lecy
commented
4 years ago Q3: How much better off are you switching in each of the three scenario with 10 doors and 1 to 3 cars? I am not sure if I should get the Pr(win|switch)−Pr(win|stay) for each scenario and compare them to each other.
Yes, you are comparing gains from strategies:
gains.01 = Pr( win | switch & 1 car ) − Pr( win | stay & 1 car )
gains.02 = Pr( win | switch & 2 cars ) − Pr( win | stay & 2 cars )
gains.03 = Pr( win | switch & 3 cars ) − Pr( win | stay & 3 cars )In other words, how does the game structure impact that payoff of the optimal strategy.
This is an invented game so we obviously don't care that much about the specific answer, but this question is a good example of how simulation can be used to do scenario planning under conditions of uncertainty. We can use models to produce ranges of outcomes and compare them under different scenarios.
For example, there are similar dashboard that allow local government leaders to do some scenario planning to control the spread of COVID by looking at current populations and the ability to impose restrictions on businesses or stay in place orders.
Hopefully that helps contextualize this question a little more.
gzbib
Hello @lecy,
I got a little confused when I started answering the 3 questions in part 2. What I understood is below:
Q1: Is SWITCH still the dominant strategy? Report your chances of winning for each strategy for each scenario?
I need to run the simulations for each scenario and compare the pr (win|switch) and pr (win|stay)
Q2: How much better off are you switching in the original game? How much did it improve your chances of winning?
Here I ran the simulation in the original game (1 car and 2 goats) and I got the difference between the Pr(win|switch)−Pr(win|stay).
Q3: How much better off are you switching in each of the three scenario with 10 doors and 1 to 3 cars?
I am not sure if I should get the Pr(win|switch)−Pr(win|stay) for each scenario and compare them to each other.
Thank you