Games for social sciences experiments (Part 2) 1

2 Hi, my name is John. I really like soccer. This is Peter, my best friend. We’re like brothers. Hi, I’m Peter. One of my favorite things to do is to go to pop concerts.

3 Hm… I’ve bought 2 tickets to watch my favorite team play this Saturday evening. Let’s go together, Peter. I’m sure it’ll be fun! Oh… What a coincidence! My favorite pop star is performing this Saturday evening too. I’ve even bought concert tickets. See, here’s the ticket I bought for you..

Fill up the table below TABLE A John and Peter’s happiness level on a scale of 1-4 JohnPeter Scenario A: When John goes to the concert with Peter Scenario B: When Peter goes to the match with John Scenario C: When John goes to his match and Peter goes to his concert Scenario D: When John goes to his concert and Peter goes to his match >4 Very unhappy very happy

Use information in Table A to fill in the matrix below Peter goes to the concert Peter goes to the match John goes to the concert ( ___, ___ ) John goes to the match ( ___, ___ ) 5

Formalizing simultaneous games Such a scenario where 2 people are making decisions at the same time that can affect each other’s outcomes are known as simultaneous games Since there are 2 players- John and Peter, and each player has 2 choices. This is a 2-player, 2 by 2 game. (i.e. 2 choices by 2 choices) The 2 by 2 game has 4 different outcomes for each player. This specific game we talked about is known as “Battle of the sexes”. Usually, simultaneous games are represented in a matrix 6

7 Luke, if you do well for your exam, I will buy you a new iPhone. Daddy, don’t worry. I know that if I study hard for my exam, I will do well.

8 But that’s the question, will you bother to study hard for your exam or not? Daddy, the question is if you will really buy me a new iPhone if I do well or not? I know you prefer to save money. You just say that to encourage me to study hard…

Formalizing sequential games Daddy and Luke’s happiness level on a scale of 1-3 DaddyAh Boy Scenario A: Luke studies, then Daddy buys phone Scenario B: Luke studies, then Daddy goes back on his promise and doesn’t buy phone Scenario C: Luke doesn’t study, yet Daddy buys phone for him Scenario D: Luke doesn’t study, and thus Daddy doesn’t buy phone for him >3 Very unhappy very happy

Formalized sequential game Outcomes Daddy’s decision to buy phone or not Luke’s decision to study or not Luke Daddy Study Don’t Study Buy Don’t Buy ( ____, ____ ) 10 ( ____, ____ ) Don’t Buy

Formalizing sequential games Such scenarios where 2 people are making decisions one after another are known as sequential games Since there are 2 players- Daddy and Luke, and each player has 2 choices. This is a 2-player, 2 by 2 game. (i.e. 2 choices by 2 choices) The 2 by 2 game has 4 different outcomes for each player. Sequential games are represented usually in an extensive form, also known as a tree diagram. 11