February 07, 2006

Prisoner's dilemma

Prisoner's dilemma, in Game Theory, is a type of Non Zero SUM Game in which two players try to get rewards from a banker by cooperating with or betraying the other player.

In which two players try to get rewards from a banker by cooperating with or betraying the other player. In this game, as in many others, it is assumed that the primary concern of each individual player ("prisoner") is self-regarding; i.e., trying to maximise his own advantage, with less concern for the well-being of the other players.

First, it identifies the natural purposes of game. Let’s think about the “negotiation”, a familiar concept we talk about here and there, actually it’s a form of extrinsic behaviors of the game. But so not much people understand what is an effective negotiation means. Some think negotiation means speaking out what you want to say, and encourage other to speak out theirs. A better answer will be to know what other wants and bring out what I want. These must be rockets. They believe “negotiation” is a processing, but in fact, it’s a purpose. Achieve the target is the essential the game, and negotiation. It’s nothing to be negotiated and no need to game if you didn’t have a clear and specific purpose at the very beginning. We all admit that we do something for purpose, but we usually forget what our targets are, during the course. Then makes “negotiation” convert into “conversation”; or “Chat” if you planned to do negotiate on MSN. “Negotiation” means the way in which you get what you want and let others do what you want them to do. Yes, thought about negotiator, what is Roman's target? To rescue the hostage, that's all what he want. So he chats with the hijacker in order to distract him from the hostage, then shootes on him. This is a successful negotiation, sometimes the crucial factors ain't sentences but actions.

It can be point out clearly, now only the behaviors contain the competition or the antagonism archery target behavior lead to game behaviors. The parties joined in the game take on different purpose or benefits with one and each others. Game theory studies decisions that are made in an environment where various players interact. In other words, game theory studies choice of optimal behavior when costs and benefits of each option are not fixed, but depend upon the choices of other individuals. Yes, in this term, we play games every moment, in every where. Game Theory is just the mathematics theory and technique that studies strategic situations where players choose different actions in an attempt to maximize their returns.

In the prisoner's dilemma, cooperating is strictly dominated by defecting, so the only possible equilibrium for the game is for all players to defect. In simpler terms, no matter what the other player does, one player will always get a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect.

In any kind of the game, no matter what the strategy other player choose, if a player still have a better strategy to choose for a better payment, then we have to say the strategy he chose is Strictly Inferior. Because he made violation for the fundamental purpose of the game, to maximize his individual returns in playing the game, as we talked earlier before. A rational player will never choose a Strictly Inferior strategy. In prisoner's dilemma, defecting makes cooperating being a Strictly Inferior strategy. So the only possible equilibrium for the game is for all players to defect. In simpler terms, no matter what the other player does, one player will always get a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect. The unique equilibrium for this game does not lead to a Pareto-optimal solution, which means all player involved in the game will play defect.

Let me explain a little more detail here. There’s conflict exist between the TOTAL REWARDS and PERSONAL REWARDS while choosing a cooperating or defecting solution. In a both side cooperating solution, the may maximize their total rewards, but the point is it’s not an averagely allocation for every single player. Thought we mentioned the concept of “Strictly Inferior”, which make players defecting so that he received a greater payment from it. And if you integrate psychology into our game theory, an unbalanced allocation is the root of defecting. People care about how much the other gets, more than how much he has been paid actually.

We assume the total reward goes to be 10 in this cooperating solution, and then we suppose the allocation proportion goes to be an unequal 4:6. Then the player paid 4 would choose to defect, maybe 5 for his defecting. On the opposite side, the player had paid 6 now lose partial benefits because of being defected by the other; a frequently used parameter for this “Being Defected Publish” is 0/1.

The unique equilibrium for this game does not lead to a Pareto-optimal solution. That is, when two rational players both play defect even though the total reward (the sum of the reward received by the two players) would be greater if they both played cooperate. In equilibrium, each prisoner chooses to defect even though both would be better off by cooperating. This is the dilemma.

Under this circumstance, TOTAL REWARDS become less, but it’s nothing important in the game. The importance is the one play defecting gains more rewards than playing cooperating. When both sides comprehend they can gain more by playing defecting but not cooperating, they will all play defecting. That’s why in the prisoner's dilemma, cooperating is strictly dominated by defecting. The ultimately purpose in the game is trying to maximize individual benefit, but absolutely not to maximize the SUM.

In the iterated prisoner's dilemma the game is played repeatedly. Thus each player has an opportunity to "punish" the other player for previous non-cooperative play. Cooperation may then arise as an equilibrium outcome. The incentive to cheat may then be overcome by the threat of punishment, leading to the possibility of a cooperative outcome. As the number of iterations approaches infinity, the Nash equilibrium tends to the Pareto optimum.

Am I just talking about a 1+1=2 equation?

It could be because defect seems to be the only choose unless the game will be kept recycle again and again. You defect once; others would “pay you back” in the next round. Of both you two keep defecting each other all the rounds, you both minimize your SUM rewords, and you lose the game.

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