Question

Brett and Carl are playing chicken in their cars. If they both stay straight they will...

Brett and Carl are playing chicken in their cars. If they both stay straight they will be horribly disfigured in a car accident, but both are hoping the other guy swerves so they can be the stronger man who stays straight. They have gotten so close that it is effectively a simultaneous move game. The table shows their possible payoffs, where the contents of each cell are (Brett’s payoff, Carl’s payoff).

Carl's option 1 Carl's option 2
Keep Straight Swerve
Brett's option 1 Keep Straight (-10 , -10) ( 1, -1)
Brett's option 2 Swerve (-1 , 1) (0 , 0)

a. Do either/both Brett and Carl have dominant strategies?
b. Does this game have one or more pure strategy Nash equilibriums? If so, what is/are it/they?
c. Is there a mixed strategy Nash equilibrium? If so, what is it?

Homework Answers

Answer #1

Ans for a)

No neither of the players have any dominant strategy here in this game

Ans for b)

Yes this game has 2 Pure Nash Equilibrium and they are as follows

(Keep Straight,Swerve) & (Swerve, Keep Straight)

Becasue these are PSNE from which no player has profitable deviation to play away from it

Ans for c)

We have 2 NE then we cn find Mixed strategy Nash Equilibrium

Lets assume Brett plays Swerve with prob (1-p) and Carl plays swerve with prob (1-q)

then we need to find value of p and q for which Brett and Carl is indifferent between any of his two strategies

therefore we have

-10q+1*(1-q)=-1*q+0(1-q)

-10q+1-q=q

1/12=q similarly for Brett we can find values of p

-10p+1(1-p)=-1*p

p=1/12

Therefore MSNE are (11/12,1/12) and (11/12,1/12) respectivelt for Brett and Carl

Hence this game has 2 PSNE and 1 MSNE

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two street races are playing a simultaneous game of chicken. They have to race towards each...
Two street races are playing a simultaneous game of chicken. They have to race towards each other and whoever swerves first is chicken and faces shame, a loss of 8, while the winner enjoys a gain of 3. If neither stop, they would crash into each other, a loss of 10. If both of them swerve at the same time, they are both chicken and face a loss of 5 each. What would the Nash equilibrium be in this game?...
Question 1. Put the following game into the normal form. That is, describe the set of...
Question 1. Put the following game into the normal form. That is, describe the set of players, the strategy sets for each player, the payoff functions, and draw the game in matrix form. What do you expect would happen in this game, and why?Two kids are playing a game of Chicken. In this game, they ride their bikes as fast as theycan at each other. The one to swerve or turn out of the way loses, he is a Chicken...
4. Suppose two bartenders are developing new cocktails for their bar and are playing a simulta-...
4. Suppose two bartenders are developing new cocktails for their bar and are playing a simulta- neous game to come up with fruit combinations. Bartender 1 can choose berries or limes as the fruit theme and bartender 2 can choose bananas or oranges. They both have to drink the new cocktail they create from mixing their choice of fruit. Based on their preferences, they get the following payoffs for different fruity combinations. If the cocktail has berries and bananas, bartender...
Payoffs below are in millions of dollars                                    &nb
Payoffs below are in millions of dollars                                                                                         Firm B                                                                                 Strategy 1        Strategy 2                                                                                                                    Strategy 1:   23, 24                25, 27                                                            Firm A                                                                                              Strategy 2:   26, 30               21, 32                                                                                                              5. (2 pts.) In this single shot simultaneous play game, identify any and all Nash equilibria.              6. (2 pts.) Suppose Firm B has the option of going first, i.e. being a first mover in a sequential game with the above payoffs. To go first though, Firm B will incur a cost of $2 million dollars....
The matrix below shows payoffs in a stag hunt game. If both hunters hunt stag, each...
The matrix below shows payoffs in a stag hunt game. If both hunters hunt stag, each gets a payoff of 4. If both hunt hare, each gets 3. If one hunts stag and the other hunts hare, the stag hunter gets 0 and the hare hunter gets 3. Hunter B hunt stag hunt hare hunt stag 4,4 0,3 Hunter A hunt hare 3,0 3,3 (a) If you are sure that the other hunter will hunt stag, what is the best...
Mike and Jake are basketball players who sometimes flop (that is, intentionally fall or feign an...
Mike and Jake are basketball players who sometimes flop (that is, intentionally fall or feign an injury in order to cause a foul on another player). It is better for each of them if both play fairly and don't flop then when both flop. But each player is better off flopping than not flopping. Their payoffs are given below. Jake Mike Flop Not Flop Flop (3, 3) (4, 1) Not Flop (1, 4) (1, 1) For instance, if Mike flops...
Sign In INNOVATION Deep Change: How Operational Innovation Can Transform Your Company by Michael Hammer From...
Sign In INNOVATION Deep Change: How Operational Innovation Can Transform Your Company by Michael Hammer From the April 2004 Issue Save Share 8.95 In 1991, Progressive Insurance, an automobile insurer based in Mayfield Village, Ohio, had approximately $1.3 billion in sales. By 2002, that figure had grown to $9.5 billion. What fashionable strategies did Progressive employ to achieve sevenfold growth in just over a decade? Was it positioned in a high-growth industry? Hardly. Auto insurance is a mature, 100-year-old industry...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT