Extensive form games

Note: These are not designed to be student facing.

I make these notes available with the intent of making it easier to plan and/or take notes from class.

Student facing resources for each topic are all available at vknight.org/gt/.

Typical Programming Exercises

During the class

Invite students to play the following game:

  • Player 1 can take or pass (if take: (2,0))
    • Player 2 can take or pass (if take: (1,3))
      • Player 1 can take or pass (if take: (4,2))
        • Player 2 can take or pass (if take (3,5))
          • Leaf: (4,4)

Now ask for two students to play but they must submit their instructions. To me (written).

Give out bribentives based on what happened.

If necessary, write down my own strategy where I pass at first two nodes but take at last two.

Give out bribentives.

Now discuss notes:

  • Connection
  • Definitions of a strategy.

Write down Normal Form Game for whole thing.

S1 = {PP, PT, TP, TT} S2 = {PP, PT, TP, TT}

Game is:

\[A = \begin{pmatrix} 4 & 3 & 1 & 1\\ 4 & 4 & 1 & 1\\ 2 & 2 & 2 & 2\\ 2 & 2 & 2 & 2\\ \end{pmatrix} \qquad B = \begin{pmatrix} 4 & 5 & 3 & 3\\ 2 & 2 & 3 & 3\\ 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0\\ \end{pmatrix}\]

Have bottom right quadrant as NE (pairs of best responses).

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