Suppose you are given a mixed strategy X for player I and a mixed strategy Y for player II. Explain in your own words how you would check if (X, Y) is a saddle point in mixed strategies.
Q: What is the unique Nash equilibirum in mixed strategies for the above question?
A: Unique Nash equilibirum in mixed strategies is provided in the original solution.
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- Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m) Giga Company Titanic Conglomerate No Change Refurbishment of existing stores Large Expansion No Change 30, 40 25, 35 15, 24 Refurbishment of existing stores 35, 30 28, 32 18, 33 Large Expansion 12, 22 18, 20 20, 25 The Nash equilibrium: (A) does not exist. (B) occurs when both firms choose Refurbishment of existing stores. (C) occurs when both firms choose Large Expansion. (D) occurs when both firms choose No Change.Two discount stores (Megastore and Superstore) are interested in expanding their market share through advertising. The table below depicts the strategic outcomes (profits) of both stores with and without advertising. Superstore - Advertise Superstore - Don't Advertise Megastore - Advertise $95, $80 $305, $55 Megastore - Don't Advertise $65, $285 $165, $115 When the game does reach Nash Equilibrium, the payoffs for both stores will be a) Megastore $95 and Superstore $80 b) Megastore $305 and Superstore $55 c) Megastore $65 and Superstore $285 d) Megastore $165 and Superstore $115In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients. Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.
- Problems associated towards unique outcomes in games where multiple Nash equilibria exist”In game theory, what does the term "payoff" refer to? a) The amount of money each player has at the beginning of the game. b) The final outcome of the game. c) The utility or benefit that a player receives based on the outcome of the game. d) The number of strategies available to each player.Which of the following would be best understood with game theory? Group of answer choices How two car dealerships choose prices when the prices of one dealership affects the sales of the other. A person choosing among retirement plans offered at her job The decision of what foods to buy at a grocery store
- Here is a table representing the gains for the server if he serves on his opponent's forehand or backhand and for the receiver the gains if he returns on his forehand or backhand. Each player can choose to play the forehand or the backhand of the other player : Server D R D 50,50 80, 20 R 90,10 |20, 80 Receiver D Determine the Nash equilibrium(s) (pure strategies and mixed strategies).Consider the Normal Form Game characterized in the following figure: P1 \ P2 b1 b2 b3 a1 (1,2) (0,1) (0,3) a2 (3,-1) (1,1) (-1,0) a3 (2,2) (1,-1) (3,0) a4 (-5,1) (-1,0) (-3,-2) a5 (-3,3) (3,0) (2,4) What is the set of actions of player 1? O la 1, a2, a3, a4, a5) O (b1,b2, b3} O {a2, a3, a4) O (bl, b2}The US and Canada have overfished North Atlantic cod stocks nearly to the point of extinction. Both countries wish to preserve the cod industry (and hence the cod stocks), so the two countries sign an agreement to limit fish hauls. Each country has two possible strategies: comply with the agreement (limit fishing) or renege on the agreement (overfish). Each country’s payoffs for different strategy combinations are given in the matrix below. The numbers in the cells represent utilities, and the payoff ordering is (US, Canada). QUESTIONS: 1.If this is a one-shot game (i.e., it is played once), do the players have a dominant strategy? If so, what is it? Briefly explain your answer. 2.What is the equilibrium of this game? Is it Pareto-optimal? How do you know?
- In a game of chicken, two drivers are heading towards each other on a collision course. The first one to swerve is considered the "chicken" and loses. What is the Nash equilibrium in this game? a) Both drivers swerve b) Neither driver swerves c) One driver swerves while the other doesn't d) It depends on the specificFred and Naomi are trying to decide how to spend Sunday. Their payoffs in terms of satisfaction are below. Fred's strategy Football Naomi strategy Football Movie There is no dominant strategy Dominant strategy is football Dominant strategy is movie There is no Nash equilibrium 5,3 1,1 Movie 0,0 3,5Game theory is a useful tool for analyzing Situations in which multiple parties make decisions that do not affect each other. Situations in which multiple parties make decisions with the potential to affect each other. Situations in which multiple parties make decisions. Situations in which one party makes a decision with the potential to affect other parties. Any situation in which a decision must be made.