Wisc ID for in-class quiz: (if your wisc email is "test@wisc.edu", please enter "test")
Token: (will be given during the lectures) 20 id,answer_id;token,answer_check
📗 Unlike sequential games, for simultaneous move games, one player (agent) does not know the action taken by the other player.
📗 Given the actions of the other players, the optimal action is called the best response.
📗 An action is dominated if it is worse than another action given all actions of the other players.
➩ For finite games (finite number players and finite number of actions), an action is dominated if and only if it is never a best response.
➩ An action is strictly dominated if it is strictly worse than another action given all actions of the other players. A dominated action is weakly dominated if it is not strictly dominated.
📗 Rationalizability (IESDS, Iterative Elimination of Strictly Dominated Strategies): iteratively remove the actions are that dominated (or never best responses for finite games): Wikipedia.
In-class Discussion
📗 [1 points] Write down an integer between and that is the closest to two thirds \(\dfrac{2}{3}\) of the average of everyone's (including yours) integers.
📗 Answer: .
[Note] Use the space to explain the steps or just take notes:
[Q1]
In-class Quiz
ID:
📗 [4 points] Perform iterated elimination of strictly dominated strategies (i.e. find rationalizable actions). Player A's strategies are the rows. The two numbers are (A, B)'s payoffs, respectively. Recall each player wants to maximize their own payoff. Enter the payoff pair that survives the process. If there are more than one rationalizable action, enter the pair that leads to the largest payoff for player A.
A \ B
I
II
III
I
II
III
IV
📗 Answer (comma separated vector): .
[Note] Use the space to explain the steps or just take notes:
📗 Another solution concept of a simultaneous move game is called a Nash equilibrium: if the actions are mutual best responses, the actions form a Nash equilibrium: Wikipedia.
In-class Quiz
ID:
📗 [4 points] What is the row player's value in a Nash equilibrium of the following zero-sum normal form game? A (row) is the max player, B (col) is the min player. Use the checkboxes in the table to highlight the best responses: the first checkbox for the row player and the second checkbox for the column player.
A \ B
I
II
III
IV
I
II
III
IV
📗 Answer: .
[Note] Use the space to explain the steps or just take notes:
📗 A symmetric simultaneous move game is a prisoner's dilemma game if the Nash equilibrium (using strictly dominant actions) is strictly worse for all players than another outcome: Link, Wikipedia.
➩ For two players, the game can be represented by a game matrix: \(\begin{bmatrix} - & C & D \\ C & \left(x, x\right) & \left(0, y\right) \\ D & \left(y, 0\right) & \left(1, 1\right) \end{bmatrix}\), where C stands for Cooperate (or Deny) and D stands for Defect (or Confess), and \(y > x > 1\). Here, \(\left(D, D\right)\) is the only Nash equilibrium (using strictly dominant actions) but \(\left(C, C\right)\) is strictly preferred by both players.
In-class Discussion
📗 Split or Steal games: (YouTube playlist: Link, Solution: 0).
📗 If you have questions, please use (i) Zoom chat, (ii) Piazza: Link, (iii) Office hours and discussion sessions. Please do NOT use Canvas mail and use email only to the course instructor (not TAs) for grading issues.
Additional In-class Discussion
📗 Sometimes a question not in the notes will be asked during the lecture, you can submit your answer here:
Notes (not visible to other students):
[Q9]
Submit your answer to see other students answers (click the submit button to refresh):
Additional In-class Quiz
📗 Sometimes a question not in the notes will be asked during the lecture, you can submit your answer here:
A.
B.
C.
D.
E.
Notes (not visible to other students):
[Q10]
Submit your answer to see other students answers (click the submit button to refresh):
📗 To get full points on the in-class quizzes for a lecture:
➩ Submit relevant answers to the questions discussed during the lecture: incorrect answers are okay.
➩ Some questions require [notes] to earn the point.
➩ Some questions require special ID (given during the lecture) to earn the point.
➩ Do not submit answers to questions that are not discussed during the lectures. Each such submission will result in a deduction of one point.
➩ Submissions after the lecture, before the midterm (first 14 lectures) and the final exam (last 14 lectures), are accepted. After the exams, no in-class quiz submissions will be accepted.
➩ The grade on Canvas Assignment Q20 is computed as number of points divided by the number of questions asked (out of 1) and updated on Canvas every weekend.
📗 If there are any issues with submission on the website, please use this Google form: Link.
📗 Bonus point opportunities during a few lectures (added to in-class quiz above 20 points).
📗 Notes and code adapted from the course taught by Professors Jerry Zhu, Blerina Gkotse, Yudong Chen, Yingyu Liang, Charles Dyer. Some content are generated using Copilot .