a formal model of firm boundaries and haggling this study provides a formal model of williamson s haggling theory in which transacting parties engage in ex post contract renegotiation we show that integration can economize bargaining costs but suffers from too much third party arbitration i e fails in selective intervention

reputation with equal discounting in repeated games with strictly conflicting interests we analyze reputation effects in two player repeated games of strictly conflicting interests in such games player 1 has a commitment action such that a best reply to it gives player 1 the highest individually rational payoff and player 2 the minmax payoff players have equal discount factors with positive probability player 1 is a type who chooses the commitment action after every history we show that player 1 s payoff converges to the maximally feasible payoff when the discount factor converges to one this contrasts with failures of reputation effects for equal discount factors that have been demonstrated in the literature journal of economic literature classification number c71

reputation in dynamic games abstract we analyze reputation in a game between a large player and a continuum of long lived small players in which state variables affect players payoffs the large player s type is private information we give conditions under which in every nash equilibrium a very patient large player will get almost the largest payoff consistent with the small players choosing a best response in a large finite truncation of the game while our results apply to the time inconsistency problem of optimal government policy we show that for the durable goods monopoly reputation may fail to improve the monopolist s payoff journal of economic literatureclassification numbers c72 c73

variance risk premium dynamics the role of jumps using high frequency stock market data and synthetic variance swap rates this paper identifles and investigates the temporal variation in the market variance risk premium the variance risk is manifest in two salient features of flnancial returns stochastic volatility and jumps the pricing of these two separate components is analyzed in a general semiparametric framework the key empirical results imply that investors fears of future jumps are especially sensitive to recent jump activity and that their willingness to pay for protection against jumps increase signiflcantly immediately after the occurrence of jumps this in turn suggests that time varying risk aversion as previously documented in the literature is primarily driven by large or extreme market moves the dynamics of risk neutral jump intensity extracted from deep out of the money put options conflrms these flndings jel c51 c52 g12 g13

commitment and compromise in bargaining abstract this paper studies observable and irrevocable commitment in bargaining we investigate when commitment tactics can cause an impasse and when compromise is feasible in the static model in which a player s commitment decision is made simultaneously with his choice of bargaining stance compromise becomes unattainable ellingsen and miettinen 2008 we first analyze a static bargaining model in which the players decide whether to attempt commitment after announcing their demands in contrast to the aforementioned strong result our model accommodates both incompatible commitments and compromises as equilibrium outcomes we then extend our analysis to a dynamic setting it is shown that compromise is possible if the players can alter their demands quickly and the chances of successful commitment are low

a two sided reputation result with long run players abstract we establish reputation results under two sided incomplete information for a class of repeated games we consider a repeated game that satisfies the assumptions of either atakan and ekmekci 2012 3 or cripps et al 2005 6 and we assume that both players are stackelberg types with positive probability if the stage game is not a common interest game then equilibrium play converges to the unique equilibrium of a continuous time war of attrition as the stage game is repeated arbitrarily frequently alternatively if the stage game is a common interest game then the players equilibrium payoffs converge to their highest payoffs as the stage game is repeated arbitrarily frequently

zooming in self emergence of movements in new product growth in this paper we propose an individual level approach to diffusion and growth models by zooming in we refer to the unit of analysis which is a single consumer instead of segments or markets and the use of granular sales data daily instead of smoothed e g annual data as is more commonly used in the literature by analyzing the high volatility of daily data we show how changes in sales patterns can self emerge as a direct consequence of the stochastic nature of the process our contention is that the fluctuations observed in more granular data are not noise but rather consist of accurate measurement and contain valuable information by stepping into the noise like data and treating it as information we generated better short term predictions even at very early stages of the penetration process using a kalman filter based tracker we demonstrate how movements can be traced and how predictions can be significantly improved we propose that for such tasks daily data with high volatility offer more insights than do smoothed annual data

reputation and dynamic stackelberg leadership in infinitely repeated games abstract the paper studies a repeated game in which a long run player without discounting faces another long run player with strict discounting the game is perturbed so that there is uncertainty in the patient player s strategy choice she may be a rational player but she may also be one of many irrational types who are committed to various repeated game strategies the rational patient player s equilibrium payoff in this perturbed game is analyzed in particular it is shown that the lower bound on her payoff in the set of extensive form trembling hand perfect equilibria is given by her stackelberg payoff in a dynamics sense journal of economic literature classification numbers c72 d82

bargaining and reputation an experiment on bargaining in the presence of behavioural types we conduct a series of laboratory experiments to understand what role commitment and reputation play in bargaining the experiments implement the abreu and gul 2000 bargaining model that demonstrates how introducing behavioral types which are obstinate in their demands creates incentives for all players to build reputations for being hard bargainers the data are qualitatively consistent with the theory as subjects mimic induced types furthermore we find evidence for the presence of complementary types whose initial demands acquiesce to induced behavioural demands however there are quantitative deviations from the theory subjects make aggressive demands too often and participate in longer conflicts before reaching agreements overall the results suggest that the abreu and gul 2000 model can be used to gain insights to bargaining behavior particularly in environments where the process underlying obstinate play is well established

reputation and cooperation in the repeated second price auctions this paper shows that there are strong reputational effects in a general class of second price auctions if reputation is one sided and bidders are patient then the bidder without reputation does not challenge the other bidder often consequently the bidder with reputation obtains most of the surplus the other bidder and the seller get very little if reputation is two sided then the bidders engage in a game akin to war of attrition the resulting payoff is very low for the bidders and very high for the seller in any case the folk theorem fails collusion in the second price auctions is impossible the predictions of the model are that prices in early auctions should reach levels that are higher than the value of the object then declining towards the reserve price a set of strong bidders emerges a recent series of auctions of spectrum for umts services in europe seems to be consistent with the predictions of the model

strategic delay in bargaining this paper analyses a bargaining model with incomplete information in which the time between offers is an endogenous strategic variable we find equilibria involving a delay to agreement that is due to the use of strategic time delay by bargainers to signal their relative strength under some specifications of the parameters delay is present in the unique sequential equilibrium whose beliefs satisfy one intuitive restriction this delay does not vanish as the minimal time between offers becomes small

bargaining with two sided incomplete information an infinite horizon model with alternating offers this paper examines an infinite horizon bargaining model incorporating five features two sided incomplete information with potentially information revealing strategies an infinite horizon uncertainty concerning the potential gains from trade an illumination of interesting qualitative bargaining issues and plausible free from arbitrarily specified out of equilibrium conjectures equilibria these features motivated in the paper have powerful implications a nash equilibrium exists and is generically both unique and sequential comparative static implications of variations in the game s specifications are developed we find that natural indications of bargaining strength emerge from the model and establish the intuitive result that an increase in a player s relative bargaining strength makes that player more likely to capture the gains from bargaining

the war of attrition in continuous time with complete information this paper provides a complete characterization of the nash equilibrium outcomes for the war of attrition when time is continuous and information is complete it allows for asymmetric payoffs and an arbitrary time horizon in addition to certain asymme tric pure strategy equilibria that always exist the authors establi sh the conditions under which there is also a continuum of mixed strategy equilibria these are most likely to exist when either the horizon is infinite or the game is symmetric copyright 1988 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

costs of implementation bargaining costs versus allocative efficiency abstract a mechanism with low direct cost of use may be preferred to alternatives implementing more efficient allocations we show this experimentally by giving pairs of subjects the option to agree on a single average price for a sequence of trades in effect pooling several small bargains into a larger one we make pooling costly by tying it to some inefficient trades but subjects nevertheless reveal strong tendencies to pool particularly when more bargains remain to be struck and when bargaining is face to face the results suggest that implementation costs could play a significant role in the use of many common trading practices

optimal stalling when bargaining this paper analyzes an alternating offer model of bargaining over the sale of an asset in a market such as that for housing in which another agent may come and compete for the right to strike a deal the analysis allows the buyer and seller to have possibly differing views as to how likely such a competition is hence the buyer and the seller disagree about their respective bargaining powers these views adjust to market realizations as the parties learn it is shown that there exists a unique subgame perfect equilibrium which can be explicitly constructed hence conditional on market conditions equilibrium prices and optimal stall lengths that is delay can be found bargaining delay can only occur if there is optimism not pessimism and only if the parties are open to learning as time elapses this delay can occur even for very small levels of optimism and the delay can be for economically significant periods

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

bargaining with arrival of new traders we study dynamic bargaining with asymmetric information and arrival of exogenous events which represent arrival of traders or information we char acterize the unique limit of stationary equilibria with frequent offers the possi bility of arrivals changes equilibrium dynamics there is delay in equilibrium and the seller slowly screens out buyers with higher valuations the seller pay off equals what he can achieve by simply awaiting an arrival in applications when buyer valuations fall average prices drop and delay increases surplus division depends on relative arrival rates of buyers sellers and expected time to trade is a nonmonotonic function of the arrival rate

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

reputation in long run relationships we model a long run relationship as an infinitely repeated game played by two equally patient agents in each period the agents play an extensive form stage game of perfect information with either locally non conflicting interests or strictly conflicting interests there is incomplete information about the type of player 1 while player 2 s type is commonly known we show that a sufficiently patient player 1 can leverage player 2 s uncertainty about his type to secure his highest pay off compatible with player 2 s individual rationality in any perfect bayesian equilibrium of the repeated game copyright 2012 oxford university press

land aggregation using contingent and guaranteed payments this article explores the use of alternative payment mechanisms to overcome the holdout problem when multiple parcels of land must be acquired to complete a real estate development project purchase offers contingent upon successful land aggregation are compared to combination offers containing both guaranteed and contingent payments to determine which approach better mitigates holdout the distribution of gains between developers and landowners is also examined the results of a series of economic experiments suggest that contingent offers expedite land aggregation but developer payoffs are higher when combination offers are used the results offer insight to real estate developers participating in land aggregation and inform government entities considering the necessity of public sector intervention in real estate markets to encourage desired development projects

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

reputational bargaining with minimal knowledge of rationality two players announce bargaining postures to which they may become committed and then bargain over the division of a surplus the share of the surplus that a player can guarantee herself under first order knowledge of rationality is determined as a function of her probability of becoming committed as is the bargaining posture that she must announce in order to guarantee herself this much this maxmin share of the surplus is large relative to the probability of becoming committed e g it equals 30 if the commitment probability is 1 in 10 and equals 13 if the commitment probability is 1 in 1000 and the corresponding bargaining posture simply demands this share plus compensation for any delay in reaching agreement

no compromise uncertain costs in reputational bargaining abstract i show how uncertainty about agents future costs of delay can lead to substantial bargaining delays when agents have reputational concerns reputational concerns arise because with positive probability agents are behavioral types committed to demanding a fixed share of the surplus in equilibrium rational agents may demand almost the entire surplus and then wait with the deadlock only broken by the arrival of news about future costs even as the probability of behavioral types vanishes although both agents would benefit from a compromise reached immediately they do not propose such agreements because doing so would increase an opponent s option value of waiting

intimidation linking negotiation and conflict challenger demands a resource from defender in each period challenger chooses whether to attack if attacked defender chooses whether to concede the resource forever each player might be committed to ghting until victory before con ict begins defender can make nitely many offers con ict begins if challenger rejects all offers in equilibrium all offers except the last are unacceptable negotiation cannot eliminate con ict because a larger offer makes con ict increasingly attractive for challenger if negotiation fails prolonged con ict can happen in equilibrium even when uncertainty is vanishingly small we provide comparative statics regarding the probability and length of con ict

uncertainty about uncertainty and delay in bargaining we study a one sided offers bargaining game in which the buyer has private information about the value of the object and the seller has private information about his beliefs about the buyer s valuation we show that this uncertainty about uncertainties dramatically changes the set of outcomes in particular second order beliefs can lead to a delay in reaching agreement even when the seller makes frequent offers we show that not all types of second order beliefs lead to a delay when the buyer assigns positive probability to the seller knowing the buyer s value then delay not only can occur but it must occur for a class of equilibria however in all other cases delay will never occur

bargaining with incomplete information an infinite horizon model with two sided uncertainty the resolution of any bargaining conflict depends crucially on the relative urgency of the agents to reach agreement and the information each agent has about the others preferences this paper explores within the context of an infinite horizon bargaining model with two sided uncertainty how timing and information affect the rational behaviour of agents when commitment is not possible since the bargainers are uncertain about whether trade is desirable they must communicate some of their private information before an agreement can be reached this need for learning due to incomplete information about preferences results in bargaining inefficiencies trade often occurs after costly delay thus the model provides an explanation for the inefficient bargaining behaviour that appears to occur often in practice

a conversational war of attrition we explore costly deliberation by two differentially informed and possibly biased jurors a hawk lones and a dove moritz alternately insist on a verdict until one concedes debate assumes one of two genres depending on bias a juror say lones is intransigent if he wishes to prevail and reach a conviction for any type of moritz next to concede in contrast lones is ambivalent if he wants the strongest conceding types of moritz to push for acquittal both jurors are ambivalent with small bias or high delay costs as lones grows more hawkish he argues more forcefully for convictions mitigating wrongful acquittals if dovish moritz is intransigent then he softens strategic substitutes leading to more wrongful convictions ambivalent debate is new and yields a novel dynamic benefit of increased polarization for if moritz is ambivalent then he toughens strategic complements and so surprisingly a more hawkish lones leads to fewer wrongful acquittals and convictions so more polarized but balanced debate can improve communication unlike in static cheap talk we also show that patient and not too biased jurors vote against their posteriors near the end of the debate optimally playing devil s advocate we shed light on the adversarial legal system peremptory challenges and cloture rules

bargaining without a common prior an immediate agreement theorem in sequential bargaining models without outside options each player s bargaining power is ultimately determined by which player will make an offer and when this paper analyzes a sequential bargaining model in which players may hold different beliefs about which player will make an offer and when excessive optimism about making offers in the future can cause delays in agreement the main result states that despite this if players will remain sufficiently optimistic for a sufficiently long future then in equilibrium they will agree immediately this result is also extended to other canonical models of optimism

bargaining with imperfect commitment abstract we study the effect of imperfect commitment in noncooperative two person bargaining games by establishing the reputation for being stubborn a player sometimes commits to her initial demand becoming unable to change her demands or to accept an inferior offer from her opponent when the probability of being stubborn is small the set of equilibria is shown to be small and agreement may be reached immediately despite the possibility of stubbornness a player has greater bargaining power when she is more patient and or is more likely to be stubborn journal of economic literature classification number c78

delays and partial agreements in multi issue bargaining abstract we model a situation in which two players bargain over two pies one of which can only be consumed starting at a future date suppose the players value the pies asymmetrically one player values the existing pie more than the future one while the other player has the opposite valuation we show that players may consume only a fraction of the existing pie in the first period and then consume the remainder of it along with the second pie at the date at which the second pie becomes available thus our model features a special form of bargaining delay in which agreements take place in multiple stages such partial agreements arise when players are patient enough when they expect the second pie to become available soon and when the asymmetry in their valuations is large enough

reputation in bargaining and durable goods monopoly this paper analyzes durable goods monopoly in an infinite horizon discrete time game we prove that as the time interval between successive offers approaches zero all seller payoffs between zero and static monopoly profits are supported by subgame perfect equilibria this reverses a well known conjecture of coase alternatively one can interpret the model as a sequential bargaining game with one sided incomplete information in which an uninformed seller makes all the offers our folk theorem for seller payoffs equally applies to the set of sequential equilibria of this bargaining game

contract negotiation and the coase conjecture a strategic foundation for renegotiation proof contracts what does contract negotiation look like when some parties hold private information and negotiation frictions are negligible this paper analyzes this question and provides a foundation for renegotiation proof contracts in this environment the model extends the framework of the coase conjecture to situations in which the quantity or quality of the good is endogenously determined and to more general environments in which preferences are nonseparable in the traded goods as frictions become negligible all equilibria converge to a unique outcome which is separating efficient and straightforward to characterize

maintaining a reputation against a long lived opponent we consider a game between a patient player 1 and a nonmyopic but less patient opponent player 2 as usual in reputation models we suppose that the patient player s type is private information and that he may be a commitment type who is locked into playing a particular strategy we investigate the extent to which an uncommitted or normal type of patient player can exploit his less patient opponent s uncertainty to maintain a reputation for playing like a commitment type

optimal value commitment in bilateral bargaining we study the role of commitment as a source of strategic power in a non cooperative bargaining game two impatient players bargain about the division of a shrinking surplus under a standard bargaining protocol in discrete time with constant recognition probabilities before bargaining a player can commit to some part of the surplus this commitment remains binding until the surplus has shrunk below the amount that the player is committed to intuitively one cannot remain committed to something which has become impossible the model offers insight on the relative importance of proposal power and commitment for the bargaining outcome in a version of the game where both players may simultaneously choose their commitments the equal split emerges from within a range of equilibrium divisions as a focal point which is robust to changes in the model parameters 2012

tough negotiations bilateral bargaining with durable commitments abstract we offer a tractable model of tough negotiations and delayed agreement the setting is an infinite horizon bilateral bargaining game in which negotiators can make strategic commitments to durable offers commitments decay stochastically but uncommitted negotiators can make new commitments the game s unique markov perfect equilibrium outcome takes the form of a war of attrition negotiators initially commit to incompatible offers but agreement occurs once a negotiator s commitment decays if commitments decay more quickly the terms of the agreement become more equal in expectation more patient committed and less risk averse negotiators obtain a larger fraction of the surplus

gambling over public opinion we consider bargaining environments in which public opinion provides leverage by making compromises costly two parties make initial demands before knowing the public opinion if deadlocked they can bargain again after public opinion forms but suffer reputation costs if they compromise i e scale back their demands we show that in equilibrium parties may choose to make incompatible demands initially and gamble over public opinion even though one or both parties must bear a cost later we characterize when deadlocks arise and how this affects the welfare of the public in a representative two party democracy compared to a direct democracy

taking sides in wars of attrition third parties often have a stake in the outcome of a conflict and can affect that outcome by taking sides this article studies the factors that affect a third party s decision to take sides in a civil or interstate war by adding a third actor to a standard continuous time war of attrition with two sided asymmetric information the third actor has preferences over which of the other two actors wins and for being on the winning side conditional on having taken sides the third party also gets a flow payoff during the fighting which can be positive when fighting is profitable or negative when fighting is costly the article makes four main contributions first it provides a formal framework for analyzing the effects of endogenous intervention on the duration and outcome of the conflict second it identifies a boomerang effect that tends to make alignment decisions unpredictable and coalitions dynamically unstable third it yields several clear comparative static results finally the formal analysis has implications for empirical efforts to estimate the effects of intervention showing that there may be significant selection and identification issues

durable goods monopoly with incomplete information this article reconsiders the durable goods monopoly problem when the monopolist s marginal cost is private information we show that the coase conjecture implies the no trade theorem in any equilibrium in which the lowest cost seller s initial offer approaches her marginal cost the aggregate probability of trade must vanish however we also construct non coasean equilibria which approximate the unique outcome of the rental version of the same model these stationary equilibria are comparatively efficient the results are equally applicable to the mathematically equivalent problem of sequential bargaining with two sided incomplete information where one party makes all the offers what are the consequences of monopoly in a market for a durable good present day understanding of this question divides into two strands of thought first the monopolist may effectively lack any ability to credibly precommit on her future output under this scenario the price will drop almost instantaneously to marginal cost apparently yielding the efficient outcome normally associated with perfect competition 1 second the monopolist may possess an explicit e g leasing the good rather than selling2 or implicit e g the maintenance of reputation3 device enabling her to adhere to an output restriction under such circumstances price will be maintained at a non competitively high level suggesting an outcome fraught with all the inefficiency of classical monopoly the conclusions of the first paragraph rest on analysis of a standard model in which the monopolist s payoff function is taken to be common knowledge a single firm with known constant marginal cost sells an infinitely durable good to consumers with a known distribution of valuations for the good 4 the firm has the ability to revise its posted price

alternating offer bargaining with two sided incomplete information i study alternating offer bargaining games with two sided incomplete information about the players discount rates for both perfect bayesian equilibrium and a rationalizability style notion i characterize the set of expected payoffs which may arise in the game i also construct bounds on agreements that may be made the set of expected payoffs is easy to compute and incorporate into applied models my main result is a full characterization of the set of perfect bayesian equilibrium payoffs for games in which the distribution over the players discount rates is of wide support yet is in a weak sense close to a point mass distribution i prove a lopsided convergence result each player cannot gain from a slight chance that she is a strong type but the player can suffer greatly if there is a slight chance that she is a weak type

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

gambling reputation repeated bargaining with outside options we study the role of incomplete information and outside options in determining bargaining postures and surplus division in repeated bargaining between a long run player and a sequence of short run players the outside option is not only a disagreement point but reveals information privately held by the long run player in equilibrium the uninformed short run players offers do not always respond to changes in reputation and the informed long run player s payoffs are discontinuous the long run player invokes inefficient random outside options repeatedly to build reputation to a level where the subsequent short run players succumb to his extraction of a larger payoff but he also runs the risk of losing reputation and relinquishing bargaining power we investigate equilibrium properties when the discount factor goes to 1 and when the informativeness of outside options diffuses in both cases bargaining outcomes become more inefficient and the limit reputation building probabilities are interior publication abstract

inefficient sales delays by a durable good monopoly facing a finite number of buyers this article offers a new explanation for unscheduled price cuts and slow adoption of durable goods we study a standard durable good monopoly model with a finite number of buyers and show that this game can have multiple subgame perfect equilibria in addition to the pacman outcome including the coase conjecture of particular interest is a class of equilibria where the seller first charges a high price and only lowers that price once some but not all high valuation buyers purchase this price structure creates a war of attrition between those buyers which delays market clearing and rationalizes unscheduled purchase and price cut dates

option prices implied price processes and stochastic volatility this paper characterizes all continuous price processes that are consistent with current option prices this extends derman and kani 1994 dupire 1994 1997 and rubinstein 1994 who only consider processes with deterministic volatility our characterization implies a volatility forecast that does not require a specific model only current option prices we show how arbitrary volatility processes can be adjusted to fit current option prices exactly just as interest rate processes can be adjusted to fit bond prices exactly the procedure works with many volatility models is fast to calibrate and can price exotic options efficiently using familiar lattice techniques

bargaining reputation and competition this paper addresses the question of whether playing the tough bargainer is a useful strategy for rational negotiators in competitive environments the unique equilibrium outcome of a continuous time multilateral bargaining game between a single seller and two buyers i e a three player war of attrition game show that it does not benefit the buyers the long side of the market if the probability of obstinacy is constant and independent of the initial demands this result is robust in the sense that the buyers heterogeneity about their flexibility does not weaken the intensity of the competition when the seller decides which buyer to negotiate first he not only chooses his bargaining partner but also picks his outside option the seller can strengthen his bargaining position against both buyers by picking the unattractive buyer who is greedier or tougher than the other buyer first and by leaving the attractive buyer aside because he starts the sequel with a strong outside option

prospect theory in a dynamic game theory and evidence from online pay per bid auctions abundant evidence exists that expected utility theory does not adequately describe decision making under risk although prospect theory is a popular alternative it is rarely applied in strategic situations in which risk arises through individual interactions this study fills this research gap by incorporating prospect theory preferences into a dynamic game theoretic model using a large field data set from multiple online pay per bid auction sites the authors empirically show that their proposed model with prospect theory preferences makes a better out of sample prediction than a corresponding expected utility model prospect theory also provides a unified explanation for two behavioral anomalies average auctioneer revenues above current retail prices and the sunk cost fallacy the empirical results indicate that bidders are loss averse and overweight small probabilities such that the expected revenue of the auction exceeds the current retail price by 25 46 the authors illustrate and empirically confirm a managerial implication for how an auctioneer can increase revenue by changing the details of the auction design

bargaining and reputation in search markets in a two sided search market agents are paired to bargain over a unit surplus the matching market serves as an endogenous outside option for a bargaining agent behavioral agents are commitment types that demand a constant portion of the surplus the frequency of behavioral types is determined in equilibrium even if the frequency of behavioral types is negligible they aect the terms of trade and eciency in an unbalanced market where the entering

commitment and conflict in bilateral bargaining building on crawford 1982 we study a model of bilateral bargaining in which negotiators can make binding commitments at a low positive cost c our primary solution concept is iterated strict dominance if commitment attempts never fail there are three solutions in two solutions all the surplus goes to one player in the third solution there is a high probility of con ict if commitment attempts succeed with probability q 1 the unique solution entails con ict with probability q 2 when c 0 analogous results hold if the requirement of iterated strict dominance is replaced by iterated weak dominance

a non cooperative bargaining model with strategically timed offers abstract rubinstein s alternating offers bargaining model is enriched by allowing players to choose when and whether or not to make an offer time is continuous and players make offers whenever they wish it is assumed that upon making an offer players must wait a fixed amount of time before making another it is shown that if players can react arbitrarily quickly to their opponent s offers then all subgame perfect equilibrium outcomes are rubinstein like in particular efficient however if it takes time to react then some delay can be supported this potential delay becomes arbitrarily large as reaction times increase journal of economic literature classification numbers c78 c72

reputation and equilibrium characterization in repeated games with conflicting interests a two person game is of conflicting interests if the strategy to which player one would most like to commit herself holds player two down to his minimax payoff suppose there is a positive prior probability that player one is a commitme nt type who will always play this strategy then player one will get a t least her commitment payoff in any nash equilibrium of the repeated game if her discount factor approaches one this result is robust against further perturbations of the informational structure and in striking contrast to the message of the folk theorem for games with incomplete information copyright 1993 by the econometric society

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

a bargaining model with incomplete information about time preferences etude d un jeu de negociation strategique sequentiel avec information incomplete caracterisation d une classe d equilibres sequentiels appeles equilibres sequentiels de negociation et demonstration de l unicite de cet equilibre

multilateral bargaining with concession costs this paper presents a new non cooperative approach to multilateral bargaining we consider a demand game with the following additional ingredients i there is an exogenous deadline by which bargaining has to end ii prior to the deadline players may sequentially change their demands as often as they like iii changing one s demand is costly and this cost increases as the deadline gets closer the game has a unique subgame perfect equilibrium prediction in which agreement is reached immediately and switching costs are avoided moreover this equilibrium is invariant to the particular order and timing in which players make demands this is important as multilateral bargaining models are sometimes too sensitive to these particular details in our context players with higher concession costs obtain higher shares of the pie their increased bargaining power stems from their ability to credibly commit to a demand earlier we discuss how the setup and assumptions are a reasonable description for certain real bargaining situations

a theory of bargaining deadlock abstract i study a dynamic one sided offer bargaining model between a seller and a buyer under incomplete information the seller knows the quality of his product while the buyer does not during bargaining the seller may receive an outside option the value of which depends on the quality of the product if the outside option is sufficiently important there is an equilibrium in which the buyer s belief about the product s quality stays constant and she continues to make the same randomized offer throughout the bargaining process as a result the equilibrium behavior produces an outcome path that resembles a bargaining deadlock and its resolution the equilibrium outcome exhibits bargaining delay that does not vanish even with frequent offers and the limiting delay may exist even without a static adverse selection problem under stronger parametric assumptions the equilibrium with deadlock is the only one in which behavior is monotonic in the buyer s belief

behavioral aspects of arbitrageurs in timing games of bubbles and crashes abstract this paper demonstrates the theoretical foundation that underlies the willingness of rational arbitrageurs to delay and reinforce the speculative attack the key assumptions are that there is a small probability that arbitrageurs are behavioral and never time the market of their own accord and it is uncertain whether arbitrageurs are behavioral or rational we model a stock market as a timing game in which arbitrageurs compete to react quickest we show that rational arbitrageurs are willing to ride the bubble for a long period we also characterize symmetric nash equilibria and show the sufficient condition for uniqueness

rent seeking and surplus destruction in unanimity bargaining abstract in non cooperative bargaining games in the tradition of rubinstein the proposer s bargaining power stems from the prospect of a delay in case of disagreement since players are impatient this delay is costly for everyone we consider a unanimity bargaining game in which the proposer can strategically choose the length of this delay we assume that the size of the surplus depends endogenously on the chosen length of the prospective delay intuitively the proposer faces the following trade off the more he exploits his proposer power the smaller is the surplus that can be divided one interpretation is that aggressive bargaining tactics hurt the fruitful cooperation among players and thus the surplus we characterize stationary equilibrium strategies and payoffs and obtain sharp predictions on the extent of surplus destruction the size of the social loss and the surplus allocation

bargaining with revoking costs abstract a simple two stage bilateral bargaining game is analyzed the players simultaneously demand shares of a unit size pie if the demands add up to more than one the players simultaneously choose whether to stick to their demand or accept the other s offer while both parties sticking to their offers leads to an impasse accepting a lower share than the original demand is costly for each party the set of pure strategy subgame perfect equilibria of the game is characterized for continuously differentiable payoff and cost functions strictly increasing in the pie share and the amount conceded respectively higher cost functions are shown to improve bargaining power the limit equilibrium prediction of the model as the cost functions are made arbitrarily high selects a unique equilibrium in the nash demand game that corresponds to a proportional bargaining solution of kalai 1977

bargaining reputation and equilibrium selection in repeated games with contracts consider a two person intertemporal bargaining problem in which players choose actions and offers each period and collect payoffs as a function of that period s actions while bargaining proceeds this can alternatively be viewed as an infinitely repeated game wherein players can offer one another enforceable contracts that govern play for the rest of the game theory is silent with regard to how the surplus is likely to be split because a folk theorem applies perturbing such a game with a rich set of behavioral types for each player yields a specific asymptotic prediction for how the surplus will be divided as the perturbation probabilities approach zero behavioral types may follow nonstationary strategies and respond to the opponent s play in equilibrium rational players initially choose a behavioral type to imitate and a war of attrition ensues how much should a player try to get and how should she behave while waiting for the resolution of bargaining in both respects she should build her strategy around the advice given by the nash bargaining with threats nbwt theory developed for two stage games in any perfect bayesian equilibrium she can guarantee herself virtually her nbwt payoff by imitating a behavioral type with the following simple strategy in every period ask for and accept nothing less than that player s nbwt share and while waiting for the other side to concede take the action nash recommends as a threat in his two stage game the results suggest that there are forces at work in some dynamic games that favor certain payoffs over all others this is in stark contrast to the classic folk theorems to the further folk theorems established for repeated games with two sided reputational perturbations and to the permissive results obtained in the literature on bargaining with payoffs as you go

bargaining under two sided incomplete information the unrestricted offers case chatterjee and samuelson chatterjee k l samuelson 1987 bargaining with two sided incomplete information an infinite horizon model with alternating offers rev econ stud 54 175 192 recently examined a noncooperative game theoretic bargaining model with two sided incomplete information and an infinite horizon results were obtained from the model with the help of restrictions on agents strategies this paper examines the model without these restrictions by doing so we will gain some insight into whether these results are robust in the sense that they do not depend upon the special structure of the model and hence might provide useful theoretical foundations for applied work we find that the basic results generalize as with the restricted model we find an equilibrium in which bargaining will proceed for a finite but endogeneously determined number of stages a terminal condition on the equilibrium sequence of agents beliefs determines the properties of the equilibrium and allows compar

evolutionary stability in a reputational model of bargaining a large and growing literature on reputation in games builds on the insight that the possibility of one or more players being boundedly rational can have significant effects on equilibrium behavior this literature leaves unexplained the presence of behavioral players in the first place as well as the particular forms of irrationality assumed and the population shares of the various types in this paper we endogenize departures from rationality on the basis of an evolutionary stability criterion under the assumption that rational players incur a cost which reflects the greater sophistication of their behavior this cost may be arbitrarily small within the context of a reputational model of bargaining we show that evolutionary stability necessitates the presence of behavioral players it also places significant joint restrictions on the set of behavioral types that can coexist their respective population shares and the long run population share of rational players

uncertainty and delay in bargaining this paper investigates the relationship between uncertainty and delay of agreement in the one sided offer bargaining model with two sided uncertainty where the seller makes offers we construct a weak stationary equilibrium in which different types of the seller charge different prices in every period we completely characterize the separating equilibrium by three regularity conditions and show that the time interval between offers converges to zero the seller s initial price offer in a separating equilibrium converges with probability 1 to the lowest valuation of the buyer if and only if the gain from trading is common knowledge we have witnessed a proliferation of sequential bargaining models that with a few remarkable exceptions fudenberg and tirole 1983 cramton 1984 and chatterjee and samuelson 1987 are based on models with one sided uncertainty the importance of studying bargaining models with one sided uncertainty is that despite their highly special informational structure we can derive valuable insights into the role of uncertainty in the delay in reaching an agreement while keeping the computational exercise tractable however the assumption of one sided uncertainty essentially excludes the situation where the buyer s actual reservation value is lower than the seller s actual reservation value though they are still engaged in the bargaining process the primary objective of this paper is to investigate the role of uncertainty about the gain from trading in a sequential bargaining model with two sided incomplete information in the models with one sided incomplete information important studies fudenberg levine and tirole 1985 and gul sonnenschein and wilson 1986 are often based on weak stationary equilibria where the equilibrium strategy of each player only depends upon the posterior conjecture about the other player and the previous period s offer although the importance of two sided uncertainty and the weak stationary equilibrium is well recognized previous research on sequential bargaining models has not combined the two features within the same framework studies on the models under two sided uncertainty have not focused on weak stationary equilibria for example cramton 1984 computes a specific sequential equilibrium with interesting properties in which the equilibrium strategies of both players depend upon histories in a rather complex fashion on the other hand it is only in models under one sided uncertainty that the weak stationary equilibrium has been extensively studied this paper computes and analyzes the weak stationary equilibria in a model under two sided uncertainty in order to investigate the effect of uncertainty on the delay in agreement we will extend the results from previous studies of one sided uncertainty models the computation of the equilibrium in models with two sided uncertainty is generally very complicated furthermore we must identify a sensible outcome if more than one equilibrium exists in the model to simplify the analysis we choose a standard bargaining

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

reputation in multi unit ascending auction with common values this paper considers a multi unit ascending auction with two players and common values a large set of equilibria in this model is not robust to a small reputational perturbation in particular if there is a positive probability that there is a type who always demands many units regardless of price then the model has a unique equilibrium payoff profile if this uncertainty is only on one side then the player who is known to be normal lowers her demand in order to stop the auction immediately at the reserve price hence her possibly committed opponent buys all the units she demands at the lowest possible price if the reputation is on both sides then a war of attrition emerges

bargaining with history dependent preferences abstract two impatient players bargain over a pie of size one according to the infinite alternating offers procedure players payoffs depend not only on the outcome but also on the process of the bargaining specifically they prefer impasse to any agreement that gives them lower discounted utility than would have been derived from accepting earlier offers we characterize the essentially unique subgame perfect equilibrium path which consists of gradual concessions the more patient players are the longer it takes them to reach an agreement when players become infinitely patient the efficiency loss is substantial yet the equilibrium division converges to the nash solution

audience costs and reputation in crisis bargaining in crisis bargaining literature it is conventional wisdom that the ability of generating higher audience costs is an advantage for a leader of a state however empirical studies show that democratic states use this mechanism only occasionally this paper formally shows that higher audience costs may be good or bad depending on 1 the benefit cost ratio of the crisis 2 initial probability of resolve and 3 how fast states generate audience costs with time in particular if the value of the prize over the cost of attacking is low or the initial probability of resolve is high enough then having greater ability to generate audience costs may undermine democratic states diplomatic success

bargaining under strategic uncertainty the role of second order optimism this paper shows that bargainers may reach delayed agreements even in environments where there is no uncertainty about payoffs or feasible actions under such conditions delay may arise when bargainers face direct forms of strategic uncertainty that is uncertainty about the opponent s play the paper restricts the nature of this uncertainty in two important ways first it assumes on path strategic certainty bargainers face uncertainty only after surprise moves second it assumes battigalli and siniscalchi s 2002 rationality and common strong belief of rationality rcsbr a requirement that bargainers are strategically sophisticated the main result characterizes the set of outcomes consistent with on path strategic certainty and rcsbr it shows that these assumptions allow for delayed agreement despite the fact that the bargaining environment is one of complete information the source of delay is second order optimism bargainers do not put forward good offers early in the negotiation process because they fear that doing so will cause the other party to become more optimistic about her future prospects

deals and delays firm level evidence on corruption and policy implementation times whether demands for bribes for particular government services are associated with expedited or delayed policy implementation underlies debates around the role of corruption in private sector development the grease the wheels hypothesis which contends that bribes act as speed money implies three testable predictions first on average bribe requests should be negatively correlated with wait times second this relationship should vary across firms with those with the highest opportunity cost of waiting being more likely to pay and facing shorter delays third the role of grease should vary across countries with benefits larger where regulatory burdens are greatest the data are inconsistent with all three predictions according to the preferred specifications ceteris paribus firms confronted with demands for bribes take approximately 1 5 times longer to get a construction permit operating license or electrical connection than firms that did not have to pay bribes and respectively 1 2 and 1 4

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

on delay in bargaining with one sided uncertainty recently attention has been given to a model of two person bargaining in which the parties alternate making offers and there is uncertainty about the valuation of one party the purpose of the analysis has been to identify delay to agreement with a screening process where agents with relatively lower valuations distinguish themselves by waiting longer to settle we point out a fundamental difficulty with this program by demonstrating that the assumptions used in the literature allow for delay only in so far as the time between offers is significant

indeterminacy of reputation effects in repeated games with contracts abstract we study whether allowing players to sign binding contracts governing future play leads to reputation effects in repeated games with long run players we proceed by extending the analysis of abreu and pearce 2007 by allowing for the possibility that different behavioral types may not be immediately distinguishable from each other given any prior over behavioral types we construct a modified prior with the same total weight on behavioral types and a larger support under which almost all efficient feasible and individually rational payoffs are attainable in perfect bayesian equilibrium thus whether reputation effects emerge in repeated games with contracts depends on details of the prior distribution over behavioral types other than its support

optimism delay and in efficiency in a stochastic model of bargaining abstract i study a bilateral bargaining game in which the size of the surplus follows a stochastic process and in which players might be optimistic about their bargaining power following yildiz 2003 i model optimism by assuming that players have different beliefs about the recognition process i show that the unique subgame perfect equilibrium of this game might involve inefficient delays i also show that these inefficiencies disappear when players can make offers arbitrarily frequently

reputational bargaining and deadlines i highlight how reputational concerns provide a natural explanation for deadline effects the high frequency of deals prior to a deadline in bargaining rational agents imitate the demands of obstinate behavioral types and engage in brinkmanship in the face of uncertainty about the deadline s arrival i also identify how surplus is divided when the prior probability of behavioral types is vanishingly small if behavioral types are committed to fixed demands outcomes converge to the nash bargaining solution regardless of agents respective impatience if behavioral types can adopt more complex demand strategies outcomes converge to the solution of an alternating offers game without behavioral types for the deadline environment

communication in multilateral bargaining one of the most robust phenomena in the experimental literature on multilateral bargaining is the failure of proposers to extract equilibrium rents however all previous experiments have overlooked the fact that outside the lab committee members are allowed to and do engage in sometimes intense communication processes prior to voting on a proposal we conduct an experimental test of the baron ferejohn model in which we allow committee members to engage in unrestricted cheap talk communication before a proposal is submitted we find that proposers extract a significantly higher share of resources when communication is allowed communication increases proposer power through two channels first it mitigates the uncertainty surrounding the amount a coalition member is willing to accept second it allows potential coalition members to compete for a place in the coalition by lowering this stated price

bayesian repeated games and reputation the folk theorem characterizes the subgame perfect nash equilibrium payoffs of an undiscounted or discounted infinitely repeated game with fully informed patient players as the feasible individually rational payoffs of the one shot game to which extent does the result still hold when every player privately knows his own payoffs under appropriate assumptions private values and uniform punishments the nash equilibria of the bayesian infinitely repeated game without discounting are payoff equivalent to tractable completely revealing equilibria and can be achieved as interim cooperative solutions of the initial bayesian game this characterization does not apply to discounted games with sufficiently patient players in a class of public good games the set of nash equilibrium payoffs of the undiscounted game can be empty while limit perfect bayesian nash equilibrium payoffs of the discounted game as players become infinitely patient do exist these equilibria share some features with the ones of multi sided reputation models