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.