Week 7 - Nash equilibrium and repeated games Flashcards
Go over slides in this week for abit more detail.
What are the 2 interpretations of Nash Equilibrium?
Normative and descriptive
What is the normative interpretation of Nash equilibrium?
How rational players should behave in a game
- if payoffs represent utility and players are rational, they should behave as NE predicts
- only applies to non cooperative games
What is the descriptive interpretation of Nash equilibrium?
How people actually behave in a game
Why does behaviour differ from NE? (3)
- NE sometimes assumes people are selfish EU maximisers
- NE assumes that people have unlimited cognitive abilities and NE is not sensitive to incentives or rewards e.g. value of penalty in travellers dilemma
- NE assumes that people have correct beliefs
Why might people not maximise their monetary payoffs?
Because people may care about other things, such as inequality, earnings of others (altruism or spite), emotions (anger, guilt) and social norms.
What is a quantal response equilibrium?
When 1 player forms a belief about how likely the other player is to choose a response
How do you work out expected payoffs for each strategy for a quantal response equilibrium?
multiply the utility by the probability and then add together (look at this in more detail on the slides)
True or false: QRE explains data better than NE? explain.
True - it takes into account incentives e.g. for travellers dilemma, it takes into the account the incentive to reduce claim when the fine is larger.
How do we expect players to converge to NE?
Through deliberation or learning. In a one-shot game, NE has a very low explanatory power
What 2 main ways to model learning in games? explain.
Belief learning - forming beliefs about what the opponent will do based on the observed past play. Then best respond to this belief.
Reinforcement learning - choosing strategies that did well in the past
Will both types of learning converge to NE? What if the decisions are noisy?
Yes. If decisions are noisy, it will typically converge to QRE.
What does it mean if the decisions are noisy?
There are other things which are affecting your ability to make a decision/learn.
When does behaviour converge to NE? (4)
- Interaction is repeated - opportunities to learn and form correct beliefs
- Players are rematched - can lead to collusion
- Players receive good feedback on mistakes - payoff based learning
- Game is simple or complexity is reduced - e.g. give them a calculator
What are 2 advantages of using simulations instead of nash equilibrium to predict behaviour in some games (e.g. 1 shot)
- Learning models explain the dynamics much better - these predictions take into account things like mistakes, game structure, feedback
- much easier - can just program any utility function and run a computer simulation without having to calculate an equilibrium
Why might players put in more effort than NE predicts? (3)
Preferences - risk, social (being spiteful), additional non-monetary joy from winning a prize
Beliefs - you might be incorrect in your assessment of what you think others will do.
Bounded rationality - learning is difficult because opponents are changing choice
