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Last problem was 0480 (HELP) |
Q191. A voter has an objective function which is to minimize the difference between her positions on two issues and those of the candidates. Here positions can be described as a 3 on issue A and an 8 on issue B. Candidate 1 has positions -2 and 9 while candidate 2 has positions 4 and 4. For whom will the voter cast her ballot?
Q192. A student wants to maximize her GPA. Three of her courses are required 3 credit courses and she estimates she will get a B in each. She has a choice between an easier 3 credit course that she can definitely get an A in and a slightly harder 4 credit course in which she expects a B+. What will she do?
Q202. (a) Set up the issue of whether to use the metric system or the English system of weights and measures as a coordination game. (b) Identify any equilibria and whether they are efficient or not. (c) If we are in the English/English cell, describe both players' motivations to unilaterally switch to metric. (d) what if we were in the metric/English cell?
Q203. Group these examples of coordination games and explain.
- do we store the ketchup in the fridge or in the cabinet?
- smokers should marry smokers and non-smokers should marry non-smokers
- cat people and dog people and dating
- people's sense of what constitutes rudeness
- infidelity is never OK, infidelity is OK in certain circumstances
- Erring on the side of caution; nothing ventured, nothing gained
- Every woman for herself; Let's work as a team.
Q204. Suppose the agents in a population have four behaviors - W, X, Y, Z - and that each behavior is either present or absent. When two agents meet they may have all the same behaviors, none of the same behaviors, or 1 or 2 behaviors in common. Suppose the probability of interaction is proportional to their similarity. IF they do interact, they flip a coin and who ever wins gets imitated by the other agent.
In the grid below, determine the probability of interaction between each pair of neighbors (assume no diagonal interaction for now)
| A 1110 |
B 1010 |
C 0010 |
D 1001 |
| E 0000 |
F 1111 |
G 1001 |
H 1011 |
| I 1000 |
J 1000 |
K 1110 |
L 0000 |
| M 0010 |
N 1100 |
O 0100 |
P 0111 |
Q205. Suppose the agents in a population have four behaviors - W, X, Y, Z - and that each behavior is either present or absent. When two agents meet they may have all the same behaviors, none of the same behaviors, or 1 or 2 behaviors in common. Suppose the probability of interaction is proportional to their similarity. IF they do interact, they flip a coin and who ever wins gets imitated by the other agent.
Use the two random number tables below (the left table for doing a Monte Carlo simulation of whether interaction occurs and the left table to determine which agent is the leader and which is the follower) to work out the next state n the grid below, determine the probability of interaction between each pair of neighbors (assume no diagonal interaction for now)
| 69 | 72 | 43 | 97 | 87 | 0 | 0 | 0 | 1 | 1 | |
| 37 | 86 | 35 | 23 | 41 | 1 | 1 | 0 | 0 | 1 | |
| 88 | 36 | 94 | 60 | 60 | 1 | 1 | 1 | 0 | 0 | |
| 84 | 26 | 3 | 87 | 12 | 0 | 0 | 1 | 1 | 0 | |
| 8 | 10 | 56 | 52 | 29 | 1 | 1 | 1 | 0 | 0 | |
| 26 | 5 | 30 | 15 | 58 | 0 | 1 | 1 | 1 | 1 | |
| 95 | 3 | 95 | 18 | 69 | 0 | 0 | 1 | 0 | 0 | |
| 71 | 42 | 55 | 64 | 21 | 0 | 0 | 1 | 1 | 0 | |
| 68 | 75 | 90 | 19 | 64 | 0 | 0 | 1 | 1 | 0 | |
| 75 | 13 | 77 | 1 | 89 | 0 | 0 | 0 | 0 | 0 |
| A 1110 |
B 1010 |
C 0010 |
D 1001 |
| E 0000 |
F 1111 |
G 1001 |
H 1011 |
| I 1000 |
J 1000 |
K 1110 |
L 0000 |
| M 0010 |
N 1100 |
O 0100 |
P 0111 |
Q206. Suppose the agents in a population have four behaviors - W, X, Y, Z - and that each behavior is either present or absent. Further suppose that there is some pressure toward consistency such that having a "don't do" behavior next to a "do do" behavior is uncomfortable and so agents have some internal urge to change their behavior to be more consistent.
Let's say that a behavior that is the only one of its type (a 0 among three 1s, for example) has a 50 percent chance of switching to make the set fully consistent. Each behavior that's one of an even split (e.g., a 0 in a 0011 agent) has a 10% chance of switching. We can put it this way: there is a 10% chance the first behavior changes, 10% the second, etc. and 60% chance no change happens.
Use the two random number table below to work out the next state n the grid below, determine the probability of interaction between each pair of neighbors (assume no diagonal interaction for now). For 50% chance use "random number above 50 = change, below 50 = stay." For the 10% chances, 0<10 is change first, 10<20 change 2, etc.
| 69 | 72 | 43 | 97 | 87 |
| 37 | 86 | 35 | 23 | 41 |
| 88 | 36 | 94 | 60 | 60 |
| 84 | 26 | 3 | 87 | 12 |
| 8 | 10 | 56 | 52 | 29 |
| 26 | 5 | 30 | 15 | 58 |
| 95 | 3 | 95 | 18 | 69 |
| 71 | 42 | 55 | 64 | 21 |
| 68 | 75 | 90 | 19 | 64 |
| 75 | 13 | 77 | 1 | 89 |
| A 1110 |
B 1010 |
C 0010 |
D 1001 |
| E 0000 |
F 1111 |
G 1001 |
H 1011 |
Q207. Convert the following logic into a set of step-by-step instructions in a manner that uses stepwise refinement.
To execute coordination we proceed as follows. Each agent will consider in turn its north, east, south, and west neighbors. First the agent determines whether interaction will take place at all based on similarity. Then, if they do interact, they flip a coin to decide who is the leader and who is the follower. Then the follower copies the traits of the leader. And then onto the next neighbor if there is one.
We can incorporate the following design decisions into our model: (1) neighbors who have already interacted in a given round do not do so again; (2) an agent can change multiple times during a given round; (3) all interactions are with the agent's current state.