Week 2 - Sequential games Flashcards
What is the benefit of moving first and what type of games see first-mover advantage
Ability to commit to preferred option. Seen in games in which players want to co-ordinate but disagree on what to co-ordinate on
What is the benefit of moving 2nd and what type of games see second-mover advantage
The flexibility to adapt to the choices of other players. Seen in sequential zero-sum games e.g. rock-paper-scissors, public auctions
What happens when there are indifferences at a node?
There are multiple equilibria
What is the ultimatum game?
Player 1 decides how to divide x between them and player 2. Player 2 can either accept or reject. If they reject, both players earn nothing
What is the rollback equilibrium in a basic ultimatum game?
The responder will accept anything.
Why might the proposer in the ultimatum game send positive amounts? (5)
- Altruism
- Inequality aversion
- Risk aversion - safe to send larger amounts
- Belief that responder is inequality averse
- Expecting negative reciprocity
Why might the responder reject positive offers in the ultimatum game? (4)
- Negative reciprocity
- Inequality aversion
- emotions
- Reputational concerns if the game is repeated
What is the utility function of the responder in the ultimatum game if the responder is inequality averse?
Ur (πr,πp) = πr - B(πp - πr)
beta = the disutility from being behind
Applying backward induction in the ultimatum game when the responder is inequality averse, what will the proposer do and what will they offer?
Maximise πp so will choose the smallest x that is acceptable to responder. Make the responder indifferent between accepting and rejecting
What condition needs to be met for the responder to accept the offer in the ultimatum game if the responder is inequality averse?
𝑥≥𝛽/(1+2𝛽)
What will the proposer offer in the ultimatum game when the responder is inequality averse?
𝑥= 𝛽/(1+2𝛽).
What is the rollback equilibrium for the ultimatum game with inequality aversion?
Proposer offers 𝑥= 𝛽/(1+2𝛽),
Responder accepts if 𝑥≥ 𝛽/(1+2𝛽) and rejects if 𝑥< 𝛽/(1+2𝛽)
(on the equilibrium path, responder accepts)
What are the monetary payoffs for the responder and proposer on the equilibrium path in the ultimatum game with inequality aversion?
𝜋_𝑃=(1+𝛽)/(1+2𝛽), 𝜋_𝑅=𝛽/(1+2𝛽)
What are the utilities on the equilibrium path in the ultimatum game with inequality aversion?
𝑢_𝑃= (1+𝛽)/(1+2𝛽), 𝑢_𝑅=0
What happens to the proposers offer if the responder is more inequality averse in the ultimatum game ?
it increases
What is the centipede game?
Player A can either take £1 or pass it to player B.
If they take 1, B earns nothing
If A passes, experimenter adds 1 more and then player B can pass or take
What is the equilibrium outcome in the centipede game when you apply backward induction?
The 1st player takes the money, the other player does not get to move.
Why would players pass in the centipede game? (4)
- Failing to carry out backward induction
- Altruism: U(£1,£0) < U(£0, £2)
- Expecting that the opponent will not do backward induction or make mistakes
- Expecting the opponent will not value rewards
What is the trust game?
Player 1 receives £x and decides how much of it to give to player 2. That amount is tripled. Player 2 then decides how much to give back to player 1
What is the rollback equilibrium in the trust game?
Player 2 would not return anything - has no incentive too. Player 1 would know this so not give anything to player 2.
Why might player 1 send something to player 2 in the trust game? (4)
Altruism or inequality aversion
expecting inequality aversion
expecting positive reciprocity
Player 2 is a friend.
Why might player 2 send something to player 1 in the trust game? (3)
Positive reciprocity
inequality aversion
reputational concerns in a repeated
