### FAQs

RECENT FAQ on the project evaluation and delivery
1. Can we go over the 4-page limit suggested for the project report?
R:
Yes. If the conducted experimental analysis are extensive, you can use up to 8 pages (double-column AASMA format). Still, remove redundancies and unnecessary/lengthy descriptions.

OLD FAQ on exercises, essays and project proposal
1.
The total grade for the four exercises is 6.0. Why it is so?
R: The grading of the exercises is 0-6 values (30%), essay is 0-4 values (20%) and project is 0-10 (50%). The sum (0-20) will be your course grade.

2. What would be the visual display of the bi-matrix given in the example provided in exercise 1.1?
R:
-1 -1  | -10  0
0 -10  |  -5 -5
The corresponding matrix of player 1 is:
-1 -10
0  -5

3. What is required for the project proposal (to be delivered in the labs during April 9-13th)?
R: Up to 2 pages with a detailed specification of your project. A brief presentation of 3-5 minutes to your colleagues is expected in the following week (16-20th April). In the 16-20th April week, we ask the groups with members attending different labs to be both present in a single lab.

4. What is the expected output of exercise 1.2? [updated answer]
R: Given a game characterized by a real-valued bi-matrix bm = [[[a b] [c d]] [[e f] [g h]]]
between two players with probabilities pij towards a specific action (where i determines the player and j the action).
If there is no mixed Nash equilibrium for player i (player i cannot place probabilities that turn the actions of player j indifferent) then pi1=pi2=-1
Please return one of the two following outputs:
- ne = [[p11,p12], [p21,p22]] (preferable)
- ne = [[[p11 p21] [p11 p22]] [[p12 p21] [p12 p22]]] and nev = [[[p11a p21b]  ... ]] (these verification matrices are still accepted)

5. What is the format of the exercises' file to upload in Fenix?
R: Please upload a single file in .PY (python file) .JAVA (Java file), .M (MatLab file) or .CPP (C/C++ file) format with the code. Guarantee the executability of your code as it can be automatically tested.

6. What is the expected output of exercise 2.1? (thanks Pedro and Daniel)
R: ne, nev and sp are lists where each position respectively specifies the actions, values (after payment) and side-payment (absolute value) of each better strategy. For the given case: ne=[[0, 1]], nev=[[4, 4]], sp=[2]. These strategies need to be better than all occurring Nash equilibria. If there is no Nash equilibrium, then ne=nev=sp=[].

7. What is the expected output of 2.2? [updated answer]
R: zeuthen returns a set of lines, where each line is a tuple (offer, player) - e.g. ([[b,c,d,e], [a]], 1).
Let us assume that we have the following utilities U1=[1, 2, 1, 2] and U2=[2, 1, 1, 1] (corresponding to the valuation of items [a, b, c, d]), then the expected output (assuming alphabetic ordering) is given by the following three lines:
([[b, c, d], [a]], 1)
([[b], [a, c, d]], 2)
([[b, d], [a, c]], 2)
The end condition (agreement in this case) is met when agent 1, while conceding, tests the offer ([[b, d], [a, c]], 1).
When two different offers have the same utility for the agent conceding, the offer that maximizes the utility for the opponent agent should be selected to guarantee a Pareto optimal solution.
Items can be displayed using either alphabet letters or numerical indices (e.g. [a, b, d] is equivalent to [0, 1, 3]).