Collective Intelligence Exam

我为什么会有这么多课

2024-12-18 A

1. Iterated Prisoner’s Dilemma

Question
What is the rational strategy in the Iterated Prisoner’s Dilemma game when the number of iterations is K?
Explain your answer.

当多轮囚徒困境（迭代次数为 K）中，什么是理性的策略？请解释你的答案。

2. Game Theory – Symmetric Two-Person Game

Analyze the following game:

分析以下博弈：

	A	B
A	5 , 5	1 , 5
B	5 , 1	0 , 0

Answer the following:

请回答下列问题：

• Is there a dominant strategy for the players?

  • If yes, which one and why?
  • If not, explain why.

是否存在占优策略？

• 如果存在，是哪一个？为什么？

• 如果不存在，请解释原因。

• Is A an evolutionarily stable strategy (ESS)? Explain your answer.

• 策略 A 是否为进化稳定策略（ESS）？请解释你的答案。

3. Foraging by Ants

In the ant foraging model, consider the grid below.

在蚂蚁觅食模型中，考虑下面的格子布局。

• The agent is in the middle cell (X).

• The agent is heading North-East.

• Numbers represent pheromone levels.

• 代理位于中间格（X）。

• 代理朝向东北（North-East）。

• 数字表示信息素浓度（pheromone levels）。

Write in each cell the probability that the agent’s next step will go to that cell.

请在每个格子中写出代理下一步移动到该格子的概率。

12	10	15
20	X 33	25
5	11	42

4. Attractors

Question
What is an attractor?

什么是吸引子（attractor）？

• Be as precise as possible.

• Give examples of at least two different types of attractors.

• 请尽量精确地描述。

• 举出至少两类不同类型吸引子的例子。

5. Replicator Dynamics

Consider the payoff matrix:

考虑以下收益矩阵：

	A	B	C
A	3	1	4
B	4	3	1
C	1	4	3

Let:

• $x_A = $ proportion of players using strategy A
• $x_B = $ proportion of players using strategy B
• $x_C = $ proportion of players using strategy C

设：

• $x_A$ = 使用策略 A 的个体比例
• $x_B$ = 使用策略 B 的个体比例
• $x_C$ = 使用策略 C 的个体比例

Using replicator dynamics, write the following equations:

使用复制者动力学，写出以下方程：

$$
\frac{dx_A}{dt} =
$$

$$
\frac{dx_B}{dt} =
$$

$$
\frac{dx_C}{dt} =
$$

2024-12-18 B

1. Axelrod’s Tournament

Question
What was the winning strategy in Axelrod’s Tournament of Iterated Prisoner’s Dilemma games?

问题
在 Axelrod 的迭代囚徒困境锦标赛中，哪个策略获胜？

• How did it work?

• Explain its basic behavior.

• 它是如何运作的？

• 解释其基本行为特征。

2. Game Theory – Symmetric Two-Person Game

Analyze the following game:

分析以下博弈：

	A	B
A	6 , 6	2 , 3
B	3 , 2	1 , 1

Answer:

请回答：

• Is there a dominant strategy? Why or why not?

• Is A an evolutionary stable strategy? Explain.

• 是否存在占优策略？请说明理由。

• 策略 A 是否为进化稳定策略？请解释。

3. Foraging by Ants

• Agent is in the middle cell (X).

• Heading South-East.

• Numbers represent pheromone levels.

• 代理位于中间格子（X）。

• 朝向东南（South-East）。

• 数字表示信息素浓度。

Write the probability that the agent’s next step goes to each cell.

写出代理下一步移动到每个格子的概率。

12	10	15
20	X 33	25
5	10	65

4. Stigmergy

Question
What is stigmergy?

什么是刺激耦合（stigmergy）？

• Explain the basic concept.

• Give examples.

• 解释其基本概念。

• 举例说明。

5. Replicator Dynamics

Consider the payoff matrix:

考虑以下收益矩阵：

	A	B	C
A	4	2	5
B	5	4	2
C	2	5	4

Let:

• $x_A$, $x_B$, $x_C$ be the proportions of strategies A, B, and C.

设：$x_A, x_B, x_C$ 为策略 A、B、C 的比例。

Write the replicator dynamics equations:

写出复制者动力学方程：

$$
\frac{dx_A}{dt} =
$$

$$
\frac{dx_B}{dt} =
$$

$$
\frac{dx_C}{dt} =
$$

2025-01-03 A

1. Iterated Prisoner’s Dilemma

Question
In the Iterated Prisoner’s Dilemma game, will the strategy called Tit-For-Tat (TFT) beat the strategy called ALLD?
Why?

在多次囚徒困境中，策略 以牙还牙（TFT） 能否战胜 始终背叛（ALLD）？为什么？

2. Game Theory – Symmetric Two-Person Game

Analyze the following game:

分析以下博弈：

	A	B
A	4 , 4	1 , 5
B	5 , 1	0 , 0

Answer the following:

请回答下列问题：

• Is there a dominant strategy for the players?

  • If yes, which one and why?
  • If not, why?

• 对玩家是否存在占优策略？

  • 如果存在，是哪一个？并说明理由。
  • 如果不存在，说明原因。

• Is there a mixed strategy Nash equilibrium?

  • If yes, what is it?
  • Explain your answer.

• 是否存在混合策略纳什均衡？

  • 若存在，是什么？
  • 解释你的答案。

3. Foraging by Ants

In the ant foraging model:

• The agent is in the middle cell (X).

• The agent is heading North-East.

• Numbers indicate pheromone levels.

• 代理位于中间格子（X）。

• 代理朝向东北（North-East）。

• 数字表示信息素浓度。

Write in each cell the probability that the agent’s next step will take it to that cell.

请在每个格子中写出代理下一步移动到该格子的概率。

10	15	15
10	X 5	20
10	5	10

5. Replicator Dynamics

Consider the payoff matrix:

考虑以下收益矩阵：

	A	B	C
A	5	1	2
B	2	5	1
C	1	2	5

Let:

• $x_A = $ proportion of players using strategy A
• $x_B = $ proportion of players using strategy B
• $x_C = $ proportion of players using strategy C

设：

• $x_A$ = 使用策略 A 的比例
• $x_B$ = 使用策略 B 的比例
• $x_C$ = 使用策略 C 的比例

Using replicator dynamics, write the following equations:

使用复制者动力学，写出以下方程：

$$
\frac{dx_A}{dt} =
$$

$$
\frac{dx_B}{dt} =
$$

$$
\frac{dx_C}{dt} =
$$

2025-01-03 B

1. Iterated Prisoner’s Dilemma

Question
What strategy will win if ALLC plays against TFT in the Iterated Prisoner’s Dilemma?
Explain.

如果 始终合作（ALLC） 与 以牙还牙（TFT） 对弈，哪种策略会胜出？请解释。

2. Game Theory – Symmetric Two-Person Game

Analyze the following game:

分析以下博弈：

	A	B
A	6 , 6	1 , 3
B	3 , 1	2 , 2

Answer:

请回答：

• Is there a dominant strategy? Why or why not?

• Is there a mixed strategy Nash equilibrium?

  • If yes, what is it?
  • Explain your answer.

• 是否存在占优策略？请说明理由。

• 是否存在混合策略纳什均衡？

  • 若存在，是什么？
  • 解释你的答案。

3. Foraging by Ants

• The agent is in the middle cell (X).

• The agent is heading South-East.

• Numbers represent pheromone levels.

• 代理位于中间格（X）。

• 代理朝向东南（South-East）。

• 数字代表信息素浓度。

Write the probability that the agent’s next step goes to each cell.

写出代理下一步移动到各格子的概率。

11	6	11
5	X 12	6
21	5	22

5. Replicator Dynamics

Consider the payoff matrix:

考虑以下收益矩阵：

	A	B	C
A	40	20	5
B	5	40	20
C	20	5	40

Let:

• $x_A$, $x_B$, $x_C$ be the proportions of strategies A, B, and C.

设：$x_A, x_B, x_C$ 分别为策略 A、B、C 的比例。

Write the replicator dynamics equations:

写出复制者动力学方程：

$$
\frac{dx_A}{dt} =
$$

$$
\frac{dx_B}{dt} =
$$

$$
\frac{dx_C}{dt} =
$$