Week 11_Part I_ECON 2101_S1_2010

# Week 11_Part I_ECON 2101_S1_2010 - ECON 2101 WEEK 11 GAME...

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1 ECON 2101 WEEK 11 GAME THEORY Part I What is a game? Cricket, Tennis, Chess …………………. . Are those really what we are going to talk about in the class? “Many continentals think life is a game, the English think cricket is a game”- A game is a triplet –(players, strategies, pay-offs) Example 1: Game 1: Consider the following game – Alan (A) and Brenda (B) caught by cops, suspected of bank robbery. They are taken to separate rooms for investigation. Each has two strategies --- Confess or Deny. The first column list Alan’s strategies while the first row list Brenda’s strategies. If both confess, each gets 10 years in prison, and get a utility of -10. If Alan confesses but Brenda does not, Alan gets only 1 year in prison while Brenda gets 20 years. If both deny, the cops might actually think that may be these are the wrong people but they could never be sure so each still get 3 years in prison. Confess Deny Confess -10, -10 -1, -20 Deny -20, -1 -3, -3 1. Players : Alan and Brenda 2. Strategies : {C, D} for Alan; {C, D} for Brenda. 3. Payoffs : See the payoff-matrix. The above game – Prisoner’s dilemma (Try to think of yourself as one of the prisoners and think you would do) How do you think about solving this sort of problems?

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2 Step 1: Alan thinks about what is best for him. That actually depends on what Brenda is doing (or does it?) Suppose B chooses to Confess. If A confesses then he gets -10 while if A denies he gets – 20. So it is best for A to confess. Suppose B chooses to Deny. If A confesses then he gets -1 while if A denies he gets – 3. Once again, it is best for A to confess. Thus no matter what B does, it is best for A to confess. We say that Confess is a dominant strategy for Alan. Dominant strategy: A strategy for a player A is a dominant strategy if that strategy gives higher payoff than other strategies at his/her disposal irrespective of other players’s strategy. Step 2: Show by using similar arguments as above that Confess is a dominant strategy for Brenda as well. So what do players choose in this game? Thinking as outline in steps 1 and 2, each player chooses to Confess and end up with 10 years in prison. The key idea: The surprising part is that even if they could both deny and get away with 3 years, acting in their self-interest, each choose to confess and end up signing for 10 years in prison. This situation, often referred to as Prisoner’s dilemma arises in a number of economic and social situations. Later we present examples of Prisoner’s dilemma arsing very naturally in a variety of settings. Let’s look at how we solved the problem. First we found the dominant strategy for each player. Then we found out that each player has a unique dominant strategy and hence that is what they should play. However, what happens if no player has a dominant strategy. Consider Example 2
3 Example 2: Once again consider the same folks – A(lan) and B(renda)--- but the situation is a bit nicer. Now they are planning to spend the evening out – whether to

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## This note was uploaded on 05/17/2011 for the course ECON 2103 taught by Professor No during the Fall '10 term at DeVry NJ.

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Week 11_Part I_ECON 2101_S1_2010 - ECON 2101 WEEK 11 GAME...

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