Prisoner's Dilemma: John Von Neumann, Game Theory and the Puzzle of the Bomb

“As von Neumann used the term, a “game” is a conflict situation where one must make a choice knowing that others are making choices too, and the outcome of the conflict will be determined in some prescribed way by all the choices made.”
“The solution is to let one child divide the cake and let the other choose which piece he wants. Greed ensures fair division. The first child can’t object that the cake was divided unevenly because he did it himself. The second child can’t complain since he has the choice of pieces.”
“This isn’t the way real people play real games. To detail every possible contingency beforehand would be the antithesis of the word “play.”
“The cutter is empowered only to decide the row of the cake division’s outcome. He expects to end up with the least amount of cake in that row, for the chooser will act to minimize the cutter’s piece. Therefore he acts so as to maximize the minimum the chooser will leave him.”
“Von Neumann analyzed a simplified form of poker. In outline, his conclusions apply to the real game. He showed that you should always bid aggressively when you have a strong hand. With a weak hand, you should sometimes bluff (bid aggressively anyway).”
“There is one rule implicit in such free fantasizing. You can’t change the other team’s strategy. If you’re talking about what the Redskins should have done, you can’t also presume to change the way their opponents played. That would make it too easy. If you could choose the opposing team’s strategy, you could sabotage their play. That’s not fair.”
“As the term is most commonly used in U.S. politics, a liberal is a “cooperator”: someone willing to put himself at risk for exploitation in order to increase the common good. Liberals favor paying taxes that go to help the homeless in the expectation that the homeless will not fritter away such aid but will use it to get on their feet. A liberal may favor cutting back in defense expenditures in the hope that other countries will do the same. By cooperating, a liberal expects to create a society with fewer homeless, or fewer missiles—something that everybody wants, but which will not come about through anyone’s unilateral effort. Conservatives are often “defectors” in that they seek to guarantee themselves the best outcome possible on their efforts alone. Taxes may be squandered, so the safest course is to let people keep as much of their income as possible and decide individually how best to spend it. Enemy nations may exploit a unilateral arms freeze to gain the upper hand. Conservative political positions avoid the “sucker payoffs” of welfare cheats and arms treaty violators.”
“Any given preference ordering of the four payoffs defines a game. For instance, when DC>CC>DD>CD —meaning that the DC outcome is preferred to CC, which is preferred to DD, which is preferred to CD—the game is a prisoner’s dilemma.”
“One instance of bully is the biblical tale demonstrating the wisdom of King Solomon (1 Kings 3:16–28). Two women claim the same child as their own. One is the real mother, and the other is an impostor. Solomon proposes splitting the child in two. Hearing this horrific suggestion, one woman abandons her claim to the child. Solomon awards the child to that woman. The real mother would love her child so much she would give it up to save its life. In other words, the true mother has the preferences of a chicken player. The knife is poised over the child. The dilemma is whether to stand firm (defect) or give in (cooperate). The real mother most wants to prevail—to stand firm on her claim while the impostor backs down. The worst outcome from the real mother’s standpoint is for neither woman to give in. Then the child is cut in two.”
“What makes the iterated prisoner’s dilemma different from a one-shot dilemma is the “shadow of the future,” to use Axelrod’s colorful phrase. It makes sense to cooperate now in order to secure cooperation in the future. But no one takes the future quite as seriously as the present. Players subjectively weight a present advantage against possible future losses. “A bird in the hand is worth two in the bush.”
“But a strategy that is too eager to cooperate often gets clobbered. TIT FOR TAT is also provocable. It defects in response to defection by the other strategy. Remember, after the first round, TIT FOR TAT echoes whatever the other strategy did. If the other strategy defects on Round 5, TIT FOR TAT defects on Round 6. That gives the other strategy an incentive to cooperate.”