Modeling emotions in negotiations is an open challenge that attracted an increasing amount of attention from researchers. Bargainers look for achieving an agreement with the opposing parties and, at the same time, try to reach their own goals. This process consists of both bargaining and (game theory) problem solving. Game theory models seek to enlighten the rational negotiations between players, but these models lack the evidence of how emotional motives may influence individuals’ behavior. This paper suggests a model for shaping emotions in negotiation using Nash’s bargaining approach. We focus on the case where negotiation between players has motives of cooperating, considering eight emotions: anger, fear, joy, sadness, surprise, disgust, guilt, and disappointment. For representing the solution of the problem, we employ a homogeneous Markov game. The simplicity of the model relies on the fact that the emotions are represented by the states of the Markov chain. The relationship between the emotions is represented by a transition matrix that determines the probability of changing between the emotions (states) at any time. Because any emotion can be reached at any time with certain probability, the bargaining Markov game is ergodic. We represent naturally the emotional process of bargaining using a proximal method, which involves the bargaining Nash product for computing the equilibrium of the game. We show the convergence of the method to the emotional equilibrium point. The solution of the Nash bargaining game consists of cooperative emotional strategies, which are transformed in emotional probability distributions. Such emotional probability distributions are measured using an asymmetric distance function that determines the “emotional distance” between players in negotiations. Emotions are measured using an asymmetric distance function because they are different between players. We present a new approach for shaping emotions in negotiations employing Nash’s bargaining model. An application example shows the influence of expressing emotions in the relationship process, and those emotions are strategically selected to gain a benefit in negotiations. We show that the magnitude and direction of emotional distance matter and that feelings have an asymmetric effect on the negotiation process.

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在谈判中塑造情感：纳什谈判解决方案

在谈判中建立情感模型是一个公开的挑战，吸引了研究人员越来越多的关注。讨价还价者寻求与对立各方达成协议，同时努力实现自己的目标。这个过程包括讨价还价和（博弈论）问题解决。博弈论模型试图启发玩家之间的理性谈判，但是这些模型缺乏情感动机如何影响个人行为的证据。本文提出了一种使用纳什讨价还价方法在谈判中塑造情绪的模型。我们着眼于玩家之间的谈判具有合作动机的情况，其中考虑了八种情绪：愤怒，恐惧，喜悦，悲伤，惊讶，厌恶，内和失望。为了表示问题的解决方案，我们采用齐次马尔可夫博弈。该模型的简单性依赖于这样一个事实，即情感由马尔可夫链的状态表示。情感之间的关系由过渡矩阵表示，该过渡矩阵确定随时在情感（状态）之间变化的可能性。因为可以随时以一定的概率达到任何情绪，所以讨价还价的马尔可夫博弈是遍历的。我们自然地表示使用近端方法进行讨价还价的情感过程，该过程涉及讨价还价纳什乘积来计算游戏的均衡性。我们展示了该方法在情绪平衡点上的收敛性。纳什讨价还价博弈的解决方案由合作情绪策略组成，这些策略在情绪概率分布中进行了转换。这种情绪概率分布是使用非对称距离函数来衡量的，该函数确定了谈判参与者之间的“情感距离”。情感是使用不对称距离函数来衡量的，因为玩家之间的情感是不同的。我们采用纳什的讨价还价模型，提出了一种在谈判中塑造情感的新方法。一个应用示例显示了表达情感在关系过程中的影响，并且从战略上选择了这些情感以在谈判中受益。我们表明，情感距离的大小和方向很重要，感情对谈判过程具有不对称的影响。情感是使用不对称距离函数来衡量的，因为玩家之间的情感是不同的。我们采用纳什的讨价还价模型，提出了一种在谈判中塑造情感的新方法。一个应用示例显示了表达情感在关系过程中的影响，并且从战略上选择了这些情感以在谈判中受益。我们表明，情感距离的大小和方向很重要，感情对谈判过程具有不对称影响。情感是使用不对称距离函数来衡量的，因为玩家之间的情感是不同的。我们采用纳什的讨价还价模型，提出了一种在谈判中塑造情感的新方法。一个应用示例显示了表达情感在关系过程中的影响，并且从战略上选择了这些情感以在谈判中受益。我们表明，情感距离的大小和方向很重要，感情对谈判过程具有不对称的影响。