物品价值变化下多人动态讨价还价的策略博弈均衡与参与者拖延行为

Delay and the equilibria in multiplayer dynamic bargaining game under the value of negotiation resources changes

拖延行为是多人讨价还价(协商)中参与人不能在首次协商中达成协议的现象.本文探讨通过动态讨价还价过程在多人间分配价值变化物品的策略博弈模型及其均衡的解析表示,并分析参与者达成协议的拖延行为特性.设计了价值变化物品分配的多人动态讨价还价过程,建立了多人动态讨价还价模型.以此为基础,构建了多人策略博弈模型,给出了物品价值变化率在不同范围内的多人动态讨价还价博弈均衡的具体形式.进一步,基于均衡分析给出了多人讨价还价过程中参与人拖延达成协议的条件,并分析了物品价值随博弈轮数发生规律性变化时,物品价值变化率对讨价还价中参与者是否愿意采取拖延行为达成协议的影响.给出了揭示拖延行为特性的上、下两个阈值.研究发现,当物品价值变化率低于下阈值时,拖延行为不会发生;当物品价值变化率高于上阈值时,一定会出现拖延行为;物品价值变化率在这两个阈值之间时,部分参与者愿意采取拖延行为.而其他参与者不愿意拖延达成协议,且其收益随着博弈轮数的增加趋近于0,在此范围内,耐心程度越高的参与者越会采取拖延行为.本文的研究为通过动态协商方式达成合作的多主体预计达成合作的时间以及设计合理的合作协议提供了一定的理论指导.

This paper studies equilibria and the conditions for the occurrence of delay in multiplayer dynamic bargaining game in which the value of negotiation resources changes regularly with the number of game stages.By using the multiplayer dynamic bargaining model to simulate the negotiation process and then study the equilibrium of the dynamic game,we get the equilibria of the dynamic bargaining game with different ranges of negotiation resources value change rate.Furthermore,the conditions for players to delay making a decision in multiplayer negotiation game are discussed through the equilibria of our dynamic model,and the upper and lower thresholds for revealing the behavior of delay are given.Our study found that when the value-added rate is lower than the lower threshold,that is,the value of negotiation resources is added at a low rate or when there is a depreciation,delay behavior will not occur.When value-added rate is higher than the upper threshold,that is,the rate of the value added of negotiation resources is high enough,delays will inevitably occur.When the value-added rate is between these two thresholds,that is,the value-added rate is not high and within a certain range,some players will procrastinate to prolong the game time.The other players will not delay to reach an agreement,and their income will approach zero with the increase in the number of game stages.Within this range,the more patient players were,the more likely they were to delay reaching an agreement.The research of this paper provides some theoretical guidance for the multi-agent to estimate the time needed to reach cooperation agreement and to design a reasonable cooperation agreement through dynamic negotiation.