AGT_ps3

Mr. and Mrs. Smith vote opposite in presidential elections in a swing state. Assign 1 point for voting your preferred candidate and 0 points if you don’t vote. If you don’t want your candidate to lose, what is the Nash equilibrium in this situation?

5) Three legislators are set to vote on a bill to raise the salary of legislators. The majority wins, so all three will receive the raise if at least two of them vote in favor of the bill. The raise is valued at R by each legislator. Voting in favor of the bill comes with political backlash from constituents, though, even if the bill fails. Let C be the cost of backlash for anyone voting in favor of the bill. Finally, suppose that 0 < C < R. There are four possible payoffs for each legislator: 0: if they vote against the bill and at least one other legislator votes against it (so the bill fails) R: if they vote against the bill and the others vote for the bill (so the bill passes) -C: if they vote for the bill and no one else votes for the bill (so the bill fails) R-C: if they vote for the bill and at least one other legislator votes for it (so the bill passes). The three legislators are named X, Y, and Z, and voting happens sequentially and orally. So X announces their vote (to…

Imagine that two firms in two different countries want to bring a new product tomarket. Due to economies of scale, if both firms do this, they will both lose £50million. But if only one firm does this, it will gain £300 million.(a) What is the best strategy for firm A, if firm B has not yet entered the market, andwhy?(b) Illustrate this with a game theory diagram, showing appropriate payouts.(c) What is the welfare-maximising strategy for a government, and why?

Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 4 units of utility from a vote for their positions (and lose 4 units of utility from a vote against their positions). However, the bother of actually voting costs each 2 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward.     Mrs. Ward       Vote Don't Vote Mr. Ward Vote Mr. Ward: -2, Mrs. Ward: -2 Mr. Ward: 2, Mrs. Ward: -4   Don't Vote Mr. Ward: -4, Mrs. Ward: 2 Mr. Ward: 0, Mrs. Ward: 0           The Nash equilibrium for this game is for Mr. Ward to (vote/not vote)   and for Mrs. Ward to (vote/not vote)  . Under this outcome, Mr. Ward receives a payoff of ____ units of utility and Mrs. Ward receives a payoff of ____ units of utility.   Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would increase utility for each spouse, compared to the Nash…

Burger King has introduced new strategy by reducing the price of its Whopper by 75 percent if customers also purchased french fries and a soft drink. Nevertheless, the sales dropped within two weeks. Based on your knowledge on game theory, what do you think had happened? The Edge magazine columnist, Jack Sparrow reported the recent findings of two academic political scientists. These scholars found out that voters are not happy with “negative campaigns” of politicians. However, the political scientists suggested it is pointless for candidates to stay positive. The damage from staying positive is heaviest when the opponent is attacking. Explain the dilemma.        Airlines practice price discrimination by charging leisure travelers and business travelers different prices. Why do you think by charging different prices; the airline companies will maximize their profits? Discuss briefly.

Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain 6 units of utility from a vote for their positions (and lose 6 units of utility from a vote against their positions). However, the bother of actually voting costs each 3 units of utility. The following matrix summarizes the strategies for both Mr. Ward and Mrs. Ward.   Mrs. Ward Vote Don't Vote Mr. Ward Vote Mr. Ward: -3, Mrs. Ward: -3 Mr. Ward: 3, Mrs. Ward: -6 Don't Vote Mr. Ward: -6, Mrs. Ward: 3 Mr. Ward: 0, Mrs. Ward: 0   The Nash equilibrium for this game is for Mr. Ward to    and for Mrs. Ward to    . Under this outcome, Mr. Ward receives a payoff of   units of utility and Mrs. Ward receives a payoff of   units of utility.   Suppose Mr. and Mrs. Ward agreed not to vote in tomorrow's election. True or False: This agreement would decrease utility for each spouse, compared to the Nash equilibrium from the previous part of the question. True…

Marie and Mike usually vote against each other’s party in the SSC elections resulting to negating or offsetting their votes. If they vote for their party of choice, each of them gains four units of utility (and lose four units of utility from a vote against their party of choice). However, it costs each of them two units of utility for the hassle of actually voting during the SSC elections.    Can you explain the scenario above?

Consider a game where each player picks a number from 0 to 60. The guess that is closest to half of the average of the chosen numbers wins a prize. If several people are equally close, then they share the prize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers   Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30;(C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization.

Game Theory Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

TRADE. Consider a bilateral trade model with two-sided asymmetric information. The buyer's value is private information to the buyer, vB and the seller's value vs is private information to the seller. (a)Derive the linear Bayes Nash Equilibrium in a double auction.   (b)Assume that the seller can credibly disclose their valuae. What is your intuition, would he want to commit to such transparency?

Imagine that two firms in two different countries want to bring a new product to market. Due to economies of scale, if both firms do this, they will both lose £50 million. But if only one firm does this, it will gain £300 million. (a) What is the best strategy for firm A, if firm B has not yet entered the market, and why? (b) Illustrate this with a game theory diagram, showing appropriate payouts. (c) What is the welfare-maximising strategy for a government, and why?

Consider the following Bayesian game. There are two players 1 and 2. Both players choose whether to play A or B. Two states are possible, L and R. In the former, players play a stag-hunt game, and in the latter, players play a matching pennies game. Suppose that Player 2 knows the state, while Player 1 thinks that the state is L with probability q and R with probability 1 ! q. Payo§s in each state respectively satisfy: Player 1 is the row player, and their payo§ is the first to appear in each entry. Player 2 is thecolumn player and their payo§ is the second to appear in each entry. (a) What is the set of possible strategies for the two players in this game?  (b) Find all the pure strategy Bayes Nash equilibria for any value of q 2 (0, 1).

Debt as a means of mitigating the common-pool problem. (Chari and Cole, 1993.) Consider the same setup as in Problem 12.15. Suppose, however, that there is an initial level of debt, D. The government budget constraint is therefore (a) How does an increase in D affect the Nash equilibrium level of G?(b) Explain intuitively why your results in part (a) and in Problem 12.15 suggest that in a two-period model in which the representatives choose D after the first-period value of G is determined, the representatives would choose D > 0.(c) Do you think that in a two-period model where the representatives choose D before the first-period value of G is determined, the representatives would choose D > 0? Explain intuitively. 

Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.

Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…

Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?

A case study in the chapter describes a phoneconversation between the presidents of AmericanAirlines and Braniff Airways. Let’s analyze thegame between the two companies. Suppose thateach company can charge either a high price fortickets or a low price. If one company charges $300,it earns low profit if the other company also charges$300 and high profit if the other company charges$600. On the other hand, if the company charges $600,it earns very low profit if the other company charges$300 and medium profit if the other company alsocharges $600.a. Draw the payoff matrix for this game.b. What is the Nash equilibrium in this game?Explain.c. Is there an outcome that would be better than theNash equilibrium for both airlines? How could itbe achieved? Who would lose if it were achieved?

. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff.   You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that

John and Jane usually vote against each other’s party in the SSC elections resulting to negating or offsetting their votes. If they vote for their party of choice, each of them gains four units of utility (and lose four units of utility from a vote against their party of choice). However, it costs each of them two units of utility for the hassle of actually voting during the SSC elections.  A. Diagram a game in which John and Jane choose whether to vote or not to vote.

Roger and Rafael play a game with the following rules. Roger is given $250 to divide between himself and Rafael. Rafael does not get to choose but he can reject Roger’s offer if he does not like it. If Rafael rejects, both get nothing. If Rafael accepts, both get the split that Roger decided.   a. What is this game called? b. Find all Nash equilibria for this game. c. When this game is played in the real world, do the predictions in part 1b materialize? Why/why not? d. Are all Nash equilibria in part 1b Pareto Optimal? Explain

The empirical evidence in the dictator games shows that it is most common for ‘dictators’ to share (A) between 10% to 30% of their endowments; (B) between 40% and 60% of their endowments; (C) nothing with the recipients; (D) their entire endowments.