Abstract: Bargaining plays an important role in economics. Bargaining is the case of economic interaction where the market only plays a role in setting the bounds of discussion and the bargaining outcomes are determined by the strategic interaction of the players. In real bargaining situations, the critical issue confronted by players is how to reach an agreement for cooperation before the actual cooperation. Each player prefers agreement to disagreement, while each player has a strong desire to reach an agreement on the most favorable division for himself. A source of the cost incurred by players comes from the following facts that bargaining between players is time consuming and that time is valuable to players. Moreover, bargaining process involves players in making offers and counteroffers to each other. The Rubinstein bargaining formally explores the role of players' discount rates that reflect players' value for time in bargaining process. The approach introduced by Bolton explains numerous experimental findings on bargaining game. However, the above two models cannot explain why players in some situations are willing to pay for fair treatment. Some scholars have explored the influence of inequity aversion through experiments. On the theoretical level, the inequity aversion model proposed by Fehr and Schmidt incorporates more conventional fairness into the utility function of participants. Ewerhart modified the Fehr and Schmidt's model to stress the fairness but not the outright altruism, in which a common agreement reached by the two players is regarded as their own reference level, and such reference points cannot capture endogenously bargaining power.
To reflect the influence of bargaining power on the fair reference level, this paper adopts Nash bargaining solution asplayers' fairness reference levels. Nash negotiation solutions satisfy Pareto efficiency, symmetry axiom, affine invariance and independence of irrelevant alternatives. Nash bargaining solution can balance fairness and efficiency if in 2-person bargaining game the payoff for each player lies between the infimum and supremum of the assigned payoffs by the egalitarian and utilitarian solutions. It formulates how much one should be assigned from the overall material payoff. In view of this, in Rubinstein negotiation game, this paper considers the situation in which players have inequity aversion preference, in which Nash negotiation solution serves as the fair reference level of players to reflect the influence of bargaining power. On this basis, the perfect equilibrium of sub-game is constructed, and the existence and uniqueness of the perfect equilibrium of sub-game is proved. This paper explores the influence of participants' inequity aversion preference and bargaining power on the perfect equilibrium of subgame. This paper adopts Nash bargaining solution as players' fairness reference levels, which is a new perspective to analyze the effect of fairness preferences on the alternating-offer bargaining.
The research results of this paper are mainly divided into the following three aspects: First, when the equilibrium offer of two players makes the share of the player (who makes the offer first) lower than its fair reference level, that player will benefit from the marginal disutility generated by the inequity aversion preference of the two players. Second, when the equilibrium offer of two players causes the share of the player (who makes the offer first) to be higher than its fair reference level, that player will suffer a loss due to the marginal disutility generated by the inequity aversion preference of the two players. In the two cases, higher bargaining power may be detrimental to the participants. Finally, as the time interval between two consecutive offers approaches zero, the player's equilibrium share is independent of the absolute magnitude of the two players' discount rates and only depends on the ratio of the two players' discount rates. The management implications provided by the research results of this paper are as follows: when the quotation of two players is lower (or higher) than the fair reference level, the higher the level of inequity aversion of the players, the higher (or the lower) the offer the player who makes the offer first should make. And whether a participant with higher bargaining power should make a higher offer depends on the degree of inequity aversion and discount factor of the participant. Therefore, the players should weigh the inequity aversion preference, bargaining power and discount factor of the two players comprehensively when making the offer, rather than simply following the rule that the offer in the current negotiation stage is higher than that in the past negotiation stage.
In this paper, we investigate Rubinstein negotiation games with inequity aversion preference, in which fairness preference is independent of time. In some cases, this assumption is reasonable, while in other cases it may not be, and the participants' share of the proceeds depends on the negotiation process. Therefore, the influence of inequity aversion preference on Rubinstein negotiation with historical dependence can be further explored in future studies.

Key words: Rubinstein bargaining games, Nash bargaining solution, inequity aversion preference, subgame perfect equilibrium

摘要： 对Fehr和Schmidt的不公平厌恶模型进行修正,考虑议价能力的影响,以Nash谈判解作为参与人的公平参考水平,研究参与人具有不公平厌恶偏好的Rubinstein谈判博弈问题。构建子博弈完美均衡,并在其满足无延迟和稳定性两个性质的条件下,证明该子博弈完美均衡的唯一性,分析子博弈完美均衡的性质。结果表明:当两个参与人的均衡报价使得最先提出报价的参与人的份额低(或高)于其公平参考水平时,该参与人的收益与参与人的不公平厌恶偏好呈正(或负)相关关系;较高的议价能力可能对参与人不利;当两次连续出价之间的时间间隔趋于零时,参与人的均衡份额取决于两个参与人贴现率的比值。

关键词: Rubinstein谈判, Nash谈判解, 不公平厌恶偏好, 子博弈完美均衡