My teacher isn't the best at explaining this topic ever since it's gone online, would you be able to help with this assignment? There's 4 questions in total.
Econ 464 Final Assignment Department of Economics Concordia University Full Grade 80 Due date: April 14, 2020 This is your Final Assignment for Course ECON 464. Please take this assignment seriously. Consider it as a take home exam.You have to submit the assignment on Moodle by 6.00 p.m. April 14, 2020. Best of luck! 1. (20 points) Two buyers bid in an auction for a single object. Each can bid any integer amount from $0 to $10. The two bids are made simultaneously and independently of each other. The buyers’ respective values are v1 = 5 and v2 = 10. The bidder with the higher bid wins (obtains the object) and pays the amount of his own bid. However, the bidder who does not win the auction and thus does not get the object is also obliged to pay half of his own bid. In case of a tie in the bids bidder 2 wins. (a) Specify the best responses to pure strategies for both bidders. (5 points) (b) Identify the pure strategy NE of the game. (3 points) (c) Find all dominated strategies for each bidder. (5 points) (d) Now restrict the possible bids to $4 and $5, and identify all pure and mixed strategy NE in this game. (7 points) 2. (20 points) Consider the game in normal form given in the following table. Player 1 is the “row” player with strategies A,B and C and player 2 is the “column” player with strategies L,C and R. The game is given in the following table: L C R A 0,0 2,-2 -2,3 B -2,2 0,0 2,-1 C 3,1 -1,2 0,1 1 (a) Find whether there is a mixed strategy Nash equilibrium (M.S.N.E) where player 1 mixes between A and C and player 2 mixes between L, C and R with positive probability. (10 points) (b) Find whether there exists a mixed strategy Nash equilibrium where each player mixes between all her strategies with positive proba- bility. (10 points) 3. (20 points) In the extensive form game below, there are two players: Player 1 , denoted by P1 and Player 2, denoted by P2. The first entry is the pay-off of player 1, and the second entry is the payoff of player 2. Find all the SPE of the game in pure strategies. P2 (2.5, 2.5) X P1 (3, 3) l (0, 2) r L (2, 0) l (2, 2) r R E P2 4. Consider a bargaining problem with two agents 1 and 2. There is a prize of $1 to be divided. Each agent has a common discount factor 0 < δ="">< 1. there are two periods, i.e., t ∈ {0, 1}. this is a two period but random symmetric bargaining model. at any date t ∈ {0, 1} we toss a fair coin. if it comes out “head” ( with probability p = 1 2 ) player 1 is selected. if it comes out “tail”, (again with probability 1−p = 1 2 ), player 2 is selected. the selected player makes an offer (x, y) where x, y ≥ 0 and x + y ≤ 1. after observing the offer, the other player can either accept or reject the offer. if the offer is accepted the game ends yielding payoffs (δtx, δty). if the offer is rejected there are two possibilities: 2 • if t = 0, then the game moves to period t = 1, when the same procedure is repeated. • if t = 1, the game ends and the pay-off vector (0, 0) realizes, i.e., each player gets 0. (a) suppose that there is only one period,i.e., t = 0. compute the subgame perfect equilibrium (spe). what is the expected utility of each player before the coin toss, given that they will play the spe. (10 points) (b) suppose now there are two periods i.e., t = 0, 1. compute the subgame perfect equilibrium (spe). what is the expected utility of each player before the first coin toss, given that they will play the spe. (10 points) 3 1.="" there="" are="" two="" periods,="" i.e.,="" t="" ∈="" {0,="" 1}.="" this="" is="" a="" two="" period="" but="" random="" symmetric="" bargaining="" model.="" at="" any="" date="" t="" ∈="" {0,="" 1}="" we="" toss="" a="" fair="" coin.="" if="" it="" comes="" out="" “head”="" (="" with="" probability="" p="1" 2="" )="" player="" 1="" is="" selected.="" if="" it="" comes="" out="" “tail”,="" (again="" with="" probability="" 1−p="1" 2="" ),="" player="" 2="" is="" selected.="" the="" selected="" player="" makes="" an="" offer="" (x,="" y)="" where="" x,="" y="" ≥="" 0="" and="" x="" +="" y="" ≤="" 1.="" after="" observing="" the="" offer,="" the="" other="" player="" can="" either="" accept="" or="" reject="" the="" offer.="" if="" the="" offer="" is="" accepted="" the="" game="" ends="" yielding="" payoffs="" (δtx,="" δty).="" if="" the="" offer="" is="" rejected="" there="" are="" two="" possibilities:="" 2="" •="" if="" t="0," then="" the="" game="" moves="" to="" period="" t="1," when="" the="" same="" procedure="" is="" repeated.="" •="" if="" t="1," the="" game="" ends="" and="" the="" pay-off="" vector="" (0,="" 0)="" realizes,="" i.e.,="" each="" player="" gets="" 0.="" (a)="" suppose="" that="" there="" is="" only="" one="" period,i.e.,="" t="0." compute="" the="" subgame="" perfect="" equilibrium="" (spe).="" what="" is="" the="" expected="" utility="" of="" each="" player="" before="" the="" coin="" toss,="" given="" that="" they="" will="" play="" the="" spe.="" (10="" points)="" (b)="" suppose="" now="" there="" are="" two="" periods="" i.e.,="" t="0," 1.="" compute="" the="" subgame="" perfect="" equilibrium="" (spe).="" what="" is="" the="" expected="" utility="" of="" each="" player="" before="" the="" first="" coin="" toss,="" given="" that="" they="" will="" play="" the="" spe.="" (10="" points)="">