From: *Handbook of Solution Focused Conflict Management* (Cambrigde MA: Hogrefe, 2010)

Nobel Prize winners Von Neumann and Morgenstern invented ‘game theory’ in 1944. They made a basic distinction between *zero-sum games* and *non-zero sum games*. In zero-sum games the fortunes of the players are inversely related, one contestant’s gain is the other’s loss as in tennis or chess. In non-zero sum games, one player’s gain need not be bad news for the other(s). In highly non-zero sum games the player’s interests can overlap entirely. Wright (2000) gives the example of the three Apollo 13 astronauts, who were trying to figure out how their stranded spaceship could be repaired to get back to earth. The outcome was good for all (or could have been bad for all).

Bill Clinton (2000) stated in an interview: ‘In game theory, a zero-sum game is one where, in order for on person to win, somebody has to lose. A non-zero sum game is a game in which you can win and the person you are playing with can win as well. The more complex societies get and the more complex the networks of interdependence within and beyond community and national borders get, the more people are forced in their own interest to find non-zero sum solutions, that is, win-win solutions instead of win-lose solutions’.

Non-zero sum games are also played in biological and cultural evolution: if you are in the same boat you will tend to perish unless you are conducive to productive cooperation.

Zero sum games are a special case of constant sum games, in which choices by players can neither increase nor decrease the available resources. In zero-sum games the total benefit to all players, for every combination of strategies, always adds to zero. Poker exemplifies a zero-sum game, because one wins exactly the amount one’s opponents lose.

Many games studied by game theorists are non-zero-sum games, because some outcomes have net results greater (positive sum games) or less than zero (negative sum games). In non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another. The best metaphor for a non-zero sum game is ‘being in the same boat’. You sink (negative sum) or float (positive sum) together.

The classic non-zero sum game is the *prisoner’s dilemma. *In that scenario two partners in crime are being interrogated separately. The state lacks the evidence to convict them of the crime they committed but does have enough evidence to convict both on a lesser charge, bringing one-year prison term for each. The prosecutor wants conviction on the more serious charge, and pressures each man individually to confess and implicate the other. He says: if you confess but your partner does not, I will let you off free and use your testimony to lock him up for ten years. And if you do not confess, yet your partner does, you go to prison for ten years. If you confess and your partner does too, I will put you both away, but only for three years. The question is: will the two prisoners cooperate with each other, both refusing to confess? Or will one or both of them cheat on the other?

The outcome is determined by the expectations that each player forms of how the other will play, where each of them knows that their expectations are substantially reciprocal. Non-zero sum games are not about relationships in which cooperation is necessarily taking place. It is usually a relationship in which, if cooperation did take place, it would benefit both parties. Whether the cooperation does take place, whether the parties realize positive sums, is another matter. Sometimes in non-zero sum situations the object of the game is not to reap positive sums, but simply to avoid negative sums.

To realize mutual profit in a non-zero sum situation, two problems must be solved: communication and trust. There are two pitfalls in non-zero sum games: there is the problem of cheating and there is also a zero-sum dimension in almost any real-life non-zero sum game. Wright (2000): ‘When you buy a car, the transaction is non-zero sum: you and the dealer both profit, which is why you both agree to the deal. But there is more than one price at which you both profit: the whole range between the highest you would rationally pay and the lowest the dealer would rationally accept. And within that range, you and the dealer are playing a zero-sum game: your gain is the dealer’s loss. That’s the reason bargaining takes place at car dealerships’ (p. 25).

Schelling (1960) states that conflicts are typically mixtures of cooperative and competitive processes. The course of the conflict is determined by the nature of this mixture. The core emphasis is on having interdependent interests: the fates of clients are woven together. Game theory recognizes that cooperative as well as competitive interest may be intertwined in conflict.

In addition to interdependence, there can be independence, such that the activities and fate of the people involved do not affect one another. If they are completely independent of one another, no conflict arises. The existence of a conflict implies some form of interdependence. In a relationship asymmetry may exist to the degree of interdependence. One person can be more dependent on the other than the other way around. In an extreme case, one person may be completely independent of the other, whereas the other may be completely dependent on the first person. As a consequence, that person will have greater power and influence in the relationship than the other person has.

In summary, from the perspective of game theory, *mediation* revolves around a non-

zero sum game, where everybody gains (win-win), whereas a judicial procedure revolves around a zero sum game (win-lose). Win-win means you swim together; win-lose means you swim and the other party sinks, and if the other party swims, you sink, whereas lose-lose means you sink together. For that same reason, I propose to change the word ‘party’ (fight) to ‘participant’ or ‘client’ (cooperation) in mediation.

In mediation the measure of success is not so much whether a client wins at the other client’s expense, but whether he gets what he wants because he enables the other(s) to achieve their dreams and to do what they want. In other words: *‘Winning will depend on not wanting other people to lose’* (Wright, 2000, p. 332)

*References*

Clinton, B. (2000). Interview *Wired Magazine, December 2000.*

Schelling, T.C. (1960). *The strategy of conflict*. Cambrigde MA: Harvard University Press.

Von Neumann. J. & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton, NJ: Princeton University Press.

Wright, R. (2000). *Nonzero. History, evolution & human cooperation*. London: Abacus.

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