2012 年 2012 巻 169 号 p. 169_139-153
This article discusses the difficulty to keep cooperation in a multilateral bargaining situation by introducing my original game theory framework. Why do players sometimes fail to keep cooperating although they think it is desirable to do so? I analyze this question by applying an original game theory model based on the Zero-Sum n+1 Person Game of John von Neumann and Oskar Morgenstern, and I argue that it is important to acquire beliefs not only from the bargaining players but also from the third party of the bargaining.
The characteristic of the Zero-Sum n+1 Person Game is that n-person players achieve to cooperate by charging the cost to the other player (the third party or player n+1), and player n+1 can show no strategy in this game. However, such a situation does not produce a hopeful result even if a gainful cooperation is constructed among the n-person players because the damaged player n+1 may try to change the situation and cause damage to the other players.
The important question regarding this situation is what condition makes the third party resist their cooperation. To solve this problem, I expanded the Zero-Sum n+1 Person Game into an iterated game by applying the subjective probability (Bayes theorem) to measure the third party's trust in n-person players, the most important variable in this bargaining game.
For the n-person players, keeping the third party's belief is one of the basic conditions to gain profit from the cooperation. N-person players' best reply is to keep charging the cost to the third party within the limits not to lose the third party's belief in each term. However, such a strategy is uncertain because they do not perfectly know the other players' subjective probability (the iterated Zero-sum n+1 Person Game is the imperfect information game). Therefore, preventing the third party's resistance is fundamentally difficult in this game situation. The effects of the simulation games applying the Markow chain verify my thesis. In many actual negotiations, n-person players tend to lose the trust of the third party before sufficient information is fully accumulated. That is, if a certain player charges costs to another player in order to maximize short-term interests, it may deteriorate the interests of those parties that have actually cooperated in the negotiation in the long run: in other words, they would have to consider the third party's interests “intentionally” in order to gain profit.