12 Game Theory

Question 1

What do games compose of? (4)

Answer 1

They describe a social interaction with:

• Players - those involved in the interaction
• Feasible strategies - actions each player can take
• Payoffs - outcomes for every possible combination of actions
• Information - what each player knows when choosing their action

Question 2

Define dominant strategy

Answer 2

A best response to all possible strategies of the other player (does not always exist).

Question 3

Define dominant strategy equilibrium

Answer 3

An outcome of a game in which everyone plays their dominant strategy.

Question 4

Define best response

Answer 4

Strategy that yields the highest payoff, given the other player’s strategy.

Question 5

Define Nash equilibrium

Answer 5

A situation in which each player is adopting a strategy which is a best response to the strategy actually played by their opponent.

Question 6

Define Pareto efficient

Answer 6

An outcome is Pareto efficient if nobody can be made better off without making somebody else worse off.

Question 7

How is Nash equilibrium useful? (2)

Answer 7

• Nash’s approach helps us narrow down the list of possible outcomes.
• Many games have Nash equilibria (if you allow people to randomise sometimes)

Question 8

Can we avoid {Defect, Defect} in the prisoners’ dilemma? (3)

Answer 8

Assumptions: (which are to be relaxed)

• Players only care about their own payoffs.

→ introduce social preferences

• Nobody could make players pay for the consequences of their actions on others.

→ introduce repeated games, social norms, and peer punishment

• Players could not coordinate their actions beforehand

→ change the rules of the game (institutions and policies)

Question 9

What do we see in repeated games?

Answer 9

It can be easier to sustain co-operation as a Nash equilibrium.

Short-run gain is therefore weighed against long-run gains.

Question 10

How can certain strategies ensure co-operation?

Answer 10

Many possible “punishment” strategies, but also ones that reward cooperation and with cooperation.

Whatever strategy it is, it must be credible and you must be prepared to take it on, otherwise it is just “cheap talk”.

Question 11

What is one strategy designed to ensure co-operation?

Answer 11

To keep defecting after the other has defects, perhaps permenantly.