Week 3 - Simultaneous move games with discrete strategies

Question 1

True or false: Sequential games are classified as simultaneous is the other player doesn’t know the move of player 1.

Answer 1

True e.g. sealed auction bids

Question 2

What is the difference between pure and mixed strategy?

Answer 2

A pure strategy is when you play a move with complete certainty, A mixed strategy is when you choose several actions with probabilities.

Question 3

What is a solution concept?

Answer 3

Prediction about which strategy profiles will be played in a game

Question 4

What are the 3 solution concepts (weakest first)

Answer 4

1. Players should not choose strategies that are always dominated by another strategy
2. Players should not choose a strategy that is never a best response to any strategy of the opponent
3. Players should not choose strategies that are never best responses to each other (NE)(

Question 5

Strategy X strictly dominates strategy Y if…

Answer 5

regardless of what the other player does, it generates a strictly higher payoff than Y for all possible strategy profiles of the other players

Question 6

Strategy X weakly dominates strategy Y if…

Answer 6

regardless of what the other player does, X generates a higher or same payoff than Y for all possible strategy profiles of the other players

Question 7

What is the difference between a strategy and a strategy profile?

Answer 7

A strategy is the move which can have multiple outcomes depending on what the other player plays. A profile is the mix of your strategy and the other players strategy (a single square on a game table)

Question 8

How do you carry out iterated elimination of strictly dominated strategies

Answer 8

1. For each players, remove all strictly dominated strategies
2. Check if any additional strategies become strictly dominated and remove any.
3. Repeat until no more can be eliminated
   4.

Question 9

When is a game dominance solvable?

Answer 9

If only 1 strategy profile remains.

Question 10

How do we expect people to get to this IESDS strategy solution? (3)

Answer 10

1. Common knowledge of rationality
2. Learning in a repeated game (more reasonable explanation)
3. Gene selection in an evolutionary process

Question 11

What do we assume of players which are rational? (3)

Answer 11

1. Consistent ranking of all outcomes in that game
2. Play the strategy that maximises utility
3. unlimited cognitive abilities

Question 12

Explain how the common knowledge of rationality will lead to an IESDS strategy solution?

Answer 12

Player 2 knows that you won’t play X because you’re rational, you know that player 2 won’t play Y because he’s rational etc. Everyone knows that everyone is rational.

Question 13

When is strategy X a better response to strategy Y?

Answer 13

If X generates a weakly higher payoff than any other strategy

Question 14

True or false: All IESDS solutions are rationalizable?

Answer 14

True

Question 15

How do you find a rationalizable strategy profile?

Answer 15

1. Circle all the best responses
2. eliminate strategies that are never a best response and repeat

Question 16

True or false: All rationalizable solutions can be obtained through IESDS?

Answer 16

False.