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Aumannova teorija igara

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Na prvu večer Hanuke, Israel Aumann je, na Hebrejskom sveučilištu u Jeruzalemu, održao svoje predavanje u povodu dobivanja Nobelove nagrade. Na popularan je način diskutirao o nekim posljedicama svojih ideja, za koje je dobio Nobela.

Imagine two players playing a game in which either can choose to cooperate or act selfishly. If both cooperate, they each get 3000. If both act selfishly, they each get 1000. If one cooperates and the other acts selfishly, the selfish one gets 4000 and the cooperative one gets 0. Note that for each player (A), regardless of what the other player (B) does, A makes 1000 more by acting selfishly than by cooperating. For that reason, the only equilibrium point of the game is the one in which both act selfishly. The result is that both end up with 1000 rather than 3000. Obviously, this is not optimal for either one. (Formally, we say that this result is not Pareto optimal, i.e., there are solutions in which both players can do better.) If the players could negotiate an agreement and trust that such an agreement would be enforced (say, by a third party), then they obviously could do better.

Now let's imagine that there is no third party enforcer but rather the same players are doomed to play the same game over and over again. It turns out that in this scenario, cooperative behavior is self-reinforcing, since a player is prevented from acting selfishly by the threat that the other player will react to selfish behavior by acting selfishly himself in subsequent games. Thus, in repeated games, players will ultimately cooperate even without an enforcer.

There is, however, one limitation to this self-reinforcement. Players must value profits in the future almost as much as profits now. If they don't, the threat of future losses as punishment for short-term profits is an inadequate threat. Aumann repeated at least three times that the practical consequence of this is that those who place too high a premium on peace now will delay peace indefinitely, while those who establish a credible threat of retaliation have a chance to achieve peace sooner.

Nakon predavanja, priređeno je primanje za prijatelje, obitelj, kolege i razne bessere mentschen. Cellist je svirao, dok su služeni hors d'ouevres; ukratko organizatori su nastojali postići pretencioznu atmosferu. Jedino što je Aumann inzistirao da se prvo skupi minjan za maariv, a zatim zapali prva svijeća za Hanuku i otpjeva Maoz Tzur - svih 6 dijelova.

Link na HUJI
Nobelovac (link na hrvatskom)


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