addition suppose that customers vary with respect to their initial reservation prices which decline over time a natural interpretation is that the monopolist is selling a good that is durable alternatively the firm is providing an entertainment or fashion good consumers may place a premium on obtaining the product quickly before it becomes less useful less stylish or less novel coase 7 conjectured that this firm s ability to extract surplus is limited because the firm has to compete with itself across time periods high valuation customers would be unwilling to pay a high initial price because they would anticipate that over time the firm will be reducing the price in order to sell to lower valuation customers subsequent literature formalizes this as a time inconsistency problem faced by a monopolist unable to make intertemporal commitments a separate strand of the literature proceeds from the polar assumption that the monopolist can precommit to any multiperiod pricing strategy comparison to coase s monopolist is simple higher profits are obtainable under precommitment because more surplus is extracted from high valuation customers an important proposition due to stokey 22 is that it will be optimal for the monopolist to precommit to a declining intertemporal price schedule if consumers with higher initial valuations have a higher rate of time preference 2 otherwise the optimal strategy is to hold price constant at the static monopoly level and to sell no more than the static monopoly quantity 3

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

a more robust definition of subjective probability the goal of choice theoretic derivations of subjective probability is to separate a decisionmaker s underlying beliefs subjective probabilities of events from their preferences attitudes toward risk classical derivations have all relied upon some form of the marschak samuelson independence axiom or the savage sure thing principle which imply that preferences over lotteries conform to the expected utility hypothesis this paper presents a choice theoretic derivation of subjective probability in a savage type setting of purely subjective uncertainty which neither assumes nor implies that the decisionmaker s preferences over lotteries necessarily conform to the expected utility hypothesis copyright 1992 by the econometric society

balancing contemporary fairness and historical justice a quasi equitable proposal for ghg mitigations abstract in this paper we analyze the impasse caused by polarizing positions of the united states and china in international negotiations on carbon mitigation by incorporating the bern carbon cycle module into the rice model developed by nordhaus and yang 1996 we set up a framework for tracking regional contributions to carbon concentration and to global climate change our proposal labeled the color preservation principle uses regional contribution share to global carbon concentration as the criterion for international cooperation through simulations in rice model with bern module rice b we examine the rationales of the arguments made by the united states and china we conclude that both countries standpoints are severely flawed to facilitate the global cooperation on carbon mitigations major concessions are needed from the two top carbon emitters

cheap talk can matter in bargaining this paper describes an intuitive way in which cheap talk can matter in a twostage bargaining game in which talk may be followed by serious negotiation the intuition that all buyers would claim to have low reservation prices is incorrect in our model instead if good faith participation is endogenously determined then the parties can use talk to trade off bargaining position against the probability of continued negotiation our cheap talk equilibrium features bargaining behavior that could not be equilibrium behavior in the absence of talk

nash equilibrium under knightian uncertainty breaking down backward induction abstract we define nash equilibrium for two person normal form games in the presence of knightian uncertainty using the formalization of schmeidler and gilboa we show that nash equilibrium exists for any degree of uncertainty aversion that maxmin behaviour can occur even when it is not rationalizable in the usual sense and that backward induction breaks down in the twice repeated prisoners dilemma we relate these results to the literature on cooperation in the finitely repeated prisoners dilemma and the literature on epistemological conditions underlying nash equilibrium the knowledge notion implicit in this model of equilibrium does not display logical omniscience journal of economic literature classification numbers c72 d81

durable goods monopoly with discrete demand we analyze a dynamic game between consumers and the sole seller of a durable good unlike previous analyses we assume that there exists a finite collection of buyers rather than a continuum none of the main conclusions of the literature on durable goods monopoly survives this change in assumption coase s conjecture that a durable goods monopolist cannot earn supracompetitive profits in the continuous time limit bulow s proposition that renting a durable is always more profitable than selling it and stokey s proposition that precommitting to a time path of prices is always optimal are all false when the set of buyers is finite thus the assumption of a continuum of consumers so innocuous and useful a simplification in other contexts has proved misleading in the context of durable goods monopoly

a multistage model of bargaining this paper presents a simple multistage model of bargaining wherein a seller makes an offer that can be either accepted or refused if rejected the process continues how the seller s ability to make commitments affects bargaining outcomes is analysed by comparing the commitment equilibria to those arising when commitment is impossible the effects of increasing uncertainty about preferences and varying the length of the bargaining horizon are analysed the ways in which the bargaining environment can be changed to improve outcomes are discussed

durable goods coasian dynamics and uncertainty theory and experiments this paper presents a model in which a durable goods monopolist sells a product to two buyers each buyer is privately informed about his own valuation thus all players are imperfectly informed about market demand we study the monopolist s pricing behavior as players uncertainty regarding demand vanishes in the limit in the limit players are perfectly informed about the downward sloping demand we show that in all games belonging to a fixed and open neighborhood of the limit game there exists a generically unique equilibrium outcome that exhibits coasian dynamics and in which play lasts for at most two periods a laboratory experiment shows that consistent with our theory outcomes in the certain and uncertain demand treatments are the same median opening prices in both treatments are roughly at the level predicted and considerably below the monopoly price consistent with coasian dynamics these prices are lower for higher discount factors demand withholding however leads to more trading period

eliminating the market for secondhand goods an alternative explanation for leasing there are a number of prominent specific instances in which a durable goods manufacturer with significant market power employed a lease only policy i united shoe in the market for shoe machinery ii ibm in the market for computers and iii xerox in the market for copiers the obvious question that arises is why would such a firm prefer leasing over selling in this article i argue that one role of the lease only policy was to eliminate the market for secondhand goods the article formally demonstrates the argument discusses the relationship between this article and earlier literature on secondhand markets and discusses the implications for antitrust policy

coase and hotelling a meeting of the minds in this paper we tie together the two literatures of durable goods monopoly and exhaustible resource pricing we show that the intertemporal no arbitrage condition that arises if the durable good monopolist seller can commit to a price path mirrors the intertemporal no arbitrage condition if the monopsonist buyer of an exhaustible resource can commit to a price path the intuition is that the durable good monopolist initially announces high future prices to get high valuation buyers to buy early and subsequently lowers the price to attract additional buyers on the other hand the monopsonist buyer of the exhaustible resource initially announces low future prices to encourage sellers to supply their units early and subsequently as the stock of the resource declines raises the price to call forth additional supply as the period of commitment shrinks to zero the durable good s price drops to its marginal cost and the exhaustible resource s price jumps to its choke level all in a twinkling of the eye a

damaged durable goods i analyze a durable goods monopolist s incentives to introduce a damaged good a stripped down version of the original good in an infinite horizon framework the damaged good helps the monopolist to mitigate the coasian time inconsistency problem however it may lead to a welfare reduction low valuation buyers are induced to purchase the low quality damaged good early rather than buy the high quality original good later and when the players are patient the surplus loss from quality reduction outweighs the gain from earlier consumptions this welfare result contrasts with the previous literature based on a static framework