Lecture 8: Extensive form games

What is extensive form of games?

Normal game theory → decisions made simultaneously

• When players make decisions sequentially

→ more realistic as you react to other players

What is backward induction?

What are higher costs example?

What is a coordination game with no focal point?

What is the coordination game with a focal point?

What is heads or tails?

The player who moves first is at a disadvantage

What is the battle of sexes: husband moves first?

The player who moves first has an advantage → the second player has to play what is best for them given what was already committed

What is the battle of sexes: wife moves first?

The player who moves first has an advantage → the second player has to play what is best for them given what was already committed

What is the stackelberg duopoly (how much do they produce)?

Finding the production level sequentially → if production decision is made at the same time, they produce the same

1st mover/leader has the advantage!

• start with profit → want to maximize profit

The 1st Firm: the leader always produces more than the 2nd firm (more production than cournot → higher profit)

• the firm that moves 1st knows the 2nd firm will produce less if the 1st firm produces more!

The 2nd Firm: the follower produces less than 1st firm (& less than cournot → lower profit)

• the 2nd firm know sthe 1st firm will increase production → the drop in price makes it cost effective to decrease production

What are information sets?

Allow some past moves to be hidden

• The extensive form of games is the same except → the 2nd player does know which node he is located

What is the perfect Bayesian equilibrium (PBE)?

2 Elements:

1. Strategy for each player in each node of information sets where a move is made

2. Each information set has assigned probabilities for each node in the set

Information set heads or tails example

What are repeated games (cooperative equilibrium)?

Can players co-operate at least in some rounds to avoid bad outcomes assuming their strategies can depend on history?

If the game is played a finite number of times, the answer is NO

If the game is played an infinite number of times, then the cooperative equilibrium can be achieved (both play C)

What is nature as a player?

Further extend the game setup by allowing some randomness

• randomness is modelled as another player → Nature (player 0)

What is signaling, screening, & self-selection?

Signaling: the person with info wants to reveal his good type through actions

• people drive carefully to avoid accidents & save on future car insurance

Screening: a player without info wants to learn about the type of other player

• bank checks credit & financial info before giving a loan

Self-selection: player without info offers several types of contracts so players with diff info can choose different contracts

• salesperson choosing fixed wage or commission percentage

What is a moral hazard vs. adverse selection?

Moral hazard → no uncertainty, solved by backward induction:

• occurs after transaction takes place → informed party changes behavior in a way that the uninformed party cannot observe or control

Adverse selection → uncertainty, find PBE:

• occurs before transaction takes place → informed party has private info that leads to selecting a transaction that’s a disadvantage for the uninformed party

*What are signaling games?

2 Players → P1 (sender), P2 (receiver)

Equilibria:

• signaling/separating equilibrium - different types of senders send different messages, by observing the message, the receiver can figure out the type of sender