Find a bayesian nash equilibrium, Game Theory

In Bontemps, Louisiana there are only two places to spend time: Merlotte's bar and Fangtasia. Sookie and Eric have made plans to spend Friday night together, but they never decided where they would go. Both Sookie and Eric like each other and will not enjoy their evening if it is spent alone. However, given that they spend the evening together, Eric prefers to go to Fangtasia, and Sookie prefers to go to Merlotte's. If both Eric and Sookie go to Fangtasia, Eric gets payoff 2; if Both Eric and Sookie go to Merlotte's, Sookie gets payoff 2. Eric's payoff if both he and Sookie meet at Merlotte's (his less preferred activity) depends on how much Eric likes Sookie, represented by Eric's type e, which is known only to Eric. Similarly, if Sookie and Eric meet at Fangtasia, Sookie's payoff depends on how much she likes Eric, represented by her type, s, which is known only to her. Both players believe that the other player's type is uniformly distributed between zero and one, Pr (s < x) = Pr (e < x) = x.

735_Find a Bayesian Nash equilibrium.png

(a) Suppose that Eric believes that Sookie will go to Merlotte's if her type s is less than s and will go to Fangtasia if her type is bigger than s*.

What is the probability that Sookie will go to Merlotte's? What is the probability that she will go to Fangtasia?

(b) What is Eric's expected payoff if his type is e and he goes to Fangtasia? What is his expected payoff if he is type e and goes to Merlotte's?

(c) What is Eric's best response to Sookie's strategy? (For which values of e does he go to his preferred activity? For which values of e does he go to Sookie's preferred activity?) Explain.

(d) Find a Bayesian Nash equilibrium in which Eric goes to Fangtasia if his type e is less than e*; and Sookie goes to Merlotte's if her type s is less than s*: Assume that the equilibrium is symmetric e* = s*.

(e) For what combinations of types (s; e) do Eric and Sookie spend Friday night together? What is ironic or peculiar about your answer? (Hint: describe what would happen if Sookie and Eric both like each other a lot)

Posted Date: 2/25/2013 2:53:51 AM | Location : United States







Related Discussions:- Find a bayesian nash equilibrium, Assignment Help, Ask Question on Find a bayesian nash equilibrium, Get Answer, Expert's Help, Find a bayesian nash equilibrium Discussions

Write discussion on Find a bayesian nash equilibrium
Your posts are moderated
Related Questions
Two individuals use a common resource (a river or a forest, for example) to produce output. The more the resource is used, the less output any given individual can produce. Denote

Game 1 Color Coordination (with Delay) This game should be played twice, once without the delay tactic and once with it, to show the difference between out- comes in the s

Rollback shows that Boeing chooses peace over war if Airbus enters, so Airbus will enter. Rollback equilibrium entails Airbus playing “Enter” and Boeing playing “Peace if entry”; e

A market mechanism in which a service, objects, or set of objects, is swapped on the basis of bids submitted by member. Auctions offer a precise set of rules that will rule the pur

The title of a "player" who selects from among her methods randomly, primarily based on some predetermined chance distribution, instead of strategically, primarily based on payoffs

You and an opponent are seated at a table, and on the table is a square board. At each of the four corners of the board, there is a disc, each one red on one side and black on the

In many cases we are interested in only one (or a few) of the equations of the model and attempts to measure its parameters statistically without a complete knowledge of the entire

A heuristic is an aid to learning, casually brought up as a rule of thumb. Formally, a heuristic may be a mechanism capable of altering its internal model of the surroundings in re

Any participant in a very game who (i)  contains a nontrivial set of methods (more than one) and (ii) Selects among the methods primarily based on payoffs. If a player is non

A sequential game is one among imperfect data if a player doesn't grasp precisely what actions different players took up to that time. Technically, there exists a minimum of one da