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Math111课程简介
The transition to the university is social. A large portion of university life is SOCIAL and NOT JUST STUDYING. We recognize this fact. One research study found that the average number of hours communicating in a face to face manner with friends is approximately 30 hours per week. Is important that you find friends that you can socialize with and rely upon in the pursuit of your academic goals. Especially as a freshman, you will find other students that are truly not interested in getting educated and more forward in the pursuit of life goals and a career. It is YOUR CHOICE with whom to socialize.
Prerequisites
We hope you choose wisely. The people around you shape your future. I remember the “party animal”, the “all-night gamer”, the “stoner”–yes, I was a student once as well. I remember being pressured to go out on a Wednesday or Thursday night. I remember the fear of missing out. But, there is only one miracle, performance-enhancing drug, and it is called SLEEP. About the fourth week of class, look around at other students in a morning class. Count how many students look exhausted. In an exhausted state, it doesn’t matter how much you study or regularly attend class: VERY LITTLE will be learned. Keep the sleep/party trade-off in mind when making your decisions.
Math111 Game theory HELP（EXAM HELP， ONLINE TUTOR）
Suppose each of our two players $(R$ and $C$ ) play the following game: Each of the two players shows one or two fingers (simultaneously) and $C$ pays to $R$ a sum equal to the number of fingers shown.
(a) Write the payoff matrix.
(b) Is this game fair? Explain why or why not.
(a) The payoff matrix for the game is:
\begin{tabular}{|c|c|c|}
\hline Player & $R$ shows 1 & $R$ shows 2 \
\hline$C$ shows 1 & $(1,1)$ & $(2,1)$ \
\hline$C$ shows 2 & $(1,2)$ & $(2,2)$ \
\hline
\end{tabular}
where the first number in each pair represents the payoff to $\$ R \$$, and the second number represents the payoff to $\$ C \$$.
(b) The game is not fair, as one player can always do better than the other regardless of the other player’s strategy. For example, if $\$ C \$$ always shows two fingers, then $\$ R \$$ will always show one finger to get a payoff of $\$ 2 \$$, whereas $\$ C \$$ will always get a payoff of $\$ 2 \$$ regardless of their strategy.
(c) Can you predict the outcome before the game is even played? Explain.
(c) No, we cannot predict the outcome before the game is played, as it depends on the strategies chosen by each player. However, we can analyze the game to find the best strategy for each player. Since there are only two possible strategies for each player, we can list all possible outcomes and payoffs for each player for each strategy combination:
\begin{tabular}{|c|c|c|c|c|}
\hline Strategy & $(1,1)$ & $(2,1)$ & $(1,2)$ & $(2,2)$ \
\hline$R$ shows 1 & $(1,1)$ & $(2,1)$ & $(1,2)$ & $(2,2)$ \
\hline$R$ shows 2 & $(2,1)$ & $(0,0)$ & $(2,2)$ & $(0,0)$ \
\hline
\end{tabular}
From this table, we can see that the best strategy for $\$ R \$$ is to show one finger if $\$ C \$$ shows one finger, and two fingers if $\$ C \$$ shows two fingers. The best strategy for $\$ C \$$ is to always show two fingers, since this guarantees a payoff of $\$ 2 \$$ regardless of $\$ R \$ ‘ s$ strategy.
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