5- Game Theory Flashcards
What are the 2 types of Game Theory?
-Analytical (normative): how agents should behave
-Behavioural (positive): how agents tend to behave
What is the definition of a game?
A decision problem in which the final outcome depends upon the decisions of all agents, as well as the state of the world
What is a strategy?
Complete plan of action that describes what a player will do under all possible circumstances
What is a strategy profile?
Vector of strategies, one for each player
What is a best response?
Strategy that maximises own utility given the specific strategy of the other players
What is a Nash Equilibrium?
Strategy profile such that each strategy in the profile is a best response to the other strategies in the profile (any deviation decreases payoff)
What is the Nash Equilibrium existence theorem?
Every finite game (in which all players have a finite number of pure strategies) has a Nash equilibrium
When does a strategy profile X dominate profile Y?
Whenever all players weakly prefer the outcome under X over the outcome under Y
When is a strategy profile Pareto optimal?
If it is not Pareto dominated by any other strategy profile
Why is pre-play communication not effective in games?
‘Cheap talk’ property means it is not credible because players still have the same incentives to deviate
What is a Nash Equilibrium in Mixed strategies?
Probability distribution over pure strategies such that each player is indifferent among the pure strategies in her equilibrium strategy given the other player randomizes according to her equilibrium distribution function
What’s a trick to find the pure strategy Nash equilibria from a payoff matrix?
Fix the other player’s responses, and mark the best response in each case, do the same for the other player, the choices with 2 marks are NE
How do you draw a sequential game in extensive form?
From a player’s decision, draw a tree showing the possible responses and respective payoffs
What is a Subgame-perfect equilibrium?
Strategy profile that constitutes a Nash equilibrium in each subgame
What is the Subgame-perfect equilibrium existence theorem?
Every finite extensive form game has a subgame-perfect Nash equilibrium
How can non-credible threats be overcome?
‘Binding hands’ or implementing an automatic non-stoppable reaction (which must be public knowledge)
What are the 5 types of social preferences?
-Altruistic
-Envious/Spiteful
-Rawlsian
-Inequality-averse
-Utilitarian
What are altruistic preferences?
Derive payoff from both agents utility with a weighting parameter e.g. a√X + b√Y
What are envious/spiteful preferences?
Negative utility from other player’s payoff
e.g. √X - √Y
What are Rawlsian preferences?
Solidarity with worst off, payoff is the minimum across players e.g. min{√X, √Y}
What are Inequality-averse preferences?
Negatively affected by differences in payoffs, in either player’s favour e.g. -|√X - √Y|
What are utilitarian preferences?
Utility derived from total payoff of all players; leads to sharing so that agents avoid diminishing utility
How do you find subgame-perfect equilibria of the ultimatum game given the preferences of other player?
- Find the utility for each player given the payoffs at the terminal nodes
- Setup an inequality to work out which payoffs agent will reject
- Proposer knows this so differentiate their utility function to optimise under that constraint
How do you find a mixed strategy Nash equilibrium?
1.Form an equation with the payoffs from each decision on each side weighted by the probability the other player makes each decision
2. Solve for p
