Question

Consider the original divide the dollar game of question (3). How many strategies does player 1 have? How many strategies does player 2 have? Write down all the strategies of player 1, and two strategies of player 2. Explain briefly (in a line or two) why you wrote the strategies of player 2 in the way you wrote them.

Question 3-Consider the following game of divide the dollar. There is a dollar to be split between two players. Player 1 can make any offer to player 2 in increments of 25 cents; that is, player 1 can make offers of 0 cents, 25 cents, 50 cents, 75 cents, and $1. An offer is the amount of the original dollar that player 1 would like player 2 to have. After player 2 gets an offer, she has the option of either accepting or rejecting the offer. If she accepts, she gets the offered amount and player 1 keeps the remainder. If she rejects, neither player gets anything. Represent the game in extensive form using a game tree. Note that here you must assign payoffs appropriately at the terminal nodes.

Answer #1

Consider the following game of divide the dollar. There is a
dollar to be split between two players. Player 1 can make any offer
to player 2 in increments of 25 cents; that is, player 1 can make
offers of 0 cents, 25 cents, 50 cents, 75 cents, and $1. An offer
is the amount of the original dollar that player 1 would like
player 2 to have. After player 2 gets an offer, she has the option
of either...

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...

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...

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...

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...

Two players, A and B, have $1 to divide between them. They agree
to spend at most three days negotiating over the division. If they
can’t come to an agreement they both get nothing, i.e. $0. The
first day, A will make an offer, B either accepts or comes backs
with a counteroffer the next day, and on the third day A gets to
make one final offer if he rejected the offer of B on day 2. Both A...

Consider the following game. Player 1 has 3 actions
(Top, middle,Bottom) and player 2 has three actions (Left, Middle,
Right). Each player chooses their action
simultaneously. The game is played only
once. The first element of the payoff vector is player
1’s payoff. Note that one of the payoffs to player 2 has been
omitted (denoted by x).
Player
2
Left
Middle
Right
Top
(2,-1)
(-2,3)
(3,2)
Middle
(3,0)
(3,3)
(-1,2)
Bottom
(1,2)
(-2,x)
(2,3)
Player
1
a)Determine the range of values for x...

Consider the following market entry game. There are two firms :
firm 1 is an incumbent monopolist on a given market. Firm 2 wishes
to enter the market. In the first stage, firm 2 decides whether or
not to enter the market. If firm 2 stays out of the market, firm 1
enjoys a monopoly profit of 2 and firm 2 earns 0 profit. If firm 2
decides to enter the market, then firm 1 has two strtegies : either...

Consider a dynamic game of “The Office or Parks and Rec”. There
are two people who are trying to make a decision about attending
either “The Office” convention in Pennsylvania or the “Parks and
Rec” convention in Indiana. The two would be happy if they both
attended the same venue, but obviously one would prefer to attend
her choice of preferred TV-show.
Suppose that player 1 announces her choice first then player 2
announces her choice. Assume that player 1...

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