MG_L2

Question 1

What is a normal form game?

Answer 1

• A framework with:
  
  • Players (agents)
  • Each player has a strategy set
  • Payoffs that depend on all players’ strategy choices

Question 2

What is the Prisoner’s Dilemma?

Answer 2

• A classic example of conflict between individual and collective interest
• Each prisoner can Confess or Not Confess
• The Nash equilibrium is both confessing, which is worse for each than mutual silence

Question 3

What is the Bach or Stravinsky (Battle of the Sexes) game?

Answer 3

• A coordination game with two players choosing between two concerts
• Two Nash equilibria where both go to Bach or both go to Stravinsky
• Shows that multiple stable outcomes can exist

Question 4

Define a Nash equilibrium in pure strategies.

Answer 4

• A strategy profile s = (s₁, …, s_n)
• No player can increase their payoff by unilaterally switching their strategy
• Formally, for each player i, s_i is a best response to the other players’ strategies

Question 5

What is a best response?

Answer 5

• A player’s strategy that maximises their payoff
• Given the other players’ chosen strategies, a best response gives the highest utility

Question 6

When is a Nash equilibrium considered Pareto inefficient?

Answer 6

• If there is another outcome that makes no one worse off and at least one player better off
• In the Prisoner’s Dilemma, both Confess is Pareto inefficient

Question 7

Why can a Nash equilibrium be inefficient?

Answer 7

• Individual incentives may conflict with collective welfare
• Players each act rationally but collectively end up worse off

Question 8

Give an example of a real-world Prisoner’s Dilemma.

Answer 8

• Climate change policies:
  
  • Each country benefits if all reduce emissions
  • Each has an incentive to free-ride if others co-operate

Question 9

What is the effect of repeated interaction?

Answer 9

• Can increase co-operative behaviour
• Players may try to build reputation or punish defectors in future rounds

Question 10

What is Pareto efficiency?

Answer 10

• No other outcome can make all players weakly better off and at least one strictly better off
• Not always related to fairness; it’s about no mutual gains left on the table