The Blackmailer Paradox

by Robert Aumann

Game Theory and negotiations with Arab countries.

Reuben and Shimon are placed into a small room with a suitcase containing $100,000 of cash. The owner of the suitcase offers them the following: “I’ll give you all the money in the suitcase, but only on the condition that you negotiate and reach an amicable agreement on its division. That’s the only way I will give you the money.”

Reuben, who is a rational person, appreciates the golden opportunity presented to him and turns to Shimon with the obvious suggestion: “Come, you take half the amount, I’ll take the other half, and each of us will go away with $50,000.” To his surprise, Shimon, with a serious look on his face and a determined voice says: “Listen, I do not know what your intentions are with the money, but I’m not leaving this room with less than $90,000. Take it or leave it. I’m fully prepared to go home with nothing.”

Reuben can not believe his ears. What happened to Shimon? he thinks to himself. Why should he get 90%, and I only 10%? He decides to try to talk to Simon. “Come, be reasonable,” he pleads. “We’re both in this together, and we both want the money. Come let’s share the amount equally and we’ll both come out ahead.”

But the reasoned explanation of his friend does not seem to register on Shimon. He listens attentively to Reuben’s words, but then declares even more emphatically, “There is nothing to discuss. 90-10 or nothing, that’s my final offer!” Reuben’s face turns red with anger. He wants to smack Shimon across his face, but soon reconsiders. He realizes that Shimon is determined to leave with majority of the money, and that the only way for him to leave the room with any money is to surrender to Shimon’s blackmail. He straightens his clothes, pulls out wad of bills from the suitcase in the amount of $10,000, shakes hands with Shimon and leaves the room looking forlorn.

This case in Game Theory is called the “Blackmailer Paradox.” The paradox emerging from this case is that the rational Reuben is eventually forced to act clearly irrationally, in order to gain the maximum available to him. The logic behind this bizarre result is that Shimon broadcast total faith and confidence in his excessive demands, and it is able to convince Reuben to yield to his blackmail in order for him to receive the minimum benefit.

Arab – Israel Conflict

The political relationship between Israel and Arab countries is also conducted according to the principles of this paradox. The Arabs present rigid and unreasonable opening positions at every negotiation. They convey confidence and assurance in their demands, and make certain to make absolutely clear to Israel that they will never give up on any of these requirements.

Absent an alternative, Israel is forced to yield to blackmail due to the perception that it will leave the negotiating room with nothing if it is inflexible. The most prominent example of this is the negotiations with the Syrians that have been conducted already for a number of years under various auspices. The Syrians made certain to clarify in advance that they will never yield even an inch of the Golan Heights.

The Israeli side, who so desperately seek a peace agreement with Syria, accept Syria’s position, and today, in the public discourse in Israel, it is clear that the starting point for future negotiations with Syria must include a full withdrawal from the Golan Heights, despite the critical strategic importance of the Golan Heights to ensure clear boundaries that protect Israel.
How to Avoid Failure

According to Game Theory, the State of Israel must make some perceptual changes to improve its position in the negotiations with the Arabs, and to ultimately win the political struggle.

A. Willingness to renounce agreements: The present Israeli political approach is based on the assumption that an agreement with the Arabs must be reached at all costs, because the present situation, with the lack of an agreement, is simply intolerable. In the “Blackmailer Paradox,” Reuben’s behavior is based on the perception that he must leave the room with some amount of money even if it is the minimum. Reuben’s inability to accept the possibility that he may have to leave the room empty-handed, inevitably causes him to surrender to extortion and to leave the room in shame as a loser, but at least with some gain. Similarly, the State of Israel conducts its negotiations from a frame of mind that does not allow her to reject suggestions that do not conform to its interests.

B. Consideration of repeat games: Based on Game Theory, one should consider a one-time situation completely differently from a situation that repeats itself again and again, for in games that repeat over time, a strategic balance that is neutral paradoxically causes a cooperation between the opposing sides. Such cooperation occurs when the parties understand that the game repeats itself many times, therefore they must consider what will be the impact of their present moves on future games, when the fear of future loss serves as a balancing factor. Reuben related to the situation as if it were a one-time game, and acted accordingly. Had he announced to Simon that he was not prepared to concede the part due him, even in light of a total loss, he would change the outcome of the game, for the future, although it is quite likely that he would leave the room empty-handed in the current negotiation. However, if both encounter a similar situation in future, Shimon would recognize Reuben’s seriousness and have to reach a compromise with him. Likewise, Israel must act with patience and with long-term vision, even at the cost of not coming to any present agreement and continuing the state of belligerence, in order to improve its position in future negotiations.

C. Faith in your position: Another element that creates the “Blackmailer Paradox,” is the absolute certainty of one side in its positions, in this case the position of Simon. Full certainty creates an internal justification of one’s convictions, and in the second round serves to convince his opponent that his positions were right. This results in the opponent’s desire to reach a compromise even by acting entirely irrationally and distancing him from his opening demands. Several years ago, I talked to a senior officer who claimed that Israel must withdraw from the Golan in any peace settlement because, from the Syrian point of view, the land is sacred and they will not give up on it. I explained to him, the Syrians convinced themselves that this is sacred ground, and it was this that succeeded to convince us as well. The deep conviction of the Syrians, cause us to surrender to the Syrian dictates. The present political situation will be resolved only if we convince ourselves of the justice of our views. Only total faith in our demands will be able to convince the Syrian opponent to consider our position.

Like all science, Game Theory does not presume to express an opinion on moral values, but rather seeks to analyze the strategic behaviors of rival parties in a common game. The State of Israel plays such a game with its enemies. Like every game, in the Arab-Israeli game there are particular interests that shape and frame the game and its rules. Unfortunately, Israel ignores the basic principles that arise in Game Theory. If the State of Israel succeeds in following these base principles, its political status and its security will improve significantly.