Your and your partner are working together on a project. Where your effort towards the project is y and your partner's effort is p, the project's value will equal a(y + p) + yp. You will share this value equally (each of you getting half of it) once the project is complete.For both you and your partner, effort is costly: y units of effort bears a cost of y? for you, and similarly p units of effort comes with a cost of p? for your partner. Therefore your payoff is 0.5[a(y + p) + yp] – y? and your partner's is 0.5|[a(y+ p) + yp] - p°.Wherever rounding is needed, please round to 3dp.Suppose a = 4 and the only effort options available are 0, 1 and 2. Suppose decisions are made simultaneously. Find the set of pure strategy Nash equilibria of this game. Add up both players' payoffs in all of these equilibria. This sum isHow many strictly dominated strategies does your partner have in the game described in the previous question?Now suppose a = 4 and that instead of being limited to three effort levels, both you and your partner can choose any nonnegative effort level. Find the effort level you exert in the unique Nash equilibrium of the game.

Assume that P owns a bookstore and has employed A as a seller. The number of books sold depends on…

Answered: ind the set of pure strategy Nash equ

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Consider whether the promises and threats made toward each other by duopolists and oligopolists are always credible (believable). Look at the figure below. Imagine that the two firms will play this game twice in sequence and that each firm claims the following policy. Each says that if both it and the other firm choose the high price in the first game, then it will also choose the high price in the second game (as a reward to the other firm for cooperating in the first game). RareÃir's price strategy High Low $12 $15 B High $12 $6 $6 D $8 Low $15 $8 a. As a first step toward thinking about whether this policy is credible, consider the situation facing both firms in the second game. If each firm bases its decision on what to do in the second game entirely on the payouts facing the firms in the second game, which strategy will each firm choose in the second game? (Click to select) b. Now move one step back. Imagine that it is the start of the first game and each firm must decide what to…
Prove the transitivity of strict preference relation.
For two sets A, B, suppose Pr(AUB) = 0.9 and Pr(AUB) = 0.7. Deter- mine the conditional probability Pr(B|A).
2. Consider a simultaneous-move auction in which two players simultaneously choose bids which must be in nonnegative integer multiples of one cent. The higher bidder wins a dollar bill. If the bids are equal, neither player receives the dollar. Each player must pay his/her own bid whether or not he or she wins the dollar. Each player's payoff is simply the net winnings. Construct a symmetric mixed-strategy equilibrium in which every bid less than 1.00 has a positive probability.
Consider the following normal-form game. A B C T 1, 1 2, 2 3, 4 9, 3 B 2, 5 3, 3 1, 2 7, 1 Find all pure Nash equilibria and one mixed Nash equilibrium of this game.
A game starts when the player pays 5 php. This gives him a chance to draw 2 balls simultaneously from a bag that contains 3 black, 3 white, and 2 red. If 2 red balls are drawn, the player wins 20 php. If only one red ball is drawn, the player wins 10 php. If no red ball is drawn, the player wins nothing. Which statement best describes the game's partiality? A B U The game's partiality cannot be determined. The game favors the player. The game neither favors the player nor the organizers. The game favors the organizers.
1. Two risk neutral players compete to win a prize, P. The probability of winning depends on effort; the probability that player i wins equals e(e++e2), where ei is the effort level of player i. The cost of effort is ciei. a) Find the Nash equilibrium effort levels. b) What is the probability player 1 wins at equilibrium?
this 'paradox be (c) Suppose we have the following simultaneous-move game, where the first value in every cell is Player 1's рayoff: Player 2 Right Left Player 1 Тор 4,8 12, 6 Bottom 6,2 8, 10 Outline and illustrate all pure strategy and mixed strategy Nash equilibria. Show that the mixed strategy Nash equilibrium is an inefficient outcome. cnlit f50 and have discount factors of 0.9 and 0.8, respectively,
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5. Define the following terms with a suitable example: d. Mixed strategy in a game. e. Simultaneous move Game.
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