Problem 5. Consider the following game.R.U 4,0 0,2D0,3 | 3,0(a) Find all Nash equilibrium in mixed strategies by constructing the bestresponse graphs. Find the Nash equilibrium payoffs.(b) Change only two payoff numbers (out of 8 numbers in the matrix) tomake joint strategy ((¿, }), (¿, })) a Nash equilibrium.

Answered: Problem 5. Consider the following game.…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1. Consider the following payoff matrix: a) b) Player 1 Strategy B Strategy A Player 2 Strategy A Strategy B (4,3) (3,5) (2,4) (6,2) Is the payoff matrix symmetric (Yes or No)? Does this game have a Nash Equilibrium? If so what is/are they? (no need to show your work) c) What is Player 1's dominant strategy (if they have one)? What is Player 2's dominant strategy (if they have one)? (no need to show your work)
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2
Consider the following game in extensive form. a В В В d f h i e (3, 2z) (9, 5) (6, 32) (2z, 19) (15, 7) (2, 20) (7, 32) Z=7 (a) How many pure strategy profiles exist in this game? (b) In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs to the two players?
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.
a, b, c
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,
Suppose we believe that with probability p a person will play a certain Nash equilibrium and that this probability is the same for all people. We do not know p, but have reason to believe it is about 25%. To test this hypothesis against the two-tailed alternative, we put 100 subjects through an experiment and observe 20 of them playing the Nash strategy. Based on the experimental results, conduct a parametric test, test whether p = 25% when α (type 1 error) = 0.05.
In the strategic form game below: (a.) What is P1's best response to each of P2's strategies. (b.) Find all Pure Strategy Nash Equilibria (PSNE). Show all work. (c.) Show an example of a Mixed Strategy Nash Equilibrium (MSNE) in this game. How many are there? Explain. Hint: we can assign probabilities of 1 or 0 if a player chooses a given strategy with certainty in a MSNE. Show your work. Player 1 a b с d Player 2 W X Y Z 0,5 1,3 1,7 0,8 1,6 0, 2 2,6 0,7 0,5 1,3 0,8 3,9 1,2 0,4 0,4 3,5
1. Suppose we have a 2-player zero-sum game where the strategy set of the row player (resp. the column player) is R = {₁,..., rk} (resp. C = {C₁,..., ce}) and where the payoff matrix is A (ai). If (r₁, c₁) and (r2, C₂) are both Nash equilibria, show that they have the same payoff (i.e. a11 a22). [Do this directly using the definitions and without using any theorems from the lectures.] = =
7. Player A and player B have a payoff matrix shown below. If A (row player) has an optimal strategy of (424) and B has an optimal strategy of (1/3 1/3 1/3), what is the expected value of the game? P = 2 5 -2 -3 1 2-2 4 3

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