Drug dealers and arch rivals Carl and Jason are both armed and find themselves unexpectedly in a dangerous stand-off. In an attempt to protect themselves, each of them has to choose from one of two actions: attempt to shoot the rival (S) or dodge and take cover (D). Each of them must decide simultaneously and independently, with each man aiming to maximize his own chance of survival. They face death not only from the rival’s shooting but also from ran- dom firing by police who are in hot pursuit of them. Their survival rates in each scenario are given as follows: · - If Carl and Jason both choose S, then their survival probabilities are 34% and 29% respectively. · - If Carl and Jason both choose D, then their survival probabilities are 36% and 39% respectively. · - If Carl chooses S while Jason chooses D, then their survival probabilities are 38% and 32% respectively. · - If Carl chooses D while Jason chooses S, then their survival probabilities are 35% and 38% respectively. Based on the above information, answer the following questions: 1. (a) Write down the normal form representation of the above described simultaneous move game between Carl and Jason. (Note: if you prefer, you can write this by hand on a white piece of paper and attach an image of your work). 2. (b) Find the corresponding pure-strategy Nash Equilibirum if it exists. Explain your answer. 3. (c) Does each player have a dominant strategy in this game? Based on your answer, com- pare and find the main differences between the game characterized in part (a) with the Prisoner’s Dilemma.
Drug dealers and arch rivals Carl and Jason are both armed and find themselves unexpectedly in a dangerous stand-off. In an attempt to protect themselves, each of them has to choose from one of two actions: attempt to shoot the rival (S) or dodge and take cover (D). Each of them must decide simultaneously and independently, with each man aiming to maximize his own chance of survival. They face death not only from the rival’s shooting but also from ran- dom firing by police who are in hot pursuit of them. Their survival rates in each scenario are given as follows:
· - If Carl and Jason both choose S, then their survival probabilities are 34% and 29% respectively.
· - If Carl and Jason both choose D, then their survival probabilities are 36% and 39% respectively.
· - If Carl chooses S while Jason chooses D, then their survival probabilities are 38% and 32% respectively.
· - If Carl chooses D while Jason chooses S, then their survival probabilities are 35% and 38% respectively.
Based on the above information, answer the following questions:
1. (a) Write down the normal form representation of the above described simultaneous move game between Carl and Jason. (Note: if you prefer, you can write this by hand on a white piece of paper and attach an image of your work).
2. (b) Find the corresponding pure-strategy Nash Equilibirum if it exists. Explain your answer.
3. (c) Does each player have a dominant strategy in this game? Based on your answer, com- pare and find the main differences between the game characterized in part (a) with the Prisoner’s Dilemma.
4. (d) Suppose now that instead of interacting simultaneously, the players move sequentially with either Carl or Jason moving first and their choice is observed by the player moving second. In particular, then answer all questions below assuming that Carl moves first. Represent the extensive form of this sequential move game using a game tree. Predict the outcome of this game. Does the player moving first have an advantage?
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