PSNE, Dominant Strategies

Run

• python3 13.py

About

Given a n-Player Game the code lists all Pure Strategy Nash Equilibria and all Very Weakly Dominant Strategies for each player.

Input Format

The input is a n-Player Game with the payoffs listed in the NFG Format (as described in the Gambit Project).

• First line contains the number of players n.
• The second line contains n space-separated numbers, the i th number corresponding to the number of strategies available to the i th player. (S _i)
• The third line contains the list of payoffs in the NFG Format.

Output Format

• First line should contain the number of PSNE. (n psne )
• Followed by n psne lines, the i th line containing n space-separated numbers corresponding to the equilibrium strategies for each player respectively.
• Next, you should output n lines, with the i th line listing the number of very weakly dominant strategies for the i th player followed by the dominant strategies.

Sample

Input 1

2

2 2

-2 -2 -2 -10 -10 -2 -5 -5

Output 1

2

1 1

2 2

1 2

1 2