(a) Transform this game into a strategic game. (b) Use backward induction to find a pure Nash equilibrium. (c) Identify all subgame perfect Nash equilibrium.
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- 60B- What is the Nash equilibrium for this game and identify the profit each player gets at this solution 5 mSolve Both Questions!2. Do we depict the equilibrium of a game in pay-offs or strategies in Game theory? 3- 3. What is meant by the phrase, "Best Response of a player"? in Game Theory?QUESTION 1: Game theory a) What is the pure strategy Nash equilibrium outcome if there is one? b) Is this a socially optimal outcome? If not, which outcome is preferred? c) Do all three solution approaches for simultaneous games work independently (not together)? If not, which do not? d) Draw the game as a game tree (extensive form). e) Switch the payoffs in cells (A, A) and (D, D). What is the pure strategy Nash equilibrium outcome if there is one?
- 10. Game theory terminology Select the term that best describes each definition listed in the following table. Definition Nash Equilibrium Dominant Strategy Collusion Tit-for-tat Strategy Payoff Matrix/Table Prisoners' Dilemma Game A set of strategies (one for each player) in which each player's strategy is the best option for that player, given the chosen strategy of the player's opponents A strategy in which a player cooperates until the other player defects and then defects until the other player cooperates again A case in which individually rational behaviour leads to a jointly inefficient outcome A player's best choice, if it exists, regardless of his or her opponent's strategy5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…Problem1 A)Provide an example of the extended form of a sequential game with perfect information. B) Provide an example of a repeated game with complete but imperfect information.
- Two takeaway restaurants, ChipAhoy and FishDish, compete for business in a small seaside town. The manager of ChipAhoy has engaged you to advise on the pricing of its main offering, a fish & chips supper. Your intention is to analyse the situation as a twoplayer competitive game. After making background investigations, you have decided to adopt the following assumptions in your analysis. A1 The cost of the producing and serving a portion of fish & chips is the same for both restaurants: £3.50.A2 In a typical week, holidaymakers buy a total of 1500 portions of fish & chips, and local residents buy 1000 portions.A3 Local residents always choose the restaurant with the lower price. If prices are the same at the two restaurants, their custom is divided equally between the two. A4 Holidaymakers divide their custom 50:50 between the two restaurants, irrespective of the prices. Derive the Nash equilibrium/equilibria for the game60A- What is the dominant strategy for Firm B? What is the dominant strategy for Firm A? Explain6 Two people will select a policy that affects both of them by applying a "veto" in a sequential and alternate manner, that is: person 1 begins to veto a policy and then person 2 exercises his "veto" with the remaining policies; the process repeats until only one policy remains. Assume that there are 3 policies: X,Y,Z, and that person 1 prefers X to Y to Z and person 2 prefers Z to Y to X. a. Represents the game extensively b. Give the number of subgames C. Indicate the total strategies of the players d. find all subgame perfect nash equilibria e. Find all Nash Equilibriums.
- 5. Individual Problems 18-5 When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Simone places a value of $65,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Simone simply bids $65,0002=$32,500$65,0002=$32,500 and wins the piece of art. The expected price paid by Simone, with no other bidders present, is . Suppose the owner of the artwork manages to recruit another bidder, Yakov, to the auction. Yakov is known to value the art piece at $52,000. The expected price paid by Simone, given the…Suppose that Bieber and Rihanna are duopolists in the music industry. In May, they agree to work together as a monopolist, charging the monopoly price for their music and producing the monopoly quantity of songs. By June, each singer is considering breaking the agreement. Assuming Bieber and Rihanna are rational, what would one expect to happen next? Question 36 options: a Bieber and Rihanna will determine that it is in each singer's self interest to maintain the agreement. b Bieber and Rihanna will each break the agreement. Both singers' profits will decrease. c Bieber and Rihanna will each break the agreement. Both singers' profits will increase. d Bieber and Rihanna will each break the agreement. The new equilibrium quantity of songs will increase, and the new equilibrium price also will increase.1. Suppose Company A is about to play a game with Company B. The following facts are known about the two players. The first Company (Company A) is a row player and uses three different strategies i.e. (Strategy X, Strategy Y and Strategy Z). Whereas the column player (Company B) has two different strategies i.e. (M and N) that can be used accordingly. The payoff matrix is given in the table below. Player B Player A M N X -5 3 Y 3 -7 Z -6 5 Answer the following questions based on the information given above a. Determine the strategies of each firm using graphical technique b. Compute the value of the game.
