Consider three players (1, 2, 3) and three alternatives (A, B, C). Players vote simultaneously for...

Consider three players (1, 2, 3) and three alternatives (A, B, C). Players vote simultaneously for an alternative and abstention is not allowed.The alternative with more votes wins. If no alternative receives a majority, alternative A is chosen.
U1 (A) = U2 (B) = U3 (C) = 2
U1 (B) = U2 (C) = U3 (A) = 1
U1 (C) = U2 (A) = U3 (B) = 0
Obtain all Nash equilibria in
pure strategies.

Expert Solution

Let us understand how the subgame pure strategies will be obtained :-

1) It is very evident from the question itself that if All the players vote for an alternative then :-

A ) In case of majority - The player with highest number of votes will win .

B ) In case of no majority the first choice will win .

2) Thus there are chances of winning for all three players .

However if Choice is player 1 then gain is 2

Choice is player 2, then equilibrium gain is 1 and

If choice is player 3 equilibrium gain is 0 for all .

3) However in case of majority only the player who backs majority wins , else all loose .

In the given figure first choice only Player 1 wins with majority ,

Second choice player 2 wins with majority

While the other two choices show all equilibrium strategies with majority of player 3 or win individual choices and no majority.

Rahul Sunny answered 1 year ago

6)Consider the following voting problem: there are 3 alternatives A, B, and C. There are 3...

6)Consider the following voting problem: there are 3 alternatives A, B, and C. There are 3 voters whose preferences are as follows: Voter 1: A > B > C Voter 2: B > C > A Voter 3: C > A > B The voting procedure is as follows: first A competes with B and then the winner competes with C. If voters are strategic what is the voting outcome? Who will each voter vote for in the first stage?

Q1. Consider the following game. Two players simultaneously and independently choose one of three venues. They...

Q1. Consider the following game. Two players simultaneously and independently choose one of three venues. They would like to choose the same venue (i.e. meet), but their favorite venues are different: Football cafe ballet Football (3,2) (1,0) (1,1) cafe (0,0) (2,2) (0,1) ballet (0,0) (0,0) (2,3) a. What are the pure-strategy Nash equilibria of this game? b. Derive a mixed-strategy Nash equilibrium in which players 1 and 2 mix over Football and Cafe only? Now suppose that player 1 is...

Consider the following three mutually exclusive investment project alternatives (A, B, C). Use the annual worth...

Consider the following three mutually exclusive investment project alternatives (A, B, C). Use the annual worth analysis (AW) to determine the best investment alternative assuming MARR=15%. Project name: A B C Cash Flow (Year 0): -200,000 -300,000 -400,000 Cash Flow (Year 1-N) +150,000 +180,000 +150,000 Salvage value at year N: +30,000 +50,000 +60,000 Project Life (N): 2 years 3 years 6 years

There are three basketball players, A, B, and C. A takes 30 shots a game, with...

There are three basketball players, A, B, and C. A takes 30 shots a game, with a shooting percentage of 70%. B takes 20 shots, hitting 60%, and C takes 10 shots, hitting 50%. write a program in java or Python. Use the above statement to simulate players A, B, and C in a season of 82 games. Generate a string of shots for each player in each game, length 30, 20, and 10 shots. Count the number of shots...

Now there are three potential entrants (firm 1, firm 2, and firm 3) that simultaneously make...

Now there are three potential entrants (firm 1, firm 2, and firm 3) that simultaneously make entry decisions. If only one firm enters, the entering firm becomes a monopolist while the other firms that stay out get zero profit. If more than one firm enter the market, they play a Cournot game. The demand in the market is given by P = 6-Q. Assume that there is no production cost, but there is an entry cost of 5 as before....

Solve the game below, assuming that both players A & B play simultaneously. What is the...

Solve the game below, assuming that both players A & B play simultaneously. What is the dominant strategy for A and for B. (payoffs shown are A, B). B B1 B2 A A1 3, 3 7, 2 A2 1, 7 6, 6 If the players could collude, would this alter the outcome? How so?

Consider three choices A, B, C. Choice A gives $30 with probability 1/2 and $70 with...

Consider three choices A, B, C. Choice A gives $30 with probability 1/2 and $70 with probability 1/2. Choice B gives $50 with certainty. Choice C gives $40 with probability 1/2 and $70 with probability 1/2. (a) [2 points] For a risk averse individual, determine if the individual (i) prefers A over B, or (ii) prefers B over A, or (iii) more information on the individual's risk attitude is needed to compare A,B for the individual. (b) [4 points] Carry...

a+b+c=(abc)^(1/2) show that (a(b+c))^(1/2)+(b(c+a))^(1/2)+(c(a+b))^(1/2)>36

A firm is considering three capacity alternatives: A, B, and C. Alternative A would have an...

A firm is considering three capacity alternatives: A, B, and C. Alternative A would have an annual fixed cost of $100,000 and variable costs of $22 per unit. Alternative B would have annual fixed costs of $120,000 and variable costs of $20 per unit. Alternative C would have fixed costs of $80,000 and variable costs of $30 per unit. Revenue is expected to be $50 per unit. A) Which alternative has the lowest break-even quantity? B) Which alternative will produce...

1. Three players, A,B, and C, each flip their coins until one person has a different...

1. Three players, A,B, and C, each flip their coins until one person has a different result from the others. The person having the different result wins. (a) Using R, simulate this experiment 10000 times and give the resulting estimate of P(A wins).

Question