5. Game Theory and Application

Question 1

The Prisoners Dilemma

Answer 1

• Both prisoner A’s and prisoner B’s best choice is to confess = In doing this they’re using their dominant strategies
• Equilibrium outcome then is (confess, confess) à this is known as Nash Equilibrium
• Neither prisoner given that the other prisoner has chosen to confess would choose to unilaterally change their mind.
• It would be better for both prisoners to stay quiet. à this is an example of social dilemma

Question 2

Conventional Assumption

Answer 2

1. Rationality: a player is rational and they seek to maximise their own payoffs
2. Common knowledge: the payoffs and strategies available to the players are common knowledge
   - Each player knows his/her own payoffs and strategies, and the other player’s payoffs and strategies
   - Each player knows that the other player knows this and so on…
3. Complete information: there is no private information; all details of the game are common knowledge to all players.

Question 3

Payoff Matrix

Answer 3

The table showing the payoffs of both players with each possible combination outcome.

Question 4

Outcome

Answer 4

(strategy combination) of the game is a pair such as (U,R) where player A chooses U and player B chooses R.

Question 5

Dominant Strategy

Answer 5

A strategy that is optimal (leading to higher payoff) no matter what one’s opponent does.

Question 6

Equilibrium in Dominant Strategies

Answer 6

The outcome when both players have a dominant strategy.

Question 7

Nash Equilibrium

Answer 7

A set of strategies, one for each player, such that no player has an incentive to unilaterally change their action.

Question 8

Maximin strategies

Answer 8

A strategy that maximises the minimum gain that can be earned (dominant strategies are also maximin strategies)

Question 9

Games of coordination

Answer 9

Simultaneous play games in which the payoffs to the players are largest when they coordinate their strategies e.g. prisoners dilemma.
- Neither know what the other is doing –> players need to move fast to enable coordination
- in practice, games played more than once: players know moves from previous periods but not within any one period because they’re all simultaneous move.

Question 10

Tit-for-Tat Strategy

Answer 10

strategy in which players respond in kind to an opponent’s previous play, cooperating with cooperative opponents and retaliating against uncooperative ones.

Question 11

Infinitely repeated games

Answer 11

Cooperation is a rational response to the t-f-t strategy

Question 12

Finitely repeated games

Answer 12

Cooperation is no longer a rational response- backward induction argument (start from the end and work backwards)

Question 13

Sequential Games

Answer 13

1 player moves first then the other chooses their strategy will full knowledge of the first players choice : represented through tree diagrams

Question 14

Pure Strategies

Answer 14

Strategies where a player makes a specific choice or action with certainty

Question 15

Games of Competition

Answer 15

Simultaneous play games where any increase in the payoff to one player is exactly offset by the decrease in the payoff to the other player