Extenstions of Game Theory

Question 1

How does repetition of a game change the nature of solution concepts?

Answer 1

There is no winning strategy in the repeated game.

Question 2

What is a good solution for iterated (repeated) Prisoner’s Dilemma?

Answer 2

Tit for tat: A strategy for playing a repeated game that is founded on the principle of retaliation. In a repeated prisoners’ dilemma game the tit for tat strategy is to play {Don’t confess} while your opponent plays {Don’t confess}, but to play {Confess} the period after your opponent plays {Confess}.

Question 3

Why is Tit for tat a good solution?

Answer 3

• It’s “nice”: it starts by cooperating.
• It’s “retaliatory”: it doesn’t let other strategies take advantage of it.
• It’s “forgiving”: it goes back to cooperating when the other strategy
  does.
• It’s “clear”: it’s easy to see what tit-for-tat is doing

Question 4

What is the dollar auction (chocolate auction) game?

Answer 4

A dollar auction is a simple game, where two participants bid on a dollar bill (chocolate) . The highest bidder receives the dollar bill (chocolate) and the loser must pay the amount that they bid as well.

Question 5

What is the solution concept for the dollar auction (chocolate auction) game?

Answer 5

Escalation dominance:
a position in which the player has a rational incentive to “escalate” to a
higher winning bid, while the other player does not.

Question 6

What is the strategy of GRIT?

Answer 6

Establishing trust by signaling a willingness to
cooperate. One player might make a small concession, for example, in the hopes that the other player will also make a concession. In this way,
cooperation can begin, and tension can “de-escalate.”

Question 7

What is a mixed strategy equilibrium and how is it calculated?

Answer 7

A mixed strategy means that a player will play each available strategy a
certain percentage of the time.

Question 8

How is Mixed strategy equilibrium calculated?

Answer 8

To find a mixed strategy solution to this game, we need to find a mix of
strategies so that the other team can’t take advantage. That is, we must
make the other team indifferent between its two strategies.
In other words: E(u)Aggressive must be equal to E(u)Prevent.