1. The whole idea behind game theory:

    What happens to me depends on what I do but also on what everyone else does.

    What did we do?

    • We played the 2/3rds of the average game.

    What do I need to be able to do?

    • Define an extensive form game and represent a game in extensive form;
    • Define an information set.

  2. Normal Form Games:

    Also called bi-matrix games. This is often used to represent situations in which players make decisions at the same time (and have a finite strategy set).

    What did we do?

    • We played some matching pennies games (I blogged about the results, links are in the discussion boards).

    What do I need to be able to do?

    • Define a normal form game;
    • Calculate expected utility with mixed strategies;
    • Plot expected utilities against/with pure strategies.

  3. Dominance:

    The idea of being able to ‘remove’ strategies that will never be played.

    What did we do?

    • Nothing too exciting.

    What do I need to be able to do?

    • Define dominated strategies (strict and weak);
    • Define Common knowledge of rationality;
    • Predict rational behaviour using iterated removal of dominated strategies;
    • Recognise games that cannot be approached using this tactic.

  4. Best responses:

    The idea of doing what ‘I’ should do if I know what ‘you’ would do.

    What did we do?

    • We played a game similar to Golden balls in class. (I blogged about it, link in the discussion board)

    What do I need to be able to do?

    • Identify best responses in pure strategies (underline stuff);
    • Identify best responses against mixed strategies;
    • Define the sets \(UD_i\) and \(B_i\);
    • State and prove certain cases of theorems connecting these two sets.

  5. Nash equilibria in pure strategies:

    Here we are officially defining what we meant by ‘predicted rational behaviour’. In essence: ‘not having a reason to change what you are doing’.

    What did we do?

    • Nothing too exciting.

    What do I need to be able to do?

    • Give definition of Nash Equilibria in pure strategies;
    • Continue to use best responses to identify these;
    • Calculate Nash equilibria in pure strategies when strategy sets are continuous.

  6. Nash equilibria in mixed strategies:

    Congratulations we’re now doing real game theory.

    What did we do?

    • We played a Rock, Paper, Scissor, Lizard, Spock game in class (I blogged about it, link on a discussion board).
    • The weak after seeing this we played against a random number generator (I blogged about that too, link in the same place).

    What do I need to be able to do?

    • Define Nash equilibrium (completely, ie in mixed strategies);
    • Identify Nash equilibrium using best responses against mixed strategies;
    • State and prove the Equality of Payoffs theorem;
    • Apply the equality of Payoffs theorem;
    • State and prove specific cases of Nash’s theorem.

  7. Extensive form games (again):

    We go back to the tree things and get a bit more precise.

    What did we do?

    • We played the centipede game but I’ll come back to that when we talk about subgames.

    What do I need to be able to do?

    • Recognize valid extensive form games;
    • Define sequential rationality;
    • Define backwards induction;
    • Prove the theorem of existence of Nash equilibrium in games of perfect information;
    • Solve extensive form games using backwards induction;

  8. Subgame perfection:

    We connect Normal form games and extensive form games and define a stronger type of equilibrium condition.

    What did we do?

    • We played the centipede game and analysed the equilibrium strategies: everyone should take AT ALL STAGES.

    What do I need to be able to do?

    • Write down the normal form representation of an extensive form game;
    • Define a subgame;
    • Define subgame perfect equilibria;
    • Obtain subgame perfect equilibria in games.