Analyzing Prisoner’s Dilemma

Building a foundation for solving simultaneous games.

At the end of my previous blog you were given an example of prisoner’s dilemma. This game is a classic in game theory modeling. Let’s begin by understanding what type of game this is. In game theory you will more than likely come across two types of games: simultaneous and sequential.  A sequential game involves one player choosing their action before the others choose theirs (like a game of chess). In a simultaneous game, each player takes an action without the knowledge of the other player’s action. Prisoner’s Dilemma is an example of a simultaneous game.

An example Prisoner’s Dilemma:

1\2 Silent Betray
Silent -1,-1 -6,0
Betray 0,-6 -4,-4

Scenario: You and your partner have been arrested for burglary (shame on you two). The police have placed both of you in separate interrogation rooms. The officers tell you that your partner is about to tell them everything and that you better come clean or else you will face major jail time. However, you do not know if the officers are being truthful or not. So what do you do?

Let’s examine the payoffs in this game. Both of you are looking at a total of 1 year each if you both choose to stay silent. However, if your partner betrays you by confessing and you stay silent, your partner will be let go and you will get 6 years in prison. This is reversed if you choose to betray and your partner stays silent. If you both choose to betray each other(no honor among thieves) then you will both get 4 years in prison.

In this game you are aware of both you and your partner’s strategies and payoffs (everything is common knowledge). This is an example of a game with complete information (versus incomplete information). Remember that you do not know what choice your partner will make.

An important concept of game theory is the assumption that players behave with perfect rationality. Perfect rationality means that you ALWAYS act in a way that maximizes your utility (payoff). With this in mind, let’s determine which actions you should take in this game.

First, if your partner chooses to stay silent you have the option of either staying silent or betraying him. Since 0 (betraying) > -1 (silent) the rational choice would be to betray your partner. If your partner chooses to betray you, you would rather betray than stay silent as -4 > -6. However, it is assumed that your partner will make rational choices as well. So he or she will betray you if you stay silent or if you betray as well.

1\2 Silent Betray
Silent -2,-2 -6,0
Betray 0,-6 -4,-4

Notice that it is in your best interest to always betray your partner regardless of the choice your partner makes. This is an example of a dominant strategy where regardless of what any other players do, the strategy earns a player a larger payoff than any other. The game has been solved as you will both choose betray\betray. Congratulations! Try solving the game from the previous blog and leave feedback in the comments below.

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