We analyse the two‐dimensional Nash bargaining solution (NBS) by deploying the standard labour market negotiations model of McDonald and Solow. We show that the two‐dimensional bargaining problem can ...be decomposed into two one‐dimensional problems, such that the two solutions together replicate the solution of the two‐dimensional problem if the NBS is applied. The axiom of “independence of irrelevant alternatives” is shown to be crucial for this type of decomposability. This result has significant implications for actual negotiations because it allows for the decomposition of a multi‐dimensional bargaining problem into one‐dimensional problems – and thus helps to facilitate real‐world negotiations.
We consider a situation in which two parties have concluded an efficient contract corresponding to one major bargaining solution. After the parties have agreed on one particular contract, an ...unanticipated shock may change the contract outcomes in a way that benefits one party but harms the other party. If this happens, they have the option to either stay with the original exchange contract or adjust some contract parameters such as the price. We propose a model to perform such adjustments automatically, to obtain the same bargaining solution as in the initial contract under the restriction that the new contract dominates the outcomes of the original contract. We study several bargaining solutions within this general framework. These bargaining solutions offer various sharing rules to distribute the benefit between the parties. To reflect practical considerations, we only consider adjustments made via one contract parameter (the price), while all other parameters result from the original contract and the random shock. To evaluate the efficiency of the proposed approach, we also compare it to a full re-negotiation scenario, in which all parameters can be modified within the boundaries resulting after the random shock. However, waiting and re-negotiation might be costly compared to the situation when the smart contract executes the adjustment automatically. Therefore, the automatic adjustment might be more efficient compared to the other types of contracts. We present several numerical examples and run large random simulations, which we also check statistically.
This paper studies majoritarian reputational bargaining. Three agents bargain over the division of one dollar under majority rule, and proposers are randomly chosen. Each agent has private ...information about whether she is a rational type that maximizes her expected share of the dollar or an obstinate type that commits to claiming a certain share of the dollar. Efficiency and surplus distribution in majoritarian reputational bargaining may differ from their counterparts in bilateral reputational bargaining. In a particular equilibrium of our majoritarian game, efficiency loss vanishes asymptotically as the agents become patient, and bargaining ends immediately if all agents are rational. Moreover, the agent who has the lowest positive ex ante probability of being obstinate achieves the highest ex ante payoff, when such probabilities for all agents are sufficiently low.
We consider a non-cooperative coalitional bargaining game with random proposers in a general situation for which players differ in recognition probability and time preference. We characterize an ...efficient equilibrium as the generalized Nash bargaining solution that belongs to the core. The model is applied to wage bargaining between an employer and multiple workers. Although involuntary unemployment may occur in equilibrium, full employment emerges as players become sufficiently patient.
We analyze a non-cooperative coalitional bargaining game with random proposers. ► The existence of a stationary subgame perfect equilibrium (SSPE) is proved. ► An efficient SSPE allocation is the generalized Nash bargaining solution in the core. ► The model is applied to wage bargaining among one employer and workers. ► Involuntary unemployment may occur.
Abstract
Does flexible pay increase the gender wage gap? To answer this question, we analyze the wages of public school teachers in Wisconsin, where a 2011 reform allowed school districts to set ...teachers’ pay more flexibly and engage in individual negotiations. Using quasi-exogenous variation in the timing of the introduction of flexible pay, driven by the expiration of preexisting collective-bargaining agreements, we show that flexible pay lowered the salaries of women compared with men with the same credentials. This gap is larger for younger teachers and smaller for teachers working under a female principal or superintendent. Survey evidence suggests that the gap is partly driven by women engaging less frequently in negotiations over pay, especially when the counterpart is a man. The gap is unlikely to be driven by observable gender differences in job mobility or teacher ability, although the threat of moving and a high demand for male teachers could exacerbate it. Our results suggest that pay discretion and wage bargaining are important determinants of the gender wage gap and that institutions, such as unions, might help narrow this gap.
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