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I develop a model of majority-rule collective bargaining between a sports league and its players when delay costs incurred by players are wealth-dependent. I propose a refinement of subgame perfect equilibrium that requires equilibrium strategies to be immune to deviations by any majority subgroup. I show this is equivalent to giving the player with median bargaining power the unilateral ability to negotiate with the league. Using this model, I demonstrate that policies reallocating surplus from high-talent to moderate-talent players, such as maximum contracts in professional sports, can improve the welfare of all players. Redistribution of surplus harmonizes players' interests, giving a majority of them a greater stake in the bargaining outcome. The model highlights the gains to be had if a heterogeneous group agrees to concessions that increase the alignment of their individual interests. [ABSTRACT FROM AUTHOR]

We report experimental results and test axiomatic models of unstructured bargaining by checking the empirical relevance of the underlying axioms. Our data support strong efficiency, symmetry, independence of irrelevant alternatives and monotonicity, and reject scale invariance. Individual rationality and midpoint domination are violated by a significant fraction of agreements that implement equal division in highly unequal circumstances. Two well-known bargaining solutions that satisfy the confirmed properties explain the observed agreements reasonably well. The most frequent agreements in our sample are the ones suggested by the equal-division solution. In terms of the average Euclidean distance, the theoretical solution that best explains the data is the deal-me-out solution (Sutton, 1986 ; Binmore et al., 1989, 1991). Popular solutions that satisfy scale invariance, individual rationality, and midpoint domination, as the well-known Nash or Kalai-Smorodinsky bargaining solutions, perform poorly in the laboratory. [ABSTRACT FROM AUTHOR]

This paper studies infinite-horizon sequential bargaining among n ≥ 3 players in which a proposer is randomly selected from the pool of potential proposers. If the proposal is rejected, the current and previous proposers are excluded from the pool of potential proposers, and the game moves on to the next round until every player has had the same number of opportunities to be the proposer. To analyze the model with a particular time dependency within each sequence of n rounds (a cycle), I characterize the stationary equilibrium of a stochastic game, which I call cycle-stationary subgame perfect (CSSP) equilibrium. The CSSP equilibrium is unique in payoffs and analogous to the subgame perfect equilibrium of some forms of finite-horizon bargaining. Even when every player is entirely patient, the proposer's share in the CSSP equilibrium is smaller than that predicted by the stationary equilibrium of the Baron–Ferejohn legislative bargaining model. [ABSTRACT FROM AUTHOR]

The paper introduces an axiomatic characterization of a solution to bargaining problems. Bargaining problems are specified by: (a) the preference relations of the bargaining parties (b) resources that are the subject of bargaining, and (c) a pre-specified disagreement bundle for each party that would result if bargaining fails. The approach is ordinal in that parties' preferences are over bundles of goods and do not imply any risk attitudes. The resulting solution is accordingly independent of the specific utilities chosen to represent parties' preferences. We propose axioms that characterize a solution matching each bargaining problem with an exchange economy, and assigning the set of equilibrium allocations corresponding to one equilibrium price vector of that economy. The axioms describe a solution that results from an impartial arbitration process, expressing the view that arbitration is a natural method to settle disputes in which agents have conflicting interests, but can all gain from compromise. [ABSTRACT FROM AUTHOR]

One feature of legislative bargaining in naturally occurring settings is that the distribution of seats or voting weights often does not accurately reflect bargaining power. Game-theoretic predictions about payoffs and coalition formation are insensitive to nominal differences in vote distributions and instead only depend on pivotality. We conduct an experimental test of the classical Baron-Ferejohn model with five-player groups. Holding real power constant, we compare treatments with differences in nominal power. We find that initial effects of nominal differences become small or disappear with experience. Our results also point to the complexity of the environment as having a negative impact on the speed at which this transition takes place. Finally, and of particular importance as a methodological observation, giving subjects a pause accelerates learning. [ABSTRACT FROM AUTHOR]

An arbitrator is often introduced into bargaining to avoid disagreement. The arbitrator's role is to impose some agreement when negotiators cannot reach an agreement. However, in models with an arbitrator, a fair agreement for negotiators is eliminated from equilibrium outcomes if the arbitrator is biased. To avoid disagreement without eliminating the achievability of a fair agreement in equilibrium, we consider introducing a mediator. While an arbitrator imposes an agreement, a mediator can only give advice. We analyze a simultaneous-offers bargaining model with a mediator and obtain the following desirable results. First, disagreement is not supported as an outcome of a stationary subgame perfect equilibrium (SSPE). Second, even if a mediator is biased, the fair agreement in the sense of the Nash bargaining solution (NBS) is always one of the SSPE agreements. Finally, if a mediator is fair, negotiators always reach an agreement with the NBS in SSPE. [ABSTRACT FROM AUTHOR]

Abstract Schelling proposed that payoff-irrelevant cues can affect the outcome of tacit bargaining games by creating focal points. Tests of this hypothesis have found that conflicts of interest between players inhibit focal-point reasoning. We investigate experimentally whether this effect is reduced if players have imperfect information about each other's payoffs. When players know only their own payoffs, they fail to ignore this information even though it cannot assist coordination; the effects of payoff-irrelevant cues on coordination success are small. When no exact information about payoffs is provided, payoff-irrelevant cues are more helpful, but not as much as when conflict is absent. [ABSTRACT FROM AUTHOR]

Abstract We study bargaining between a country and a multinational firm over the firm's entry to sell a patented product when the firm has private information about its profits and the country has the threat of issuing a compulsory license (CL). We assume the CL expands the surplus for some firm types, so that efficiency calls for all firms with sufficiently high valuations to enter immediately and those with lower valuations to wait for a CL. We establish the existence of two types of equilibria, depending on the maximum initial valuation: a bargaining pause equilibrium in which negotiations lie dormant for a finite period before the deadline and a licensing delay equilibrium in which bargaining continues for a finite time beyond the deadline. Two types of inefficiency arise—too many firms wait for the license and some firms who do not wait for the license are forced to delay agreements. [ABSTRACT FROM AUTHOR]

Abstract This paper constructs a continuous-time model of bilateral bargaining to study how fluctuations in bargaining power affect the outcomes of negotiations. The paper deals with the technical complexities that arise when modeling games in continuous time by building strategy restrictions into the equilibrium definition. These restrictions select a unique equilibrium, which is characterized by a system of ordinary differential equations. This unique equilibrium corresponds to the limiting subgame perfect equilibrium of discrete-time bargaining games with frequent offers. [ABSTRACT FROM AUTHOR]

Abstract This study examines a dynamic process of n -person coalitional bargaining problems. We investigate the evolution of social conventions by embedding a coalitional bargaining setting in a dynamic process. In each period, a group of players may make some coalitional move, that is, forming a new team or negotiating the division of a surplus. Players revise their coalitions and surplus divisions over time in the presence of stochastic noise, which leads players to make a suboptimal decision. Under a logit specification of choice probabilities, we find that the stability of a core allocation decreases in the wealth of the richest player. Furthermore, stochastically stable allocations are core allocations that minimize the wealth of the richest player. [ABSTRACT FROM AUTHOR]

Abstract Richman games are zero-sum games, where in each turn players bid in order to determine who will play next (Lazarus et al., 1999). We extend the theory to impartial general-sum two player games called bidding games , showing the existence of pure subgame-perfect equilibria (PSPE). In particular, we show that PSPEs form a semilattice, with a unique and natural Bottom Equilibrium. Our main result shows that if only two actions available to the players in each node, then the Bottom Equilibrium has additional properties: (a) utilities are monotone in budget; (b) every outcome is Pareto-efficient; and (c) any Pareto-efficient outcome is attained for some budget. In the context of combinatorial bargaining, we show that a player with a fraction of X % of the total budget prefers her allocation to X % of the possible allocations. In addition, we provide a polynomial-time algorithm to compute the Bottom Equilibrium of a binary bidding game. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We study a legislative bargaining game in which failure to agree in a given round may result in a breakdown of negotiations. In that case, each player receives an exogenous ‘disagreement value’. We characterize the set of stationary subgame perfect equilibria under all q-majority rules. Under unanimity rule, equilibrium payoffs are strictly increasing in disagreement values. Under all less-than-unanimity rules, expected payoffs are either decreasing or first increasing and then decreasing in disagreement values. We conduct experiments involving three players using majority and unanimity rule, finding qualitative support for several, but not all, of our main predictions. Having a high disagreement value is indeed an advantage under unanimity rule. Under majority rule, the player with the highest disagreement value is more likely to be excluded, but this does not consistently result in a lower average payoff. [ABSTRACT FROM AUTHOR]

This paper studies a complete-information bargaining game with one buyer and multiple sellers of different “sizes” or bargaining strengths. The bargaining order is determined endogenously. With a finite horizon, there is a unique subgame perfect equilibrium outcome, in which the buyer purchases in order of increasing size–from the smallest to the largest. With an infinite horizon, if the sellers have sufficiently different sizes, there is a unique equilibrium outcome, which has the same bargaining order. If the sellers have similar sizes with an infinite horizon, there may be multiple equilibrium outcomes with different bargaining orders. [ABSTRACT FROM AUTHOR]

We study a model of strategic network formation prior to a Manea (2011a) bargaining game: ex ante homogeneous players form costly undirected links, anticipating expected equilibrium payoffs from the subsequent bargaining game. Assuming patient players, we provide a complete characterization of generically pairwise stable networks: specific unions of separated pairs, odd circles, and isolated players constitute this class. We also show that many other structures, such as larger trees or unbalanced bipartite networks, cannot be pairwise stable at all. The analysis implies that the diversity of possible bargaining outcomes is small in (generically) pairwise stable networks. [ABSTRACT FROM AUTHOR]

We study a model of decentralised bilateral interactions in a small market where one of the sellers has private information about her value. In addition to this seller with private information, there are two identical buyers and another seller, whose valuation is commonly known to be in between the two possible valuations of the seller with private information. We consider an infinite horizon game with simultaneous one-sided offers and simultaneous responses. We construct one particular PBE of the game and show that, as the discount factor goes to 1, prices in all transactions converge to the same value. We then show that this is the case with any stationary equilibrium of the game. That is, the asymptotic outcome is unique across all stationary equilibria. [ABSTRACT FROM AUTHOR]

We study non-stationary markets in which traders are randomly matched to bargain over the price of a heterogeneous good or the terms of a partnership. The economy consists of a continuum of players drawn from a finite set of types. Players exogenously enter the market over time and exit upon trading. At every date, matching probabilities for each pair of types are determined by the endogenous distribution of trader types in the market. The balance of bargaining power at any stage depends on variations in potential gains from trade, the inflows of new traders, the structure of agreements at future dates, and the induced frequency of trading opportunities. We establish that an equilibrium always exists. Moreover, all equilibria that lead to the same evolution of the economy are payoff equivalent. However, we show that multiple self-fulfilling expectations about the trajectory of the economy, generating distinct equilibrium dynamics and payoffs, may coexist. [ABSTRACT FROM AUTHOR]

In the Approval Bargaining game, two players bargain over a finite set of alternatives. To this end, each one simultaneously submits a utility function u jointly with a real number α ; by doing so she approves the lotteries whose expected utility according to u is at least α . The lottery to be implemented is randomly selected among the most approved ones. We first prove that there is an equilibrium where players truthfully reveal their utility function. We also show that, in any equilibrium, the equilibrium outcome is approved by both players. Finally, every equilibrium is sincere and Pareto efficient as long as both players are partially honest. [ABSTRACT FROM AUTHOR]

We report data from a laboratory experiment with 576 participants that was designed to test Aghion and Tirole's (1994a) management of innovation theory which is based on the Grossman–Hart–Moore property rights approach. A research unit and a customer can invest to increase the probability of making an innovation. When the innovation is made, the parties bargain over the division of the revenue. In line with the theoretical predictions, we find that ownership matters for the division of the revenue and the investments. However, communication can mitigate Aghion and Tirole's (1994a) concern that the customer will not relinquish ownership to the cash-constrained research unit. [ABSTRACT FROM AUTHOR]

We study the role of an imbalance in fighting strengths when players bargain in the shadow of conflict. Our experimental results suggest: In a simple bargaining game with an exogenous mediation proposal, the likelihood of conflict is independent of the balance of power. If bargaining involves endogenous demand choices, however, the likelihood of conflict is higher if power is more imbalanced. Even though endogenous bargaining outcomes reflect the players' unequal fighting strengths, strategic uncertainty causes outcomes to be most efficient when power is balanced. In turn, the importance of exogenous mediation proposals depends on the balance of power. [ABSTRACT FROM AUTHOR]

This note examines the structure of stationary bargaining equilibria in the finite framework of Anesi (2010) . The main result establishes a tight connection between the set of equilibrium absorbing points and the von Neumann–Morgenstern solutions: assuming that players are patient, that the voting rule is oligarchical, and that there is at least one veto player with positive recognition probability, a set of alternatives corresponds to the absorbing points of an equilibrium if and only if it is a von Neumann–Morgenstern solution. We also apply our analysis of ergodic properties of equilibria to the persistent agenda setter environment of Diermeier and Fong (2012) . We show that all equilibria are essentially pure, and we extend their characterization of absorbing sets to allow an arbitrary voting rule and by removing the restriction to pure strategy equilibria. [ABSTRACT FROM AUTHOR]

We study strategies with one-period recall in the context of a general class of multilateral bargaining games. A strategy has one-period recall if actions in a particular period are only conditioned on information in the previous and the current period. We show that if players are sufficiently patient, given any proposal in the space of possible agreements, there exists a subgame perfect equilibrium such that the given proposal is made and unanimously accepted in period zero. As a corollary we derive that also perpetual delay can be sustained as a subgame perfect equilibrium. Our strategies are pure and have one-period recall, and we do not make use of a public randomization device. The players' discount factors are allowed to be heterogeneous. We also construct a finite automata representation of our strategy profile. [ABSTRACT FROM AUTHOR]

We address the issue of bidder ring formation in single and multi-unit Vickrey auctions. We analyze this issue in a bargaining game set up under the assumption that valuation of bidders is commonly known only amongst themselves. In the single unit case, we show that the equilibrium coalition structure can only be an order preserving r-ring , that includes the winner and the top ( r − 1 ) losers. In the multiple units case, we specify sufficient conditions for formation of an interesting class of equilibrium coalition structures, which we call single winner ring with free riding , where exactly one winner colludes with all the losers and generates maximum possible bidders' surplus, and, depending on the protocol, the remaining winners free ride either by staying alone or by colluding in pairs. [ABSTRACT FROM AUTHOR]

Third-party intervention can reduce the risk of conflict in situations where the bargaining failure is due to asymmetric information. In this paper, I consider the selection of a third party in a two-person bargaining problem where each disputant has private information about its relative strength or weakness. For a class of problems, I find that the disputants choose the third party that is best for the strong type but worst for the weak type due to the incentive of each disputant to avoid seeming weak to their adversary. The selected third party's intervention entails a higher ex ante chance of conflict than intervention by any other alternative. This paper shows how the process of interim third-party selection can have important consequences for the outcome of a third-party intervention in bargaining. [ABSTRACT FROM AUTHOR]

We develop, and experimentally test, models of informal agreements. Agents are assumed to be honest but suffer costs of overcoming temptations. We extend two classical bargaining solutions – split-the-difference and deal-me-out – to this informal agreement setting. For each solution there are two natural ways to do this, leaving us with 2 × 2 models to explore. In the experiment, a temptations-constrained version of deal-me-out emerges as the clear winner. [ABSTRACT FROM AUTHOR]

This paper addresses the question of existence of stationary Markov perfect equilibria in a class of dynamic games that includes many known bargaining models and models of coalition formation. General sufficient conditions for existence of equilibria are currently lacking in a number of interesting environments, e.g., models with non-convexities, consumption lower bounds, or an evolving state variable. The main result establishes existence of equilibrium under compactness and continuity conditions, without the structure of convexity or strict comprehensiveness used in the extant literature. The proof requires a precise selection of voting equilibria following different proposals using a generalization of Fatou's lemma. [ABSTRACT FROM AUTHOR]

We present a three-player queuing game to study procedural preferences in a laboratory experiment. Together with markets, queues and waiting lists are universal procedures for allocating goods and services. We designed our queuing game to disentangle motivations of outcome-oriented egoistic preferences, outcome-oriented distributional (inequality aversion) preferences and outcome-independent procedural preferences. In a series of treatments, we introduce a market element and allow two of the three players to bargain over a queue jump, thus violating the queuing procedure. A third player is able to engage in peer punishment to sanction queue jumping. We provide evidence that a simple model of procedural preferences is able to explain the behavior of a share of the subjects in our experiment. [ABSTRACT FROM AUTHOR]

A new feature pertaining to proposer's ability to implement offers is introduced in the extensive form bargaining mechanism studied in Okada (1996). This mechanism is used to analyze the coalitional setting of strictly supermodular games. The new feature in the mechanism is that the proposer has a choice to implement his proposal with any subset of responders who have accepted it. Thus the institutional feature of ‘every responder has veto power’ is relaxed here. It is shown that for all sufficiently high discount factors δ , there exists an efficient subgame perfect equilibrium in pure stationary strategies (SSPE) whose limiting outcome is the core-constrained Nash Bargaining Solution. Moreover, all efficient SSPE are payoff-equivalent in the limit as δ → 1 . [ABSTRACT FROM AUTHOR]

We investigate the implications of imperfect best response—in combination with different assumptions about correct (QRE) or incorrect beliefs (Quantal-Gambler's Fallacy or QGF)—in the alternating offer multilateral bargaining game. We prove that a QRE of this game exists and characterize the unique solution to the proposer's problem—that is, the proposal observed most frequently in a QRE. We structurally estimate this model on data from laboratory experiments, and show that it explains behavior better than the model with perfect best response: receivers vote probabilistically; proposers allocate resources mostly within a minimum winning coalition of legislators but do not fully exploit their bargaining power. Incorporating history-dependent beliefs about the future distribution of proposal power into the QRE model (QGF) leads to an even better match with the data, as this model implies slightly lower shares to the proposer, maintaining similar or higher frequencies of minimum winning coalitions and similar voting behavior. [ABSTRACT FROM AUTHOR]

What makes a bargaining proposal credible? We study how hard leverage (binding commitment) influences soft leverage (appealing to a focal point) in a rich-context bargaining game known to exhibit competing claims to focality. In three treatments, our experiment varies one bargainer's ability to commit, holding the soft leverage condition fixed. As in previous studies, we observe that opening offers are consistent with the available soft leverage. The influence of hard leverage is most evident in the concessionary stage. Hard and soft leverage interact to influence outcomes: Hard leverage advantages its holder, yet settlements largely stay between the two focal points. We posit that focal points induce mutual expectations of bargainer social preferences that, when combined with the Nash bargaining solution, imply the comparative statics concerning the settlements observed. A similarly modified version of the Zeuthen–Harsanyi model of the bargaining process, agrees with the comparative statics on opening offers and concessions. [ABSTRACT FROM AUTHOR]

It is widely accepted among axiomatic bargaining theorists that if one bargainer is more risk averse than a second, the second will be a tougher bargaining opponent than the first against all opponents. We argue that this relationship between risk aversion and bargaining toughness is both highly fragile, and more nuanced than previously articulated. In the Nash and Kalai–Smorodinsky bargaining frameworks, we establish that when a bargainer is compared with a second who is “almost globally” more risk averse than the first, the supposedly immutable relationship between bargaining effectiveness and risk aversion evaporates. Specifically, we identify an upper-hemicontinuity failure of a correspondence which maps the power set of all lotteries to those utility pairs that satisfy our “almost global” comparative risk aversion relation on these subsets. We trace the consensus view that tougher bargainers are less risk-averse to an exclusive focus on precisely the point at which this correspondence implodes. [ABSTRACT FROM AUTHOR]

Computation of exact equilibrium values for n -player divide-the-dollar legislative bargaining games as in Baron and Ferejohn (1989) with general quota voting rules, recognition probabilities, and discount factors, can be achieved by solving at most n bivariate square linear systems of equations. The approach recovers Eraslan's (2002) uniqueness result and relies on a characterization of equilibria in terms of two variables that satisfy a pair of piecewise linear equations. [ABSTRACT FROM AUTHOR]

The paper illustrates how people who need to make a joint decision may have an incentive to withhold information regarding the existence of Pareto improving options. The resulting level of inefficiency varies with the way compromises are reached when the parties have to choose among multiple options. Various reasonable compromise rules can be ranked unequivocally, and a rule resulting in a minimal level of inefficiency is identified. Qualitative results extend to sequential disclosure. Enforcing a hard deadline for disclosure may be welfare improving in some circumstances. [ABSTRACT FROM AUTHOR]

We consider the canonical non-cooperative multilateral bargaining game with a set of feasible payoffs that is closed and comprehensive from below, contains the disagreement point in its interior, and is such that the individually rational payoffs are bounded. We show that a pure stationary subgame perfect equilibrium having the no-delay property exists, even when the space of feasible payoffs is not convex. We also have the converse result that randomization will not be used in this environment in the sense that all stationary subgame perfect equilibria do not involve randomization on the equilibrium path. Nevertheless, mixed strategy profiles can lead to Pareto superior payoffs in the non-convex case. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In 1985 Aumann axiomatized the Shapley NTU value by non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives. We show that, when replacing unanimity by “unanimity for the grand coalition” and translation covariance, these axioms characterize the Nash solution on the class of n-person choice problems with reference points. A classical bargaining problem consists of a convex feasible set that contains the disagreement point here called reference point. The feasible set of a choice problem does not necessarily contain the reference point and may not be convex. However, we assume that it satisfies some standard properties. Our result is robust so that the characterization is still valid for many subclasses of choice problems, among those is the class of classical bargaining problems. Moreover, we show that each of the employed axioms – including independence of irrelevant alternatives – may be logically independent of the remaining axioms. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Most real-life bargaining is resolved gradually. During this process parties reach intermediate agreements. These intermediate agreements serve as disagreement points in subsequent rounds. We identify robustness criteria which are satisfied by three prominent bargaining solutions, the Nash, Proportional (and as a special case to the Egalitarian solution) and Discrete Raiffa solutions. We show that the “robustness of intermediate agreements” plus additional well-known and plausible axioms, provide novel axiomatizations of the above-mentioned solutions. Hence, we provide a unified framework for comparing these solutionsʼ bargaining theories. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

Abstract: We examine experimentally how link costs affect the formation of links between a single seller and two potential buyers as well as the ensuing bargaining. Theory predicts that link costs lead to less competitive networks, with one link rather than two links, and that link costs do not affect the bargaining outcomes conditional on the network. We find support for the first but not the second prediction. 2-link networks form less frequently when there are link costs. Given that a 2-link network forms, however, a seller on average offers a smaller share of the pie to the buyers in the presence than in the absence of link costs. This impact of link costs can be explained by a disutility for (advantageous) inequality on the part of the seller. [Copyright &y& Elsevier]

Abstract: We generalize the dynamic bargaining game of to arbitrary quota rules to provide a non-cooperative characterization of the von Neumann–Morgenstern stable set. Assuming that players are sufficiently patient and have strict preferences, a pure-strategy stationary equilibrium exists and in any such equilibrium, a policy is a steady state if and only if it is in the stable set. The result provides a non-cooperative foundation of stable sets in settings with dynamic policy-making and a persistent agenda setter. [Copyright &y& Elsevier]

Abstract: In this note, I extend the work of to show that a model of many-to-many matching with contracts may be embedded into a model of many-to-many matching with wage bargaining whenever (1) all agentsʼ preferences are substitutable and (2) the matching with contracts model is unitary, in the sense that every contractual relationship between a given firm–worker pair is specified in a single contract. Conversely, I show that unitarity is essentially necessary for the embedding result. [Copyright &y& Elsevier]

Abstract: The preference between public and private negotiations for a buyer who sequentially visits two sellers is examined. It is shown that the buyer (weakly) prefers private negotiations so as to create strategic uncertainty about the trade history. With substitute goods, such uncertainty is valuable only when price offers have short deadlines that prevent a head-to-head competition. With complementary goods, strategic uncertainty is valuable to the extent that price coordination becomes a concern for sellers, which is likely to be the case when sellers possess high bargaining powers; their price offers have short deadlines; and/or goods are weak complements. Sellersʼ strategic deadline choices as well as their incentives to disclose information about negotiations are also investigated. [Copyright &y& Elsevier]

Abstract: This article 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. Our central result is that the severity of holdout (i.e. inefficiency) is critically dependent on three issues, (a) the transparency of the bargaining protocol, (b) the outside option of the buyer, and (c) the marginal contribution of the last seller. We find that although the accepted wisdom that holdout is severe, goes through whenever either the buyer has no outside option, or the bargaining protocol is secret, the holdout problem however is largely resolved whenever either the bargaining protocol is transparent and the buyer has a positive outside option, or if the marginal contribution of the last seller is not too large. [Copyright &y& Elsevier]

Abstract: We study the Markov perfect equilibria (MPEs) of an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain. Players who reach agreement are removed from the network without replacement. We establish the existence of MPEs and show that MPE payoffs are not necessarily unique. A method for constructing pure strategy MPEs for high discount factors is developed. For some networks, we find that all MPEs are asymptotically inefficient as players become patient. [Copyright &y& Elsevier]

Abstract: Following we consider bargaining problems in which no exogenous disagreement outcome is given. A bargaining solution assigns a pair of outcomes to such a problem, namely a compromise outcome and a disagreement outcome: the disagreement outcome may serve as a reference point for the compromise outcome, but other interpretations are given as well. For this framework we propose and study an extension of the classical Kalai–Smorodinsky bargaining solution. We identify the (large) domain on which this solution is single-valued, and present two axiomatic characterizations on subsets of this domain. [Copyright &y& Elsevier]

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 otherʼs 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). [Copyright &y& Elsevier]

Abstract: This paper investigates how families decide how juveniles use their time. The problem is analyzed in three variations: (i) a ‘decentralized’ scheme, in which parents control the main budget, but their children dispose of their time as they see fit, together with any earnings from work on their own account; (ii) ‘hierarchy’, in which parents can enforce, at some cost, particular levels of schooling and supervised work contributing to the main budget; and (iii) the cooperative solution, in which resources are pooled and the threat point is one of the non-cooperative outcomes. Adults choose which game is played. While the subgame perfect equilibrium of the overall game is pareto-efficient, it may yield less education than ‘hierarchy’. Restrictions on child labor and compulsory schooling generally affect both the threat point and the feasible set of bargaining outcomes. Families may choose more schooling than the legal minimum. [Copyright &y& Elsevier]

Abstract: This paper shows that a modified alternating offers Rubinstein model can provide a Pareto superior outcome in the context of the right-to-manage union–firm bargaining. Two examples of bargaining protocols that yield a superior outcome are provided. In the first example, the parties engage in a game in which the order of play is determined as part of the bargaining. We show that the game has a unique subgame perfect equilibrium in which the firm always moves first in the wage bargaining game. The equilibrium wage is, therefore, unique. In the second example, we examine a two-part-tariff alternating offers bargaining protocol, where the parties bargain over the wage and transfer payments. We show that this bargaining protocol has a Pareto efficient, unique subgame perfect equilibrium. Thus, although the parties do not bargain over the level of employment, the outcome under this protocol is, nevertheless, socially optimal. [Copyright &y& Elsevier]

Abstract: We study a majoritarian bargaining model in which players make payoff demands in decreasing order of voting weight. The unique subgame perfect equilibrium outcome is such that the minimal winning coalition of the players that move first forms with payoffs proportional to the voting weights. This result advances previous analysis in terms of one or more of the following: a) the simplicity of the extensive form (finite horizon with a predetermined order of moves); b) the range of the majority games covered; c) the equilibrium concept (subgame perfect equilibrium is sufficient for a unique prediction). [Copyright &y& Elsevier]