Trading bargaining weights

We consider a model, in which two agents are engaged in two separate bargaining problems. We introduce a notion of bargaining weights (bargaining power), which is basically given by asymmetric versions of the Perles–Maschler bargaining solution. Thereby, we view bargaining power as ordinary goods that can be traded in an exchange economy. With equal initial endowment of bargaining power there exists a Walrasian equilibrium in this exchange economy such that the utility allocation in equilibrium coincides with the Perles–Maschler bargaining solution of the aggregate bargaining problem. Equilibrium prices are given by the primitives of the two bargaining problems.     

The relationship between product market competition and unemployment with profit sharing

We investigate the implications of product market imperfections on negotiated wages and equilibrium unemployment under profit sharing. We show that intensified product market competition reduces equilibrium unemployment in a strictly monotonic way when the trade union's bargaining power exceeds the profit share. If the profit share exceeds the trade union's bargaining power, the effect of product market competition is ambiguous: there is a threshold for the benefit–replacement ratio above (below) which intensified product market competition increases (decreases) equilibrium unemployment. The profit share and the union's bargaining power affect the wage mark-up, and thereby equilibrium unemployment, in different directions.     

Endogenous scope of bargaining in a union–oligopoly model: when will firms and unions bargain over employment?

The scope of firm–union bargaining is shown to be endogenously determined in a union–oligopoly model with decentralized negotiations. If the unions' power is sufficiently high, all bargaining units choose to negotiate over wages alone, i.e., universal right-to-manage bargaining emerges in equilibrium. Otherwise, wage/employment bargaining and right-to-manage bargaining coexist in the same industry. In equilibrium, some firm–union pairs will always choose to bargain over employment as well, since the firms become Stackelberg leaders in the market by committing to a particular output during the negotiations. The firms and their unions both benefit from the additional Stackelberg rents, provided that the unions' power is small enough. Our analysis suggests that there is not necessarily a negative relationship between unions' power and sectoral employment rates.     

The <Emphasis Type="Italic">n</Emphasis>-person Kalai-Smorodinsky bargaining solution under pre-donations

This study examines the behavior of simple n-person bargaining problems under pre-donations where the Kalai-Smorodinsky (KS) solution is operant. Pre- donations are a unilateral commitment to transfer a portion of one’s utility to someone else, and are used to distort the bargaining set and thereby influence the bargaining solution. In equilibrium, these pre-donations are Pareto-improving over the undistorted solution; moreover, when the agents’ preferences are sufficiently distinct, the equilibrium solution coincides with the concessionary division rule.     

Recursive Nash bargaining over a productive asset

We propose an equilibrium concept (the recursive Nash bargaining solution) that describes the outcome of repeated negotiations between two rational agents under the assumptions that the state of the economic system under consideration changes according to the actions of the players and that neither party can make binding commitments to future behavior. This equilibrium is dynamically consistent but typically not Pareto-efficient. As an application, we compute the recursive Nash bargaining solution in a model of two heterogeneous agents bargaining over the use of a productive asset with constant gross rate of return and study how the time-preference rates and the elasticities of substitution affect the solution.     

Threats and bargaining in capitalism a differential game view

The paper examines the Nash bargaining equilibrium in a simple model of growth and distribution formulated as a differential game between workers, who may save or consume, and capitalists, who may consume or invest. Optimal threats announced by the social classes to affect the negotiated solution to their own advantage are also derived. It is demonstrated that the workers' threat takes the form of refusing to save while capitalists threaten to refrain from investing. The threats as well as the possible gains from cooperation determine the players' relative importance or bargaining power. It is shown that capitalists are in general in a stronger bargaining position than workers. The dependence of the bargaining power on the parameters of the model is examined.     

Wage Bargaining in Industries with Market Power

We develop a game-theoretic version of the right-to-manage model of firm-level bargaining where strategic interactions among firms are explicitly recognized. Our main aim is to investigate how equilibrium wages and employment react to changes in various labor and product market variables. We show that our comparative statics results hinge crucially on the strategic nature of the game, which in turn is determined by the relative bargaining power of unions and managers.     

A noncooperative foundation of the asymmetric Nash bargaining solution

We consider a noncooperative multilateral bargaining model with heterogeneous time preferences in which the first rejector of a proposal in the current round becomes the proposer in the next round. We show the existence of a stationary subgame perfect equilibrium (SSPE), characterize SSPEs and show the efficiency of SSPEs. We show that any sequence of SSPE payoff profiles converges to the asymmetric Nash bargaining solution weighted by the inverses of discount rates as the bargaining friction vanishes.     

Sequential bargaining with common values

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own this object. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium outcome of this game which is unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent.     

Equilibrium unemployment with outsourcing under labour market imperfections

We study the effects of international outsourcing on equilibrium unemployment in a high-wage economy with labour market imperfections. We demonstrate, consistent with empirical results, that the wage elasticity of labour demand is increasing as a function of outsourcing. Furthermore, we show that a production mode with more outsourcing reduces the negotiated wage in a high-wage country with labour market imperfections if the relative bargaining power of the labour union is sufficiently high. Under such circumstances outsourcing reduces equilibrium unemployment. Finally, we characterize the optimal production mode showing that stronger labour market imperfections induce a production mode with more outsourcing.     

Price versus Quantity in a Duopolistic Market with Bargaining over Managerial Delegation Contracts

This paper studies the endogenous choices of strategic contracts in a duopoly with bargaining between the owner and manager of each firm over the content of the managerial delegation contract. We show that when the bargaining power of the manager relative to that of the owner within each firm is sufficiently high, quantity competition based on the quantity contracts chosen by the owners of both firms can be uniquely observed in the equilibrium, whereas quantity competition and price competition can be observed in the equilibrium when this relative bargaining power is sufficiently low. Copyright © 2015 John Wiley & Sons, Ltd.     

An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

Coalition formation in general NTU games

A general nontransferable utility (NTU) game is interpreted as a collection of pure bargaining games that can be played by individual coalitions. The threatpoints or claims points respectively, in these pure bargaining games reflect the players' opportunities outside a given coalition. We develop a solution concept for general NTU games that is consistent in the sense that the players' outside opportunities are determined by the solution to a suitably defined reduced game. For any general NTU game the solution predicts which coalitions are formed and how the payoffs are distributed among the players.     

Mediation and the Nash bargaining solution

This paper analyzes a model of bargaining in which two parties use a mediator who sequentially makes random proposals until agreement by both parties is reached. I show that as the cost of delay shrinks to zero, the subgame perfect payoff converges to the asymmetric Nash bargaining solution with weights determined by the relative discount rates of the players. I also establish conditions for the uniqueness of the subgame perfect equilibrium for arbitrary discount rates.     

Indeterminacy in a finance constrained unionized economy

We introduce labor unions and unemployment in a finance constrained monetary economy with heterogenous agents and productive labor externalities. We find that unions, introducing endogenous markup variability, influence the dynamics of the model. Although a lower bound for labor externalities is always required for indeterminacy, this lower bound decreases with union power when the elasticity of substitution between capital and labor is above one. For values of this elasticity below one, this result is reversed. We also show that Hopf bifurcations may occur as union bargaining power crosses a critical value. Finally, we find that unions increase simultaneously steady state employment, capital accumulation and welfare iff the (equilibrium) marginal productivity of labor is decreasing in employment.     

供应链中双方供应的竞争和合作博弈研究

针对当前供应链中供应方面存在的相关局限性。构造了双方供应和制造商之间的博弈模型。该模型主要特点是双方 供应之间的二阶段博弈所形成的质量和价格策略。在此条件下制造商和供应商之间进行讨价还价。以分配整体利润。指出了供 需双方在讨价还价时存在惟一的子博彝精炼纳什均衡。     

Buying cooperation in an asymmetric environmental differential game

We consider a two-player asymmetric differential game of pollution control. One player is non-vulnerable to pollution, or unwilling to consider damages when choosing her production policy in a non-cooperative game. We characterize the feedback-Nash equilibrium and the cooperative solution. We establish conditions under which the vulnerable player can buy the cooperation of the non-vulnerable player to control her emissions. We further use the Nash bargaining solution to allocate the total cooperative dividend between the two players and propose a time-consistent decomposition overtime of the total payoff.     

Efficient Delegation by an Informed Principal

Motivated by examples from the automobile industry, insurance, retailing, and multinational strategy, we study an organizational structure we refer to as "partial delegation." In a bargaining problem between an informed party and an uninformed party, partial delegation involves the informed party delegating bargaining to an agent while retaining control of its private information. We show that partial delegation enables the informed party to earn information rents without creating quantity distortions. First‐best quantities are traded in equilibrium. We argue that partial delegation allows an informed party to implement efficient trade with outside parties by endogenously improving its bargaining power.     

A note on linked bargaining

A recent result by Jackson and Sonnenschein (2007) describes a general framework for overcoming incentive constraints by linking together independent copies of a Bayesian decision problem. A special case of that work shows that if copies of a standard two-player Bayesian bargaining problem are independently linked (players receive valuations and trade simultaneously on a number of identical copies), then the utility cost associated with incentive constraints tends to 0 as the number of linked problems tends to infinity. We improve upon that result, increasing the rate of convergence from polynomial to exponential and eliminating unwanted trades in the limit, by introducing a mechanism that uses a slightly richer and more refined strategy space. Although very much in the same spirit, our declarations are constrained by a distribution which is skewed away from the expected distribution of player types. When a sufficiently large number of bargaining problems are linked, “truth” is an equilibrium. Moreover, this equilibrium is incentive compatible with the utility cost of incentive constraints almost surely equal to 0.