00:02
Hello everyone, so solving the first part of the question to determine the question says that are there any dominant strategies in this game.
00:11
So to determine whether there are dominant strategies we need to compare the payoffs for each strategy for each player.
00:19
We're talking about dominant strategy so a dominant strategy is one that yields a higher payoff for a player regardless of the strategy chosen by the other player.
01:21
Now looking at the table we can see that there are no dominant strategies for either player for example if bobby chooses high gary's best response depends on whether she chooses left or center in both cases he would receive a higher payoff than if he chooses right.
01:40
Similarly if gary chooses center bobby's best response depends on whether she chooses right or low.
01:50
So we can say that there are no dominant strategies.
02:06
Coming to next part of the question that says finding the likely outcome of this complex game appears difficult.
02:17
Can you simplify the game by finding a strategy that booby should never reasonably play and redraw the game with the strategy eliminated.
02:29
So we can simplify the game by identifying any strategies that are dominated by other strategies.
03:05
A dominant strategy or a dominated strategy is one that is always worse than another strategy regardless of the other player's strategy.
04:07
One strategy that booby should never reasonably play is high.
04:14
If booby chooses high gary's best response would be to choose center which would yield a higher payoff for him than if he chooses left or right.
04:29
So then it would be formed like gary left center and right and this is booby middle low.
04:52
Now in this case it would be 8 ,3 10 ,6 2 ,4 9 ,1 and 1 ,12 and 4 ,3.
05:07
Coming to next part that says is your simplified game game in your simplified game find a strategy that gary should never reasonably play.
05:25
Did that strategy appear to be unreasonable in the original game? redraw the simplified game...