关键词: 随机交替出价谈判, 损失厌恶, 参考点, 马尔科夫均衡

Abstract: In a real negotiation, the bargaining power of the enterprise has an important impact on the negotiation result. For example, Wal-Mart and Carrefour, as the retail giants, tend to make the profits of their suppliers very low when negotiating with their suppliers, because Wal-Mart and Carrefour have a greater bargaining power. One of the characteristics of stochastic alternating-offer negotiation game is that the preference of players is independent of time. In reality, the “pie share” finally obtained by players depends not only on the offer at the current moment, but also on the offer at all previous moments, that is, the preference of players depends on the history of negotiation game.
In addition, the economic and psychological experimental studies show that players often show loss aversion in the negotiation process. People are more motivated to minimize losses than maximize gains. Given the situations in which the psychological factors inherent in loss aversion play an important role in negotiation, a natural extension of the classical random alternating-offer negotiation game model is considered by incorporating the loss aversion behavior of players. In real negotiation, if the player's share in the current negotiation stage is lower than that in the previous negotiation stage, the participant may not accept the offer in the current negotiation stage. This is called loss-aversion phenomenon. Loss aversion was introduced by KAHNEMAN and TVERSKY. The simple and elegant version of SHALEV is adopted, where player's preference is characterized by a basic utility function, a reference point as well as a loss aversion coefficient. Therefore, this paper will explore the influence of loss aversion behavior of players on random alternating-offer negotiation game, in which the reference point of player is equal to the highest offer rejected by opponents in the past negotiation stage.
In view of the fact that the bargaining power of enterprises has an important influence on the negotiation results in the negotiation of practical problems, in order to make the model more reasonable and make its conclusion more scientific, this paper considers random alternating-offer negotiation game with loss aversion by incorporating player's bargaining power, where the probability of making proposals in each round of negotiations reflects the bargaining power of a player and the initial reference point is not equal to zero. A random alternating-offer negotiation game with loss aversion is proposed. Different from the classical stochastic alternating-offer negotiation game model, our work incorporates players' loss aversion behavior into the stochastic alternating-offer negotiation game model. Furthermore, a Markov equilibrium is constructed, and the existence and uniqueness of Markov equilibrium are proven. This paper analyzes the influence of loss aversion and bargaining power on Markov equilibrium, discusses the convergence of Markov equilibrium when the probability of negotiation breakdown tends to zero.
This paper explores the influence of loss aversion on two-player stochastic alternating-offer negotiation game. We construct Markov equilibrium and show its uniqueness based on the assumptions of immediate acceptance of equilibrium offers, indifference between accepting and rejecting equilibrium offers, and strategies depending only on the current reference points. The main results of this study include the following points: First, Markov equilibrium strategy is unique, and the players' strategy only depends on the current reference point. Second, the players are hurt by their own loss aversion behavior and benefit from the loss aversion behavior of their opponents. Third, when the probability of negotiation breakdown tends to 1, although the loss aversion level of a player is higher than that of the opponent, this player can still get more than half of the share as long as the bargaining power in the negotiation process is high enough.

Key words: alternating-offer bargaining with random proposers, loss aversion, reference point, Markov equilibrium