Draw the whole game tree and write down the pure strategies

Assignment Help Game Theory

Reference no: EM131252394

Building Trust:

A graduating senior (player 1) has an idea for two start-up ventures, a small one and a large one. He can trust (T ) his ideas with his roommate (player 2), who is the only one who can implement these ideas, or he can not trust (N) player 2, forget his dreams, and get a boring job, resulting in the status quo payoffs of (0, 0) for players 1 and 2, respectively. There are two types of player 2: an honest type that always honors trust (H) and a normal type that can choose to honor trust(H) or abuse trust(A). It is common knowledge that a quarter of the people in the world are honest, but only player 2 knows whether he is honest or not.
The sequence of play is as follows:

First, player 1 can choose T or N with respect to sharing his small idea. A choice of N (no trust) ends the game and the payoffs are (0, 0). Following T player 2 can honor the trust, resulting in payoffs of (1, 1), or abuse the trust and expropriate the idea, resulting in payoffs of (-1, 2). (Recall that an honest player 2 cannot abuse trust.)

If trust was offered in the first stage then first-stage payoffs are determined (i.e., the outcome is known to both players), and player 1 can then choose whether or not to trust player 2 with his big idea. (If trust was not offered in the first stage then the game ended.) No trust in the second stage will result in no payoffs in addition to those obtained in the first stage. Following trust in the second stage, if player 2 honors trust then the additional payoffs will be (7, 7), while if he abuses trust and expropriates the idea the additional payoffs will be (-5, 11). There is no discounting between these stages.

a. Draw the whole game tree and write down the pure strategies of each player for the whole game. How many pure strategies does each player have?

b. Using sequential rationality argue that following an abuse of trust in the first stage, there will be no trust in the second stage, effectively ending the game. Write down the reduced game tree that is implied by this argument, and the resulting pure strategies for each of the two players. From now on focus on the reduced game you derived, in which the game ends after an abuse in the first stage.

c. Can there be a pooling perfect Bayesian equilibrium in which the normal type in the first period honors trust for sure?

d. Can there be a separating perfect Bayesian equilibrium in which the normal type in the first period abuses trust for sure?

e. Find the perfect Bayesian equilibrium of this game. Is there a unique one?

Reference no: EM131252394

Questions Cloud

What are the perfect bayesian equilibria : Draw the extensive form of this game. - What are the Bayesian Nash equilibria of this game? - What are the perfect Bayesian equilibria?

Determine two competencies of the model : Determine two competencies of the model that you can apply to the organization.

Prepare an informal proposal in the business memo format : Provide a brief summary of the types of social media options that are available - Discuss the advantages and disadvantages of using social media in the workplace and Compare and contrast at least 2 of the current social media options.

How each party uses information about economic growth : Discuss how each party uses information about economic growth, jobs, and inflation to support their respective positions. State which party you believe is most objective in its use of economic data and explain the reason(s) for your choice.

Draw the whole game tree and write down the pure strategies : Draw the whole game tree and write down the pure strategies of each player for the whole game. How many pure strategies does each player have?

What do you think the court should decide and why : On page 174 of your textbook, read the story of the flight attendants whose conditional job offer was rescinded for failure to disclose HIV-positive status on the medical questionnaire. What do you think the court should decide and why? Look up th..

Make a right turn at a specific point : In Alice programming environment how do you get will and tires to rotate while the vehicle moves then how can you get all the vehicles to make a right turn at a specific point?

What influenced variations in order cycles and deliveries : What do the current number of orders by aircraft model, indicate about the future of air travel? What did the record numbers of orders in past years indicate? What influenced variations in order cycles and deliveries?

What would be the effort level e and the price p : If this game had only one period, what would be the effort level e and the price p in the unique perfect Bayesian equilibrium?

User Account

All Pages