bilateral bargaining with externalities this paper provides an analysis of a non cooperative pairwise bargaining game between agents in a network we establish that there exists an equilibrium that generates a coalitional bargaining division of the reduced surplus that arises as a result of externalities between agents that is we provide a non cooperative justification for a cooperative division of a non cooperative surplus the resulting division is related to the myerson shapley value with properties that are particularly useful and tractable in applications we demonstrate this by examining buyer seller networks and vertical foreclosure

pricing the strategic value of putable securities in liquidity crises putable security holders have a de facto rst claim on the rm s liquid assets and can threaten to force solvent issuers to bear nancial distress costs their threatening power implies that the puts have a strategic value larger than their intrinsic value strategic value depends on the issuer s size potential distress costs and the distribution of put ownership relative to the rm s liquidity position the analysis of kmart s put induced crisis in 1995 and a calibration to observed secondary market yield reductions on poison put bonds shows that strategic value is an important determinant of payouts received by bondholders 2001 elsevier science s a all rights reserved

dynamic efficiency in overlapping generations models with stochastic production abstract we consider an overlapping generations economy as in diamond amer econ rev 55 1965 1126 1150 with stochastic production we define two types of efficiency for feasible production consumption allocations using first and second degree stochastic dominance we obtain a complete characterization of inefficiency of type i in this model for each given sequence of strictly concave utility functions for all generations the existence of a competitive equilibrium is proved it is shown that each competitive allocation is short run efficient of type ii

one to many bargaining when pairwise agreements are non renegotiable abstract we study a model where a central player the principal bargains bilaterally with each of several players the agents to create and share the surplus of a coalitional game it is known that if the payments that were previously agreed with each of the remaining agents are renegotiated in case any bilateral negotiation permanently breaks down then the shapley value is the unique efficient and individual rational outcome consistent with bilateral nash bargaining here we show that when instead the agreed payments cannot be renegotiated the outcome is also unique but it now coincides with the nucleolus of an associated bankruptcy problem we provide a strategic foundation for this outcome then we study how such renegotiation affects the principal s payoff according to the properties of the surplus function we find for example that renegotiation benefits the principal when agents are complements and it hurts him when they are substitutes situations with respectively increasing and decreasing marginal contributions

on the endogenous allocation of decision powers in federal structures abstract this paper provides a political economy explanation of the degree of centralization in economic policy making to determine which policies are to be centralized regions select representatives who then negotiate the degree of centralization and the regional cost shares of centrally decided policies we show that the resulting degree of centralization is suboptimally low voters strategically delegate to representatives who are averse to public spending and hence prefer decentralized decisions in order to reduce their region s cost share when spillovers are asymmetric strategic delegation is stronger at the periphery than at the center

models of stock returns a comparison in this paper a discrete mixture of normal distributions is proposed to explain the observed significant kurtosis fat tails and significant positive skewness in the distribution of daily rates of returns for a sample of common stocks and indexes stationarity tests on the parameter estimates of this discrete mixture of normal distributions model revealed significant differences in the mean estimates that can explain the observed skewness and significant differences in the variance estimates that can explain the observed kurtosis an alternative explanation for the observed fat tails is the symmetric student model the result of a comparison between the models is that the discrete mixture of normal distributions model has substantially more descriptive validity than the student model for many years both financial economists and statisticians have been concerned with the description of stock market returns the form of the distribution of stock returns is a crucial assumption for mean variance portfolio theory theoretical models of capital asset prices and the prices of contingent claims for example understanding the behavior of the variance is essential to option pricing models empirical tests of asset pricing models and the efficient markets hypothesis draw statistical inferences that are also conditional on distributional assumptions the most convenient assumption for financial theory and empirical methods is that the distribution of security rates of return be multivariate normal with parameters that are stationary over time since the normal distribution is stable under addition any arbitrary portfolio of stocks will also be normally distributed with the additional assumption of risk aversion mean variance theory follows furthermore the assumptions of normality and parameter stationarity are required for most of the econometric techniques typically used in empirical research tests of the normality hypothesis on the daily returns of the dow jones industrial stocks by fama 121 revealed more kurtosis fatter tails than that predicted from a sample of independent and identically distributed normal variates fama concluded from this evidence that the distribution of price changes conforms better to the stable paretian distribution with characteristic exponent

multiple equilibrium overnight rates in a dynamic interbank market game abstract we analyse a two period model of the interbank market i e the market where banks trade liquidity we assume that banks do not take the interbank interest rate as given but instead negotiate on interest rates and transaction volumes with each other the solution concept applied is the shapley value we show that there are a multiplicity of average equilibrium interest rates of the first period so that the average interest rate in this period does not convey any information on the expected liquidity situation on the interbank market as the banks control not only the transaction volumes but also the interest rates they can leave the interest rates constant and adjust the transaction volumes when for example a liquidity deficit becomes more likely

dynamic processes of social and economic interactions on the persistence of inefficiencies an economy with a finite number of agents and a finite number of states is considered an exogenous institutional rule prescribes which moves from one state to another are feasible to each coalition at each time an agent is called to act with some exogenous probability and he chooses a coalition a feasible new state to move the economy to and side payments between the agents in the coalition the setup can be applied to various dynamic processes of social and economic interactions such as legislative bargaining coalition formation or exchange economies whenever agents are unable to write long term contracts but are otherwise unconstrained both in their ability to write arbitrary spot contracts and in their ability to collude there can be long run inefficiencies with cycles or inefficient steady states however when agents are sufficiently patient the initial state from which the process starts plays no role in the long run moreover when there exists an efficient state that is free of negat

coalition and party formation in a legislative voting game we examine a legislative voting game where decisions are being made over both ideological and distributive dimensions and legislators preferences are separable over the two dimensions in equilibrium legislators prefer to make proposals for the two dimensions together rather than offering sequential proposals on the two dimensions separately the equilibria exhibit interaction between the ideological and distributive dimensions and in any equilibrium there is a positive probability that a proposal is made and approved which excludes the median legislator as defined over the ideological dimension in contrast with a game where no distributive decision is being made moreover in any stationary equilibrium there is more than one ideological decision that has a positive probability of being proposed and approved we show that legislators can gain from forming political parties and consider examples where predictions can be made about the composition of parties we discuss the impact of political parties on the outcome

bargaining foundations of shapley value1 a transferable utility economy in which each agent holds a resource which can be used in combination with the resources of other agents to generate value according to the characteristic function v is studied using a dynamic model of bargaining the main theorem establishes that the payoffs associated with efficient equilibria converge to the agents shapley values as the time between periods of the dynamic game goes to zero in addition it is demonstrated that an efficient equilibrium exists and is unique when an additivity condition is satisfied to demonstrate the sensitivity of the solution to the institutional detail we modify the model to allow for partnerships and show that the shapley value is no longer achieved

a theory of endogenous coalition structures consider an environment with widespread externalities and suppose that bind ing agreements can be written we study coalition formation in such a setting our analysis proceeds by defining on a partition function an extensive form bargaining game we establish the existence of a stationary subgame perfect equilibrium for such a game our main results are concerned with the characterization of equilib rium coalition structures we develop an algorithm that generates under certain conditions an equilibrium coalition structure our characterization results are especially sharp for symmetric partition functions in particular we provide a uniqueness theorem and apply our results to a cournot oligopoly journal of economic literature classification numbers c71 c72 c78 d62 q 1999 academic press

majority rules and incentives a club s majority rule defines the number of members that must approve a policy proposed to replace the status quo since the majority rule thus dictates the extent to which winners must compensate losers it also determines the incentives to invest in order to become a winner of anticipated projects if the required majority is large members invest too little because of a holdup problem if it is small members invest too much in order to become a member of the majority coalition to balance these opposing forces the majority rule should increase in the project s value and the club s enforcement capacity but decrease in the heterogeneity in preferences externalities can be internalized by adjusting the rule with heterogeneity in size or initial conditions votes should be appropriately weighted or double majorities required

marginal contributions and externalities in the value our concern is the extension of the theory of the shapley value to problems involving externalities using the standard axiom systems behind the shapley value for an arbitrary exogenous coalition structure leads to the identification of bounds on players payos around an externality free value in endogenizing the coalition structure we analyze a two stage process of coalition formation in whose second stage our axiomatic results are applied we find reasons to explain inecient coalition structures and provide sucient conditions for eciency

bargaining and value we present and analyze a model of noncooperative bargaining among n participants applied to situations describable as games in coalitional form this leads to a unified solution theory for such games that has as special cases the shapley value in the transferable utility tu case the nash bargaining solution in the pure bargaining case and the recently introduced maschler owen consistent value in the general nontransferable utility ntu case moreover we show that any variation in a certain class of our bargaining procedure which generates the shapley value in the tu setup must yield the consistent value in the general ntu setup

forming coalitions and the shapley ntu value a simple protocol for coalition formation is presented first an order of the players is randomly chosen then a coalition grows by sequentially incorporating new members in this order the protocol is studied in the context of non transferable utility ntu games in characteristic function form if weighted utility transfers are feasible when everybody cooperates then the expected subgame perfect equilibrium payoff allocation anticipated before any implemented game is the shapley ntu value

collusion exclusion and inclusion in random order bargaining this paper examines the profitability of three types of integration in a cooperative game solved by a random order value e g the shapley value collusion between players i and j is a contract merging their resources in the hands of one of them say i this contract can be represented as a combination of exclusion which lets i exclude j s resource but not use it himself and inclusion which lets i use j s resource but not exclude j from it this representation yields a third difference condition on the characteristic function that determines the profitability of collusion generalizing existing results for specific games namely collusion is profitable unprofitable when the complementarity of the colluding players is reduced increased by other players

bargaining one dimensional social choices we analyze bargaining over the one dimension characteristic of a public good among n impatient players when decisions require q favorable votes q 2 stationary subgame perfect equilibrium strategies are characterized for all games with deterministic protocol we provide a monotonicity condition satisfied by all single peak strictly quasi concave and concave utilities that assures uniqueness for every q whenever player s utilities are symmetric around the peak without symmetry the monotonicity condition assures uniqueness for qualified majorities q n 2 provided that agents are sufficiently patient and utilities satisfy an additional regularity condition asymptotic uniqueness is assured for qualified majorities by imposing only the monotonicity condition

optimal capital structure and bankruptcy choice dynamic bargaining versus liquidation abstract we model a firm s optimal capital structure decision in a framework in which it may later choose to enter either chapter 11 reorganization or chapter 7 liquidation creditors anticipate equityholders ex post reorganization incentives and price them into the ex ante credit spreads using a realistic dynamic bargaining model of reorganization we show that the off equilibrium threat of costly renegotiation can lead to lower leverage even with liquidation in equilibrium if reorganization is less efficient than liquidation the added option of reorganization can actually make equityholders worse off ex ante even when they liquidate on the equilibrium path

interpersonal authority in a theory of the firm this paper develops a theory of the flrm in which a flrm s centralized asset ownership and low powered incentives give a manager interpersonal authority over employees in a world with difiering priors the paper derives such interpersonal authority as an equilibrium phenomenon one key result is that a manager s control over critical assets through its efiect on the level of outside options allows the manager to order employees what to do the paper thus provides microfoundations for the idea that bringing a project inside a flrm gives the manager authority over that project while in the process explaining concentrated asset ownership low powered incentives and centralized authority as typical characteristics of flrms it also leads to a new perspective on the flrm as a legal entity and building on the insights of a parallel paper to a new theory for flrm boundaries based on the idea of break up a key feature of the latter theory is that flrm boundaries matter even though both ex ante investments and ex post actions are perfectly contractible

coalition formation and bargaining protocols a review of the literature this paper offers a review of the vast literature regarding bargaining and coalition formation this topic has been generally described as the attempt to provide strategic foundations to cooperative solution concepts it can therefore be seen as the linking ring between the non cooperative and the cooperative game theoretic approach to coalition formation its central role in economic theory and its relatively long history that goes back to the nash program have fostered a large academic production including surveys nonetheless this paper will focus on an aspect that is often neglected in the dedicated surveys the specificities of the bargaining protocols leading to different outcomes although generally downgraded to the rank of details the differences in bargaining protocols even when minor can cause significant changes in fundamental aspects such as the possibility to reach full cooperation the distribution of final pay offs and the time taken to reach an agreement focused on externalities free games therefore on bargaining protocols sustaining solution concepts for cooperative games in characteristic function form the paper aims at providing a brief but exhaustive review of the topic that could result in a very useful tool for any researcher approaching the subject of coalitional bargaining

bidding for the surplus a non cooperative approach to the shapley value abstract we propose a simple mechanism to determine how the surplus generated by cooperation is to be shared in zero monotonic environments with transferable utility the mechanism consists of a bidding stage followed by a proposal stage we show that the subgame perfect equilibrium outcomes of this mechanism coincide with the vector of the shapley value payoffs we extend our results to implement the weighted shapley values finally we generalize our mechanism to handle arbitrary transferable utility environments the modified mechanism generates an efficient coalition structure and implements the shapley values of the super additive cover of the environment journal of economic literature classification numbers c71 c72

bargaining in committees as an extension of nash s bargaining theory abstract this paper addresses the following issue if a set of agents bargain on a set of feasible alternatives in the shadow of a voting rule that is any agreement can be enforced if a winning coalition supports it what general agreements are likely to arise in other words what influence can the voting rule used to settle possibly nonunanimous agreements have on the outcome of consensus we model the situation as an extension of the nash bargaining problem in which an arbitrary voting rule replaces unanimity in this setting a natural extension of nash s solution is characterized

equilibrium in a market with sequential bargaining this paper considers a market where pairs of agents who are interested in carrying out a transaction are brought together by a stochastic process and upon meeting initiate a bargaining process over the terms of the transaction the basic bargaining problem is treated with the strategic approach the paper derives the steady state equilibrium agreements analyzes their dependence on market conditions such as the relative numbers of agents of different types and discusses their relations with the competitive equilibrium outcome and other results in the search equilibrium literature this paper considers a market that operates in the following way pairs of agents who have mutual interest in carrying out a transaction are brought together by a stochastic process when two agents meet they initiate a bargaining process over the terms of the transaction if two agents reach an agreement a transaction takes place and they leave the market of course the bargaining positions and hence the agreement reached in any particular meeting will be affected by the conditions prevailing in the market these will include the chances that each of the negotiating parties have of meeting other partners in the event that the agreement in the current negotiations is delayed also the expected length of time required to achieve an alternative transaction and the expected behavior of alternative partners the study of such a market mechanism is of interest for two reasons firstly it captures some realistic aspects of the trade in certain specific markets e g asset markets such as housing and some labor markets secondly it contributes to an understanding of the micro mechanisms of price formation and their role in shaping market outcomes in both cases the features studied are largely neglected in the traditional market equilibrium analyses the related literature includes the articles by diamond 4 5 diamond and maskin 6 mortensen 8 9 and zusman and bell 13 these articles consider markets of the type described above in which transactions are concluded at pairwise meetings of agents the major difference between our work and these articles is in the approach to the basic bargaining problem in the cited articles it is assumed that a meeting is concluded with an instantaneous agreement which divides the associated surplus in an arbitrary predetermined way when the surplus is assumed to be divided equally the division rule is in fact nash s axiomatic bargaining solution in contrast the present paper treats the basic bargaining problem with the strategic approach see rubinstein 19 which constitutes an attempt to look into the bargaining black box this approach explicitly models the time dimension of the bargaining process describes in detail the bargaining procedure and justifies the agreement as a perfect equilibrium in

noncooperative foundations of bargaining power in committees and the shapley shubik index abstract in this paper we explore the noncooperative foundations of the bargaining power that a voting rule gives to each member of a committee that bargains in search of consensus over a set of feasible agreements under a voting rule assuming complete information we model a variety of bargaining protocols and investigate their stationary subgame perfect equilibria we show how the shapley shubik index and other power indices can be interpreted as measures of bargaining power that appear in this light as limit cases

intra firm bargaining and shapley values we study two wage bargaining games between a firm and multiple workers we revisit the bargaining game proposed by stole and zwiebel we show that in the unique subgame perfect equilibrium the gains from trade captured by workers who bargain earlier with the firm are larger than those captured by workers who bargain later as well as larger than those captured by the firm the resulting equilibrium payoffs are different from those reported in stole and zwiebel as they are not the shapley values we propose a novel bargaining game the rolodex game which follows a simple and realistic protocol in the unique no delay subgame perfect equilibrium of this game the payoffs to the firm and to the workers are their shapley values

an ordinal shapley value for economic environments abstract we propose a new solution concept to address the problem of sharing a surplus among the agents generating it the problem is formulated in the preferences endowments space the solution is defined recursively incorporating notions of consistency and fairness and relying on properties satisfied by the shapley value for transferable utility tu games we show a solution exists and call it the ordinal shapley value osv we characterize the osv using the notion of coalitional dividends and furthermore show it is monotone and anonymous

risk aversely efficient random variables characterization and an application to growth under uncertainty abstract consider a problem of choice from a set r of multivariate random variables let us examine only efficient elements of r which are optimal choices of risk averse decision makers whose aim is to maximize expected utility over r we obtain a price characteristic of all risk aversely efficient random variables in r this result has been applied to multi sector optimal growth model to obtain a characterization by competitive prices of all risk aversely efficient stationary consumption programs

values for cooperative games with incomplete information an eloquent example myerson s 1984 extension of the lambda transfer value to cooperative games with incomplete information focus among other things on the strength of the incentive constraints at the solution for determining the power of coalitions we construct an intuitive three player game where the player whose only contribution is to partly release the two other players from the incentive constraints they face when they cooperate receives a zero payoff according to myerson s solution on the contrary the random order arrival procedure attributes a strictly positive payoff to him our example is thus an analog of the banker game of owen 1972 that was designed for evaluating the lambda transfer value under complete information asymmetric information now takes up the role that was formerly attributed to the lack of transferability of utilities

a theory of dynamic oligopoly ii price competition kinked demand curves and edgeworth cycles we provide game theoretic foundations for the classic kinked demand curve equilibrium and edgeworth cycle we analyze a model in which firms take turns choosing prices the model is intended to capture the idea of reactions based on short run commitment in a markov perfect equilibrium mpe a firm s move in any period depends only on the other firm s current price there are multiple mpe s consisting of both kinked demand curve equilibria and edgeworth cycles in any mpe profit is bounded away from the bertrand equilibrium level we show that a kinked demand curve at the monopoly price is the unique symmetric renegotiation proof equilibrium when there is little discounting we then endogenize the timing by allowing firms to move at any time subject to short run commitments we find that firms end up alternating thus vindicating the ad hoc timing assumption of our simpler model we also discuss how the model can be enriched to provide explanations for excess capacity and market sharing keiiwords tacit collusion markov perfect equilibrium kinked demand curve edgeworth cycle excess capacity market sharing endogenous timing

proposal rights and political power in a canonical model of sequential collective bargaining over a divisible good we show that equilibrium expected payoffs are not restricted by players voting rights or their impatience for all monotonic voting rules and discount factors and for all divisions of the good among players there exists a stationary proposal making rule such that this division represents players expected payoffs in a stationary subgame perfect nash equilibrium in pure strategies the result highlights the significance of proposal rights in determining political power in collective deliberations t he purpose of this article is to further our understanding of political power in a committee environment we consider the problem of a group of two or more agents who must split a fixed divisible good agents cannot use physical force to divide this good our goal is to clarify the role and relative significance of other features of the political environment such as voting rights proposal rights agents patience etc in determining political power following shapley and shubik 1954 we gauge political power in terms of expected outcomes rather than a priori equate it with individual prerogatives 1 in that spirit political power is the share of the divisible good that agents can expect to obtain when their behavior conforms to an appropriately defined equilibrium notion 2 we model committee interaction using a canonical sequential bargaining game in each period a member of the committee is recognized with some probability that is fixed across periods and proposes a division of the good committee members then vote on the proposal if the proposal is approved in accordance with the underlying voting rule the proposed division is implemented and the

finite horizon bargaining and the consistent field this paper explores the relationships between noncooperative bargaining games and the consistent value for non transferable utility ntu cooperative games a dynamic approach to the consistent value for ntu games is introduced the consistent vector field the main contribution of the paper is to show that the consistent field is intimately related to the concept of subgame perfection for finite horizon noncooperative bargaining games as the horizon goes to infinity and the cost of delay goes to zero the solutions of the dynamic system associated to the consistent field characterize the subgame perfect equilibrium payoffs of the noncooperative bargaining games we show that for transferable utility hyperplane and pure bargaining games the dynamics of the consistent field converge globally to the unique consistent value however in the general ntu case the dynamics of the consistent field can be complex an example is constructed where the consistent field has cyclic solutions moreover the finite horizon subgame perfect equilibria do not approach the consistent value

the coalitional nash bargaining solution the coalitional nash bargaining solution is defined to be the core allocation for which the product of players payoffs is maximal we consider a non cooperative model with discounting in which one team may form and every player is randomly selected to make a proposal in every period the grand team consisting of all players generates the largest surplus but a smaller team may form we show that as players get more patient if an efficient and stationary equilibrium exists it must deliver payoffs that correspond to the coalitional nash bargaining solution we also characterize when an efficient and stationary equilibrium exists which requires conditions that go beyond the nonemptiness of the core

bargaining with asymmetric threat points abstract the 2 person version of hart and mas colell econometrica 64 1996 357 is studied reinterpreted as a bargaining game with asymmetric threat points multiplicity of stationary subgame perfect equilibria is necessary for multiplicity of subgame perfect equilibria and depends on risk aversion and the point constructed with the payoff that responders get if breakdown occurs

harsanyi values of large economies nonequivalence to competitive equilibria abstract we consider economies with many agents and compare the competitive equilibria and the value allocations of the resulting coalitional games in particular we provide a smooth and robust example where the value principle does not hold for the harsanyi ntu value there is a unique competitive equilibrium which however does not belong to the nonempty set of harsanyi value allocations journal of economic literature classification numbers c71 d51

reinterpreting the kernel the reduced game relevant for the consistency of the prekernel is used to reinterpret this solution concept in a way that makes it independent of interpersonal utility comparisons based on this reinterpretation a non cooperative model is presented that yields in stationary equilibria the prekernel kernel for the class of monotonic transferable utility games next we apply the same non cooperative model to more general coalitional games for pure bargaining problems the model yields the nash solution for general non transferable utility games a natural extension of the prekernel arises thus the prekernel is obtained as the set of payoffs where the relevant bargaining range between every pair of players is split in half journal of economic literatureclassification numbers c71 c72 c78

auctioning and selling positions a non cooperative approach to queueing conflicts abstract complementary to the axiomatic and mechanism design studies on queueing problems this paper proposes a strategic bargaining approach to resolve queueing conflicts given a situation where players with different waiting costs have to form a queue in order to be served they firstly compete with each other for a specific position in the queue then the winner can decide to take up the position or sell it to the others in the former case the rest of the players will proceed to compete for the remaining positions in the same manner whereas for the latter case the seller can propose a queue with corresponding payments to the others which can be accepted or rejected in this paper we show that when the players are competing for the first position in the queue then the subgame perfect equilibrium outcome of the corresponding mechanism coincides with the well known maximal transfer rule while an efficient queue is always formed in equilibrium we also argue that changing the mechanism so that the players compete for the last position implements the minimal transfer rule the analysis discovers a striking relationship between pessimism and optimism in this type of decision making

a noncooperative view of consistent bankruptcy rules abstract we introduce a game form that captures a noncooperative dimension of the consistency property of bankruptcy rules any consistent and monotone rule is fully characterized by a bilateral principle and consistency like the consistency axiom our game form together with a bilateral principle yields the corresponding consistent bankruptcy rule as a result of a unique outcome of nash equilibria the result holds for a large class of consistent and monotone rules including the constrained equal award the propositional rule and many other well known rules moreover all of the subgame perefect equilibria are coalition proof in the associated game in strategic form journal of economic literatureclassification numbers c72 and d63

legislative bargaining under weighted voting organizations often distribute resources through weighted voting we analyze this setting using a non cooperative bargaining game based on the baron ferejohn 1989 model unlike analyses derived from cooperative game theory we find that each voter s expected payoff is proportional to her voting weight an exception occurs when many high weight voters exist as low weight voters may expect disproportionately high payoffs due to proposal power the model also predicts that ex post the coalition formateur the party chosen to form a coalition will receive a disproportionately high payoff using data from coalition governments from 1946 to 2001 we find strong evidence ofsuch formateur effects

eliciting information from a committee abstract the paper addresses the mechanism design problem of eliciting truthful information from a committee of informed experts who collude in their information disclosure strategies it is shown that under fairly general conditions full information disclosure is possible if and only if the induced outcome is pareto undominated for the committee members

non cooperative bargaining and union formation we study a union formation decision problem when workers consist of two groups distinguished by different productivities workers may form either a joint union or two separate unions the whole decision process is modelled as an extensive form bargaining game workers form a joint union when the sizes or productivities of the groups are similar in the first case there is a wage differential which is more less than proportional to the productivity difference if the size of the more productive is smaller larger than that of the less productive in the second case there is no wage differential in this paper we study a union formation decision problem when workers consist of two groups distinguished by different productivities they may form either a joint union or two separate unions depending on the relative size and productivity of the two groups the whole decision process is modelled as an extensive form bargaining game in which the two groups of workers bargain with each other as well as with a firm the labour market is sharply distinguished from the goods market by the widespread practice of collective bargaining usually several groups of workers with different characteristics for example skill level or geographical location are represented as a single unit and or several employers form a single bargaining unit against a giant union this multiplicity of bargaining units creates a complicated bargaining structure and makes the outcome hard to analyse the purpose of this paper is to provide a model which captures this complexity and at the same time clarifies the underlying structure of bargaining power although economists have been aware of the multiplicity problem for a long time it has been received little rigorous theoretical treatment until recently davidson 1985 examined the possible gains that can be obtained by trade unions through joint bargaining in an oligopolistic industry there is a positive externality due to the fact that a higher wage rate in one firm generates a larger demand hence a higher wage in competing firms when a joint union is organized these externalities are internalized to the benefit of workers horn and wolinsky 1985 investigated the equilibrium pattern of unionization in an industry where a firm employs two types of workers they found that workers tend to form a single union when the two types are substitutes in the sense that the incremental contribution of one group to the firm s revenue is decreasing with respect to the size of the other group since workers bargaining power comes from the loss that they can

bargaining and cooperation in strategic form games in this paper we view bargaining and cooperation as an interaction superimposed on a game in strategic form a multistage bargaining procedure for n players the proposer commitment procedure is presented it is inspired by nash s two player variable threat model a key feature is the commitment to threats we establish links to classical cooperative game theory solutions such as the shapley value in the transferable utility case however we show that even in standard pure exchange economies the traditional coalitional function may not be adequate when utilities are not transferable jel c70 c71 c78 d70

secession and value abstract a model with random proposals where secession of coalitions is the only threat yields exploitative allocations if proposals for coalition s involve randomization the responders pay off vector consists of shapley values for coalition sizes ranging from 1 to s 1

a comment on the nash program and the theory of implementation abstract the nash program for cooperative games is made compatible with the framework of the theory of implementation it is shown that the core is the only major cooperative solution that is maskin monotonic the mechanisms in the nash program are adapted into our model closer to that of the theory of implementation

efficiency in economic growth models under uncertainty abstract we consider an infinite horizon economy with stochastic production and consumption we define efficiency of feasible production consumption programs without referring to a particular utility function using stochastic ordering a complete characterization of inefficiency of type i is obtained equivalence between type ii efficiency and a certain optimality notion when decision makers are risk averse is proved when the number of states of nature is finite at each date

on the convergence to the nash bargaining solution for action dependent bargaining protocols we consider a non cooperative multilateral bargaining game and study an action dependent bargaining protocol that is the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected an important example is the frequently studied rejector becomes proposer protocol we focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player we consider the limit as the bargaining friction vanishes in case no player has a positive probability to propose conditional on his rejection each player receives his utopia payoff conditional on being recognized otherwise equilibrium proposals of all players converge to a weighted nash bargaining solution where the weights are determined by the probability to propose conditional on one s own rejection

bargaining and bargaining sets abstract we argue that in exchange economies various versions of the bargaining set cannot be implemented in nash equilibrium we then propose an extensive form mechanism that exactly implements the aumann davis maschler bargaining set in subgame perfect equilibrium the mechanism corresponds closely to the description of the bargaining set and respects feasibility in and out of equilibrium journal of economic literature classification numbers c71 c72 c78 d51

bounds and prices of currency cross rate options abstract this paper derives the pricing bounds of a currency cross rate option using the option prices of two related dollar rates via a copula theory and presents the analytical properties of the bounds under the gaussian framework our option pricing bounds are useful because 1 they are general in the sense that they do not rely on the distribution assumptions of the state variables or on the selection of the copula function 2 they are portfolios of the dollar rate options and hence are potential hedging instruments for cross rate options and 3 they can be applied to generate bounds on deltas the empirical tests suggest that there are persistent and stable relationships between the market prices and the estimated bounds of the cross rate options and that our option pricing bounds obtained from the market prices of options on two dollar rates and the historical correlation of two dollar rates are highly informative for explaining the prices of the cross rate options moreover the empirical results are consistent with the predictions of the analytical properties under the gaussian framework and are robust in various aspects

noncooperative foundations of the nucleolus in majority games abstract this paper studies coalition formation payoff division and expected payoffs in a divide the dollar by majority rule game with random proposers a power index is called self confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector unlike the shapley value and other commonly used power indices the nucleolus has this property the proof uses a weak version of kohlberg s siam j appl math 20 1971 62 balancedness result reinterpreting the balancing weights as probabilities in a mixed strategy equilibrium

bidding for surplus in network allocation problems in this paper we study non cooperative foundations of network allocation rules we focus on three allocation rules the myerson value the position value and the component wise egalitarian solution for any of these three rules we provide a characterization based on component efficiency and some balanced contribution property additionally we present three mechanisms whose equilibrium payoffs are well defined and coincide with the three rules under consideration if the underlying value function is monotonic non monotonic value functions are shown to deal with allocation rules applied to monotonic covers the mechanisms are inspired by the implementation of the shapley value by perez castrillo and wettstein bidding for the surplus a non cooperative approach to the shapley value j econ theory 100 2 2001 274 294

rational bargaining in games with coalitional externalities this paper provides a flexible strategic framework to analyze bargaining and values in environments with coalitional externalities within this framework we propose a new value that extends the shapley value to partition function form games the so called rational belief shapley rbs value we investigate the strategic foundation of the rbs value by constructing an implementation mechanism this mechanism extends existing models of multilateral bargaining by allowing players a higher degree of freedom to form coalitions the same framework of bidding and renegotiation allows for natural variations of the rbs mechanism in this way alternative shapley like values are obtained and a unified platform to analyze and compare these solutions is provided

on the asymptotic uniqueness of bargaining equilibria abstract this note reexamines the connection between the asymmetric nash bargaining solution and the equilibria of strategic bargaining games a first example shows non convergence to the asymmetric nash bargaining solution a second example demonstrates the possibility of multiple limits

an implementation of the owen value abstract we present an implementation of the owen value owen 1977 essays in mathematical economics and game theory pp 76 88 inspired by the bidding mechanism introduced by perez castrillo and wettstein 2001 j econ theory 100 274 294 the idea is the following first players of each coalition play the bidding mechanism trying to obtain the resources of the coalition later players who obtained the resources play the bidding mechanism in order to share the surplus

insider trading abnormal return and preferential information supervising through a probabilistic model abstract the enforcement of the ban on insider trading requires an evaluation of the disgorgement i e the capital gain of the insider trader who takes advantage of the exploitation of preferential information an initial step forward on this topic has been taken by the sec the united states securities and exchange commission which has developed a quantitative procedure based on the event study methodology this paper develops an adaptation of this procedure for the italian market and explains the limits of these methodologies in the analysis of the insider trading phenomenon in particular it emerges that the econometric approach cannot be applied to all insider trading schemes in fact in order to work out statistically significant results it relies on a series of assumptions such as the existence of a robust reference market index or the availability of long time series data for this reason a new procedure for computing the economic value of the information exploited by the insider based on a probabilistic approach has also been developed this methodology overcomes the issues connected to the event study procedure and can be applied by construction to all insider trading schemes and not only to the simplest ones in fact the model parameters are defined by using the trading strategy of the single insider thus if insider trading takes place the model is able to offer a disgorgement computation hence by hypotheses of its construction it is able to detect the difference between insiders and followers the new procedure has been adopted by consob and has been presented to the judicial system which is in charge of inflicting the fine

a theory of strategic venture investing some venture capital investors seek purely financial gains while others such as corporations also pursue strategic objectives the paper examines a model where a strategic investor can achieve synergies but can also face a conflict of interest with the entrepreneur if the start up is a complement to the strategic partner it is optimal to obtain funding from the strategic investor if the start up is a mild substitute the entrepreneur prefers an independent venture capitalist with a strong substitute syndication becomes optimal such that the independent venture capitalist is the active lead investor and the strategic partner a passive co investor the expected returns for the entrepreneur are nonmonotonic lowest for a mild substitute and higher for a strong substitute as well as for a complement the paper also explains why a strategic investor often pays a higher valuation than an independent venture capitalist

transparency complementarity and holdout this paper characterizes the conditions under which holdout i e bargaining inefficiency may or may not be significant in a two sided one buyer many seller model with complementarity we address this problem in a very general setup with a bargaining protocol that is symmetric and allows for both publicly observable as well as secret offers and a technology that allows for variable degrees of complementarity the central insight is that the transparency of the bargaining protocol formalized by whether offers are publicly observable or secret as well as the extent of complementarity play a critical role in generating efficiency even with perfect complementarity holdout seems to be largely resolved whenever the bargaining protocol is public but not if it is secret further irrespective of the bargaining protocol holdout is resolved if the marginal contribution of the last seller is not too large

a general distribution for describing security price returns this paper introduces a generalized distribution called the gb2 distribution for describing security returns the distribution is extremely flexible containing a large number of well known distributions such as the lognormal log t and log cauchy distribu tions as special or limiting cases and allowing large even infinite higher moments this flexibility allows a direct representation of different degrees of fat tails in the distribution the properties of the gb2 make it useful in empirical estimation of security returns and in facilitating the development of option pricing models and other models that depend on the specification and mathematical manipulation of distributions copyright 1987 by the university of chicago

a noncooperative theory of coalitional bargaining the authors explore a sequential offers model of n person coalitional bargaining with transferable utility and with time discounting their focus is on the efficiency properties of stationary equilibria of strictly superadditive games when the discount factor delta is sufficiently large it is shown that delay and the formation of inefficient subcoalitions can occur in equilibrium the latter for some or all orders of proposer however efficient stationary equilibrium payoffs converge to a point in the core as delta approaches one strict convexity is a sufficient condition for there to exist an efficient stationary equilibrium payoff vector for sufficiently high delta

a noncooperative view of coalition formation and the core a noncooperative implementation of the core is provided for games with transferable utility the implementation obtained here is meant to reflect the standard motivation for the core as closely as possible in the model proposed time is continuous this idealized treatment of time is most amenable for capturing an essential feature of the core there is always time to reject a noncore proposal before it is consumated

one dimensional bargaining we study a model of multilateral bargaining over social outcomes represented by the points in the unit interval the acceptance or rejection of a proposal is determined by an acceptance rule represented by the collection of decisive coalitions the focus of the paper is on the asymptotic behavior of subgame perfect equilibria in stationary strategies as the players become infinitely patient we show that along any sequence of stationary subgame perfect equilibria the social acceptance set collapses to a point this point called the limit of bargaining equilibria is independent of the sequence of equilibria and is uniquely determined by the set of players the utility functions the recognition probabilities and the acceptance rule the central result of the paper is a characterization of the limit of bargaining equilibria as a unique zero of the characteristic equation

monotonic solutions to general cooperative games etude de jeux cooperatifs qui sont des jeux a plusieurs joueurs mis sous la forme de coalition dans lesquels l utilite n est pas supposee etre transferable

strategic delegation and voting rules abstract the selection of political representatives depends on the political system principals such as voters or districts may benefit by strategically electing representatives different from themselves while a status quo biased delegate may be a better negotiator an enthusiastic representative has a better chance of being included in the majority coalition a larger majority requirement leads to conservative delegation and hence a status quo bias a poor minority protection does the opposite through strategic delegation the political system also determines whether centralization or decentralization is beneficial

the bootstrap approach for testing skewness persistence this study presents a new methodology for testing changes in skewness between time periods or samples using the bootstrap method a monte carlo simulation experiment was conducted to compare the effectiveness of the bootstrap method with the method suggested by lau wingender and lau 1989 to test skewness persistence the results show the bootstrap method to be more powerful than the other method the bootstrap method was also used to determine the persistence of skewness in stock returns the results show that in a large percentage of stocks skewness persists over time

bargaining delay under partial breakdowns and externalities abstract we consider a noncooperative coalitional bargaining game where partial breakdowns such as the rejecter of a proposal exiting from the game take place with a positive probability and externalities accompany the formation of coalitions we present an example in which there exists a stationary subgame perfect equilibrium sspe such that a bargaining delay occurs we also show that under no partial breakdowns or no externalities delay does not occur in any sspe

a theory of gradual coalition formation we study noncooperative multilateral bargaining games based on underlying tu games in which coalitions can renegotiate their agreements we distinguish between models in which players continue to bargain after implementing agreements reversible actions and models in which players who implement agreements must leave the game irreversible actions we show that renegotiation always results in formation of the grand coalition if actions are reversible but that the process may otherwise end with smaller coalitions on the other hand we show that the grand coalition cannot form in one step if the core of the game is empty irrespective of the reversibility of actions agreements between players form the basis of much that game theory seeks to explain there are obviously many useful ways to categorize such agreements in multilateral negotiations that is with more than two participants it seems natural to distinguish between cases in which the coalition forms in one step and those in which the coalition grows to its eventual size by attracting new members thus recipients of marshall aid collectively agreed to american terms at the ceec in 1947 whereas a strict subset of these countries agreed to the schuman plan in 1950 with the other current members joining the eu over time similarly negotiations on climate change culminated in universal agreement at rio in 1992 whereas india and china only agreed to reduce cfc emissions in london in 1990 after other countries had signed up to the montreal protocol finally un security council resolution 242 urged that a multilateral conference be set up to establish a comprehensive settlement in the middle east whereas the process initiated by the oslo agreements and arguably camp david has consisted of a sequence of agreements between israel and its neighbours we will refer to cases in which the grand coalition forms in one step as involving immediate coalition formation or icf for short and cases in which a coalition grows as involving gradual coalition formation

an extension of the black scholes model of security valuation abstract this paper provides a formula for the market value of a security whose dividends and liquidation value depend on securities with diffusion dividend and price processes the solution is in terms of the feynman kac formula solving the partial differential equation determining the derivative sucurity s unique arbitrage free value the interest rate process may be stochastic markets need not be dynamically complete

the time variance relationship of security returns implications for the return generating stochastic process using a test statistic which specifically allows for parameter shifts over time we investigate the time variance relationship of security returns the null hypothesis of stationary and independent increments is rejected and the existence of a complex short term reversal phenomenon is reported

the bilateral consistent prekernel for ntu games abstract a bilateral consistency principle is used to generalize the nash bargaining solution to a new ntu solution concept it coincides with the prekernel for tu games and can be formulated in terms of a generalized concept of excess journal of economic literature classification number c71