Question

- Below is a game between player A and player B. Each player has two possible strategies: 1 or 2. The payoffs for each combination of strategies between A and B are in the bracket. For example, if A plays 1 and B plays 1, the payoff for A is 1 and the payoff for B is 0.

Player B |
|||

Strategy 1 |
Strategy 2 |
||

Player A |
Strategy 1 |
(1,0) |
(0,1) |

Strategy 2 |
(0,1) |
(1,0) |

- How many pure strategy Nash equilibria does this game have? Explain your answer.

Answer #1

Below is a game between player A and player B. Each player has
two possible strategies: 1 or 2. The payoffs for each combination
of strategies between A and B are in the bracket. For example, if A
plays 1 and B plays 1, the payoff for A is 1 and the payoff for B
is 0. Player B Strategy 1 Strategy 2 Player A Strategy 1 (1,0)
(0,1) Strategy 2 (0,1) (1,0) How many pure strategy Nash equilibria
does...

QUESTION 3
Below is a game between player A and player B. Each player has
two possible strategies: 1 or 2. The payoffs for each combination
of strategies between A and B are in the bracket. For example, if A
plays 1 and B plays 1, the payoff for A is -3 and the payoff for B
is -2.
Player B
Strategy 1
Strategy 2
Player A
Strategy 1
(-3,-2)
(10,0)
Strategy 2
(0,8)
(0,0)
How many pure strategy Nash...

4. Consider the following non-cooperative, 2-player game. Each
player is a middle manager who wishes to get a promotion. To get
the promotion, each player has two possible strategies: earn it
through hard work (Work) or make the other person look bad through
unscrupulous means (Nasty). The payoff matrix describing this game
is shown below. The payoffs for each player are levels of
utility—larger numbers are preferred to smaller numbers. Player 1’s
payoffs are listed first in each box. Find...

In the “divide two apples” game, player 1 suggests a division
scheme (x,y) from the set {(2, 0), (1, 1), (0, 2)} where x is the
number of apples allocated to player 1, and y is the number of
apples allocated to player 2. Player 2 counters with a division
scheme of her own that comes from the same set. The final
allocation is obtained by averaging the two proposed division
schemes. The apples can be cut if the resulting...

Venus and Serena are playing a tennis match. Each of them uses
two strategies: Hit left or hit right. The payoffs from each
strategy combination are given below (The rows correspond to
Venus's strategies, and the columns correspond to Serena's
strategies. The first number in each payoff combination (x,y) is
Venus's payoff, and the second number is Serena's payoff. )
Left
Right
Left
30,70
80,20
Right
90,10
20,80
11. What is Venus's dominant strategy?
12. What is Serena's best response,...

24. Two players are engaged in a game of Chicken. There are
two possible strategies: swerve and drive straight. A player who
swerves is called Chicken and gets a payoff of zero, regardless of
what the other player does. A player who drives straight gets a
payoff of 432 if the other player swerves and a payoff of −48 if
the other player also drives straight. This game has two pure
strategy equilibria and
a. a mixed strategy equilibrium in...

A game has two players. Each player
has two possible strategies. One strategy is Cooperate, the other
is Defect. Each player writes on a piece of paper either a C
for cooperate or a D for defect. If both players write
C, they each get a payoff of $100. If both players
write D, they each get a payoff of 0. If one player
writes C and the other player writes D, the
cooperating player gets a payoff of S...

Which of the following is true for a Nash equilibrium of a
two-player game?
a) The joint payoffs of the two players are highest compared to
other strategy pairs.
b) It is a combination of strategies that are best responses to
each other.*?
c) Every two-player game has a unique Nash equilibrium.
d) None of the above is correct.

16. Two gas stations, A and B, are locked in a price war. Each
player has the option of raising its price (R) or continuing to
charge the low price (C). They will choose strategies
simultaneously. If both choose C, they will both suffer a loss of
$100. If one chooses R and the other chooses C, (i) the one that
chooses R loses many of its customers and earns $0, and (ii) the
one that chooses C wins many...

Game Theory:
John and Dave are playing a game where they only have two
strategies, either to move left or move right. The payoffs from
this game are the points that each player will earn given the
strategies that each play. The higher the points, the higher the
payoffs each player will receive. The normal form representation of
the game is presented below.
DAVE
Left
Right
Left 1,1
0,3
Right 3,0
2,2
John's name label should be on...

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