Game+Theory+1


 * || sleep in || wake up early ||
 * sleep in || -10,-10 || 4,1 ||
 * wake up early || 4,4 || 4,1 ||

Scramble for Sleep: Two brothers are in the same carpool and have to use the same shower every morning. They have to decide how they are going to both take a shower with out getting into each others way. Each of them has the decision to either sleep in or get up early. If the first brother sleeps in and the other doesn't, the one who slept in gets 4 points for the extra sleep and the one who woke up early gets only one point. The fist brother, unlike the second, likes to wake up early so he gets 4 points whether he sleeps in or not. so if the second brother sleeps in and the first brother doesn't they both get 4 points. If they both wake up early then they both get to school on time so the first brother gets 4 points for waking up early and the second gets one for getting to school on time. But if they both wake up late then they are both late and they both get -10 points.

Materials Required: Light Switch Mr. Szporn to turn off/on the light switch Desks Rules: 1. Two people partner together and sit in desks facing each other. 2. Classify one person as the individual who likes to wake up early. 3. The lights will turn off for two seconds so that the players cannot see the choice of the other. 4. Each player has two choices: -Stand up out of your chair to symbolize waking up early -Put your head down to symbolize sleeping in. 5. Lights go back on and players can see the outcome. 6. Record scores/discuss to find a colluding solution and repeat.

Results: In this example only the first brother has a dominant strategy. This is only due to the fact that he is indifferent to whether he wakes up early or not. Unfortunately the second brother does not get the same joy out of getting up early. So when his brother wakes up early he would rather sleep in and when his brother sleeps in he would rather wake up early. Since the first brother's dominant strategy is to wake up early and the second doesn't have a dominant strategy the nash equilibrium occurs when the first brother wakes up early and the second one sleeps in.