Compute pure strategy and mixed strategy equilibria of game, Game Theory

Assignment Help:

Ronaldo (Brazil) kicks a penalty against Casillas (Spain) in the 2006 World Cup nal. Sup- pose that Ronaldo can kick the ball to Casillas' upper left (UL), lower left (LL), upper right (UR) and lower right (LR) side. Casillas simultaneously decides whether to jump to his left (L), stay in the center (C), or jump to his right(R). Players do not care about the cost of jumping or kicking the ball to one side or the other. Ronaldo only cares about the probability of scoring and Casillas only about the probability of avoiding a goal.

Ronaldo sometimes misses the goal even if Casillas jumps to the other side. - The probability of scoring when Ronaldo kicks to Casillas' upper left is: 0.7 if Casillas jumps to the right, 0.5 if Casillas stays in the center and 0.5 if Casillas jumps to the left. - The probability of scoring when Ronaldo kicks to Casillas' lower left is: 0.9 if Casillas jumps to the right, 0.8 if Casillas stays in the center and 0.4 if Casillas jumps to the left. - The probability of scoring when Ronaldo kicks to Casillas' upper right is: 0.4 if Casillas jumps to the right, 0.8 if Casillas stays in the center and 1 if Casillas jumps to the left. - The probability of scoring when Ronaldo kicks to Casillas' lower right is: 0.3 if Casillas jumps to the right, 0.5 if Casillas stays in the center and 0.7 if Casillas jumps to the left.

(a) What are the strategies available for Ronaldo and Casillas?

(b) Write down the Normal form of this game (the bimatrix of strategies and payoffs).

(c) Compute all the pure strategy and mixed strategy equilibria of the game. Find the expected payoff of each player in each equilibrium.


Related Discussions:- Compute pure strategy and mixed strategy equilibria of game

Find all ne of the game, 1. Find all NE of the following 2×2 game. Determin...

1. Find all NE of the following 2×2 game. Determine which of the NE are trembling-hand perfect. 2. Consider the following two-person game where player 1 has three strategie

Reserve worth , A reserve worth is that the minimum acceptable bid in an au...

A reserve worth is that the minimum acceptable bid in an auction. If no bidder submits a bid higher than the reserve worth, the auctioneer keeps the item offered for sale. Alternat

Determine the linear regression function of y on x, QUESTION ONE. (a) Th...

QUESTION ONE. (a) The probability that, a bomber hits a target on a bombing mission is 0.70 Three bombers are sent to bomb a particular target. (i)  What is the probabilit

Multiunit auction, An auction during which many (more than one) things are ...

An auction during which many (more than one) things are offered for sale. Mechanisms for allocating multiple units embody discriminatory and uniform worth auctions.

Game playing in class-equilibrium payoffs are (2, Equilibrium payoffs are ...

Equilibrium payoffs are (2, 3, 2). Player A’s equilib- rium strategy is “N and then N if b follows N or N if d follows N” or “Always N.” Player B’s equilibrium strategy is “b if N

Trede cycle theory, what are the theories of financial crisis

what are the theories of financial crisis

Find the nash equilibria - strategic game, Two people are engaged in a join...

Two people are engaged in a joint project. If each person i puts in the e ort xi, a nonnegative number equal to at most 1, which costs her c(x i ), the outcome of the project is wo

Assurance game, Assurance game Scenario "Assurance game" may be a generi...

Assurance game Scenario "Assurance game" may be a generic name for the sport a lot of commonly called "Stag Hunt." The French thinker, Jean Jacques Rousseau, presented the subse

Game playing in class-equilibrium payoffs example, (a) Equilibrium payoffs ...

(a) Equilibrium payoffs are (1, 0). Player A’s equilibrium strategy is S; B’s equilibrium strategy is “t if N.”   For (a): Player A has two strategies: (1) N or (2) S. P

Games with sequential moves, Games with Sequential Moves Most students ...

Games with Sequential Moves Most students find the idea of rollback very simple and natural, even without drawing or understanding trees. Of course, they start by being able to

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd