In Exercises 15-20, decide whether the game is strictly deter- mined. If it is, give the players' optimal pure strategies and the value of the game. [HINT: See Example 4.] 16. b -1 10
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answer both 16 and 18, or dont answer at all
![In Exercises 15-20, decide whether the game is strictly deter-
mined. If it is, give the players' optimal pure strategies and the
value of the game. [HINT: See Example 4.]
16.
18.
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b
10
Р
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-2
9
1
3
2
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- A tennis tournament has 85 participants. Players who lose a game are immediately eliminated; players who win a game keep playing. Still, the organizers have a lot of choices to make. They could give a first round bye to some players so that after the first round there are 26 = 64 players and no more bye are needed. Or they could give even a second round bye to the best players, or possibly even a third round bye to the very best ones. What is the best strategy for the organizers if they want to choose the winner of the tournament using as few games as possible?3.4 The system is tested on a sample of one hundred computers and the average connection speed is found to be far below 400 kilobits. What hypothesis should probably be rejected? Explain. If the customer needs a connection speed of 400 kilobits to run her application programs, what is the business decision that corresponds to the decision regarding the hypotheses?A particular two-player game starts with a pile of diamonds and a pile of rubies. Onyour turn, you can take any number of diamonds, or any number of rubies, or an equalnumber of each. You must take at least one gem on each of your turns. Whoever takesthe last gem wins the game. For example, in a game that starts with 5 diamonds and10 rubies, a game could look like: you take 2 diamonds, then your opponent takes 7rubies, then you take 3 diamonds and 3 rubies to win the game.You get to choose the starting number of diamonds and rubies, and whether you gofirst or second. Find all starting configurations (including who goes first) with 8 gemswhere you are guaranteed to win. If you have to let your opponent go first, what arethe starting configurations of gems where you are guaranteed to win? If you can’t findall such configurations, describe the ones you do find and any patterns you see.
- In baseball, League A allows a designated hitter (DH) to bat for the pitcher, who is typically a weak hitter. In League B, the pitcher must bat. The common belief is that this results in League A teams scoring more runs. In interleague play, when League A teams visit League B teams, the League A pitcher must bat. So, if the DH does result in more runs, it would be expected that league A teams will score more runs in League A park than when visiting League B parks. To test this claim, a random sample of runs scored by league A teams with and without their DH is given in the accompanying table. Complete parts c) through d) below.Abstract To cooperate effectively, both in small-scale interactions and large-scale collective-action problems, people frequently have to delay gratification (i.e., resist short-term temptations in favor of joint long-term goals). Although delay-of- gratification skills are commonly considered critical in children’s social-cognitive development, they have rarely been studied in the context of cooperative decision-making. In the current study, we therefore presented pairs of children (N = 207 individuals) with a modified version of the famous marshmallow test, in which children’s outcomes were interdependently linked such that the children were rewarded only if both members of the pair delayed gratification. Children from two highly diverse cultures (Germany and Kenya) performed substantially better than they did on a standard version of the test, suggesting that children are more willing to delay gratification for cooperative than for individual goals. The results indicate that from…Abstract To cooperate effectively, both in small-scale interactions and large-scale collective-action problems, people frequently have to delay gratification (i.e., resist short-term temptations in favor of joint long-term goals). Although delay-of- gratification skills are commonly considered critical in children’s social-cognitive development, they have rarely been studied in the context of cooperative decision-making. In the current study, we therefore presented pairs of children (N = 207 individuals) with a modified version of the famous marshmallow test, in which children’s outcomes were interdependently linked such that the children were rewarded only if both members of the pair delayed gratification. Children from two highly diverse cultures (Germany and Kenya) performed substantially better than they did on a standard version of the test, suggesting that children are more willing to delay gratification for cooperative than for individual goals. The results indicate that from…
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