Repeated games

Introduction

In previous chapters of game theory we introduced one-shot games like prisoners dilemma. In other words situations when we are allowed to do one action that result in some outcome (payoff). For example a situation when someone wants to enjoy fast car ride. If he drives really fast he enjoys fast ride and he´s happy but he also rist that police will catch him and arrest. So he must choose between driving fast or not fast according to his ulitily from one decision. But in the real world we often meet situations that repeat or their consequences affect other situations. We can say that our live is set of games in some order and we are playing them. And all of us know that this games, this situations repeat very often. We go to work every day or go shopping for example. Sequence of games that affect other games and are played by the same players is called repeated game.

We can say that every human is rational and follows his own profit. That in other words mean that a person should not have problem with betrayal of other person to get higher payoff. But what if game continues and this betrayal can be avenger? Under these circumstances is the first person willing to betray the second in the first round? It depends on the situation. It depends on the payoff. So we can say that in a game of various number of persons we can achieve cooperation for a time that players benefit from cooperation.

Game theory is often quoted by politicians to gave their opinios seriousness and as a way how to look smarter that they are. And it is also a great example of repeated game. Politicians like senators often vote about laws they propose. Options for the vote are support or not to support. If the vote was only a matter of good proposal/bad proposal, politicians would vote exactly the same. But because they follow their own goals the vote depends on many different things. Lets say that senator A propose a law that after the adoption brings a great popularity to him. But he needs senator B to support his proposal. So he asks senator B for support and he agrees only on the condition that he will in return later vote for his proposal. Regardless of what they promised to each other they now have several options. Senator B can vote for proposel and than expect support for his proposal or defect already in round 1, gain some profit from senator A not having that popularity but senator A will be probably angry and not support his proposal too. If he chooses to support him now have senator A some options. He has gained popularity for his law proposal and he can now return the favor or betray. Remember he already gained popularity so he can make additional profit from betraying his opponent. But if he do so he can probably expect revenge every time he wants to cooperate with senator B. There will be surely more voting in the future so what is the best strategy to maximize the payoff? That is the knowledge we gain from studying repeated games.

The Evolution of Cooperation

The evolution of cooperation can refer to:

• the study of how cooperation can emerge and persist (also known as cooperation theory) as elucidated by application of game theory
• a 1981 paper by political scientist Robert Axelrod and evolutionary biologist W. D. Hamilton in the scientific literature
• a 1984 book by Axelrod that expanded on the paper and popularized the study.