Question

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 which each player swerves
with probability 0.10 and drives straight with probability
0.90.

b. a mixed strategy in which each player swerves with
probability 0.05 and drives straight with probability 0.95. c. a
mixed strategy equilibrium in which one player swerves with
probability 0.10 and the other swerves with probability 0.90.

d. two mixed strategies in which players alternate between
swerving and driving straight.

Answer #1

Question 1.
Put the following game into the normal form. That is, describe
the set of players, the strategy sets for each player, the payoff
functions, and draw the game in matrix form. What do you expect
would happen in this game, and why?Two kids are playing a game
of Chicken. In this game, they ride their bikes as fast as theycan
at each other. The one to swerve or turn out of the way loses, he
is a Chicken...

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...

Two street races are playing a simultaneous game of chicken.
They have to race towards each other and whoever swerves first is
chicken and faces shame, a loss of 8, while the winner enjoys a
gain of 3. If neither stop, they would crash into each other, a
loss of 10. If both of them swerve at the same time, they are both
chicken and face a loss of 5 each.
What would the Nash equilibrium be in this game?...

Brett and Carl are playing chicken in their cars. If they both
stay straight they will be horribly disfigured in a car accident,
but both are hoping the other guy swerves so they can be the
stronger man who stays straight. They have gotten so close that it
is effectively a simultaneous move game. The table shows their
possible payoffs, where the contents of each cell are (Brett’s
payoff, Carl’s payoff).
Carl's option 1
Carl's option 2
Keep Straight
Swerve...

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...

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...

(4) In this game, each of two players can volunteer some of
their spare time planting and cleaning up the community garden.
They both like a nicer garden and the garden is nicer if they
volunteer more time to work on it. However, each would rather that
the other person do the volunteering. Suppose that each player can
volunteer 0, 1, 2, 3, or4 hours. If player 1 volunteers x hours and
2 volunteers y hours, then the resultant garden...

There are two players. First, Player 1 chooses Yes or
No. If Player 1 chooses No, the game ends and
each player gets a payoff of 1.5. If Player 1 chooses Yes,
then the following simultaneous-move battle of the sexes game is
played:
Player 2
O
F
Player 1
O
(2,1)
(0,0)
F
(0,0)
(1,2)
Using backward induction to find the Mixed-Strategy
Subgame-Perfect Equilibrium.

In a game, a Nash equilibrium is reached only if the
players:
understand the game and the payoffs associated with each
strategy.
use backward induction method to develop their strategies.
follow a mixed strategy.
have no best response for the choices made by other players.

Two players can name a positive integer number from 1 to 6. If
the sum of the two numbers does not exceed 6 each player obtains
payoff equal to the number that the player named. If the sum
exceeds 6, the player who named the lower number obtains the payoff
equal to that number and the other player obtains a payoff equal to
the difference between 6 and the lower number. If the sum exceeds 6
and both numbers are...

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