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.
Raiffa's solution to the bargaining problem, outlined in Luce and Raiffa (1957), is the point where the negotiation curve - a sequence of points that constitute step-by-step improvements from the ...status quo in the feasible payoff space - meets (possibly in the limit) the efficient boundary of the feasible region. A bargaining model with interim agreements yields a negotiation curve in equilibrium (in the spirit of Raiffa), and as the bargaining frictions disappear, the Raiffa path of payoffs converges to the Nash solution.
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.
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 examine multilateral bargaining in vertical supply relationships that involve an upstream manufacturer who sells through two competing retailers. In these relationships the negotiations are ...interdependent, and bargaining externality may arise across the retailers. In addition, the timing by which the manufacturer negotiates with the retailers becomes important. In simultaneous bargaining the retailers negotiate without knowing if an agreement has been reached in the other retail channel, whereas in sequential bargaining the retailer in the second negotiation is able to observe whether an agreement was reached in the first negotiation. We show that simultaneous bargaining is optimal for the manufacturer when the retail prices (and profitability) are similar, and sequential bargaining is preferred when the dispersion in the retail prices is sufficiently large. As a result of ex post renegotiations, the manufacturer may strategically stock out the less profitable retailer who charged a relatively low retail price and exclusively supply only the retailer who charged a relatively high retail price and maintained high channel profitability. Moreover, ex post multilateral bargaining can buffer downstream competition and thus lead to positive retail profits even in markets that are close to perfect competition.
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