### Introduction

In this report is to introduce what is the Prisoner's Dilemma and the meaning about Cartel Union. First is to analyze the correlation of manufacturers and the prisoners' dilemma due to the correlation. The effectiveness of Cartel coalition is investigated and the principle of output dispense is given. Explain the factors affecting the stability of Cartel. From the game theory it is a rational behavior for interactive decision problems. In a game, several agents strive to maximize their (expected) utility index by choosing particular courses of action, and each agent's final utility payoffs depend on the profile of courses of action chosen by all agents. The interactive situation, specified by the set of participants, the possible courses of action of each agent, and the set of all possible utility payoffs, is called a game; the agents 'playing' a game are called the players. From this precondition to understand about the prisoner's dilemma from the Dominant Strategies, Extensions of the Prisoner's Dilemma and the Issues with Respect to the Prisoners' Dilemma these three parts to analysis the problem of Prisoner's Dilemma. And used the Oligopoly Problem to explain the reason why Prisoner's Dilemma can solutions the problem of oligopoly pricing and the situation in the market. Combine whit the Cartel and the Nash equilibrium### The Prisoner's Dilemma

The Prisoner's Dilemma is one of the best-known models in game theory. In the picture, figure 1, the natural world in a ridiculous role to prove that two suspicious people help each other, or opposing each other. In this assumptive situation, two confederates have been locked up in prison, and they tried to fake evidence of a crime and not sell out the other side do not recognize the crime. And the next step is give the serious of the punishment that each receives is determined not only by his behavior, but also by the behavior of his or her accomplice. The two prisoners are separated and cannot communicate with each other. And the result should be have four different possible.- If one confesses to the crime and turns in the accomplice his sentence will be reduced.
- If one confesses while the accomplice does not, the first can make a deal with the police, and will be set free. But the information he provides will be used to incriminate his accomplice, who will receive the maximum sentence.
- If both prisoners confess to the crime, then each receives a reduced sentence, but neither is set free.
- If neither confesses to the crime, then each receives the minimum sentence because of the lack of evidence. This option may not be as attractive to either individual as the option of striking a deal with the police and being set free at the expense of one's partner. Since the prisoners cannot communicate with each other, the question of whether to "trust" the other not to confess is the critical aspect of this game.

### Dominant Strategies

What has happened here is that the two prisoners have fallen into something called” dominant strategy equilibrium." The first is Dominant Strategy: Let an individual player in a game evaluate separately each of the strategy combinations he may face, and, for each combination, choose from his own strategies the one that gives the best payoff. If the same strategy is chosen for each of the different combinations of strategies the player might face, that strategy is called a "dominant strategy" for that player in that game. The second is Dominant Strategy Equilibrium: If in a game, each player has a dominant strategy, and each player plays the dominant strategy, then that combination of strategies and the corresponding payoffs are said to constitute the dominant strategy equilibrium for that game. In the Prisoners' Dilemma game to confess is a dominant strategy, and when both prisoners confess, that is dominant strategy equilibrium. This remarkable result -- that individually rational action results in both persons being made worse off in terms of their own self-interested purposes -- is what has made the wide impact in modern social science. For there are many interactions in the modern world that seem very much like that, from arms races through road congestion and pollution to the depletion of fisheries and the overexploitation of some subsurface water resources. These are all quite different interactions in detail, but are interactions in which individually rational action leads to inferior results for each person, and the Prisoners' Dilemma suggests something of what is going on in each of them. That is the source of its power.### Extensions of the Prisoner's Dilemma

Few social situations can be modeled accurately by a single interaction. Rather, most situations result from a series of interactions over a long period of time. An extended version of the Prisoner's Dilemma scenario includes repeated interaction, which increases the probability of cooperative behavior. The logic of this version of Prisoner's Dilemma suggests that a player's strategy depends on his or her experience in previous interactions, and that that strategy will also affect the future behavior of one's opponent. The result is a relationship of mutual reciprocity; a player is likely to cooperate if his or her opponent previously demonstrated willingness to cooperate, and is unlikely to cooperate if the opponent previously did not. The knowledge that the game will be played again leads players to consider the consequences of their actions; one's opponent may retaliate or be unwilling to cooperate in the future, if one's strategy always seeks maximum payoffs at the expense of the other player.### Issues With Respect to the Prisoners' Dilemma

This remarkable result -- that individually rational action results in both persons being made worse off in terms of their own self-interested purposes -- is what has made the wide impact in modern social science. For there are many interactions in the modern world that seem very much like that, from arms races through road congestion and pollution to the depletion of fisheries and the overexploitation of some subsurface water resources. These are all quite different interactions in detail, but are interactions in which individually rational action leads to inferior results for each person, and the Prisoners' Dilemma suggests something of what is going on in each of them. That is the source of its power. A number of critical issues can be raised with the Prisoners' Dilemma. That is a two-person game, but many of the applications of the idea are really many-person interactions. We have assumed that there is no communication between the two prisoners. If they could communicate and commit themselves to coordinated strategies, we would expect a quite different outcome. In the Prisoners' Dilemma, the two prisoners interact only once. Repetition of the interactions might lead to quite different results. Compelling as the reasoning is that leads to the dominant strategy equilibrium may be, it is not the only way this problem might be reasoned out. Perhaps it is not really the most rational answer after all. We will consider some of these points in what follows. Oligopoly prices and "Solutions" to Pricing Games there is a example to Table 1Perrier | |||

price = $1 | price = $2 | ||

Apollinaris | price = $1 | 0,0 | 5000,-5000 |

price = $2 | -5000,5000 | 0,0 |