Game theory
● Strategic situations occur when players are interdependent
● Interdependent problems are analysed using game theory
○ Interdependence - one person’s actions affect what the other should do
● If actions are independent, use decision theory
● Game theory was developed mainly by John Von Neumann and John Nash
Normal form
● Parties with decisions are players - N
● Choices available are actions - A
● Outcomes are payoffs - π
○ Encode everything players care about and
○ Players maximise payoffs
Solving a game
● Difficulties in solving a game include:
○ Understanding the game
○ Forming expectations about the other player’s actions
○ Finding the best response
● Coordination games involve the players coordinating with others and
understanding the actions of other players
● Solution concepts narrow down the set of outcomes to reasonable ones
○ Makes better predictions about how people will play (positive)
○ Allows you to give better advice about how to play (normative)
Best response
● An action (𝑎𝑖 ) is the best response if it has the highest payoff given the
opponent’s action profile (𝑎−𝑖 )
○ An action profile is a list of possible actions
● The best response: 𝑎𝑖∗ = 𝑎𝑟𝑔𝑚𝑎𝑥𝜋𝑖 (𝑎𝑖 , 𝑎−𝑖 )
○ Players need to predict the actions of others and decide their best
response
Dominant strategies
● PD is non-strategic - can see the incentives
○ Confess is always the best strategy
● The dominant strategy is always the best
response
● Strategic situations occur when players are interdependent
● Interdependent problems are analysed using game theory
○ Interdependence - one person’s actions affect what the other should do
● If actions are independent, use decision theory
● Game theory was developed mainly by John Von Neumann and John Nash
Normal form
● Parties with decisions are players - N
● Choices available are actions - A
● Outcomes are payoffs - π
○ Encode everything players care about and
○ Players maximise payoffs
Solving a game
● Difficulties in solving a game include:
○ Understanding the game
○ Forming expectations about the other player’s actions
○ Finding the best response
● Coordination games involve the players coordinating with others and
understanding the actions of other players
● Solution concepts narrow down the set of outcomes to reasonable ones
○ Makes better predictions about how people will play (positive)
○ Allows you to give better advice about how to play (normative)
Best response
● An action (𝑎𝑖 ) is the best response if it has the highest payoff given the
opponent’s action profile (𝑎−𝑖 )
○ An action profile is a list of possible actions
● The best response: 𝑎𝑖∗ = 𝑎𝑟𝑔𝑚𝑎𝑥𝜋𝑖 (𝑎𝑖 , 𝑎−𝑖 )
○ Players need to predict the actions of others and decide their best
response
Dominant strategies
● PD is non-strategic - can see the incentives
○ Confess is always the best strategy
● The dominant strategy is always the best
response
