Calculate expected payoff, Game Theory

1. The town of Sunnydale, CA is inhabited by two vampires, Spike and Anya. Each night Spike and Anya independently hunt for food, which each one finds with probability 1/2 . Because of a telepathic link, each vampire knows whether the other vampire has found food. A food source contains 3/2 liters of blood, but in one session a vampire can only eat 1 liter of blood. If each vampire finds food they both eat 1 liter, giving each vampire a payoff of 1. If neither vampire finds food, both vampires have a payoff of 0. If one vampire finds food and the other doesn't, the vampire who found food may choose to share his or her food with the other vampire. If the vampire chooses to share, both vampires experience a payoff of 3/4 . If the vampire with food does not choose to share, the vampire who found food receives a payoff of 1 and the other vampire receives a payoff of 0. A vampire only has to make a decision if one of them finds food and the other doesn't.

(a) Suppose that the situation described above happens only one time. If Spike finds food but Anya doesn't, will he share? Would Anya share with Spike if she found food but he didn't? Does a vampire who found food have a dominant strategy?

(b) What is the expected payoff to each vampire if they follow the strategy in a.? Vampires live forever. Therefore, imagine that this situation is repeated an infinite number of times, and both vampires have the same discount factor. Suppose Spike and Anya agree to share food (if one finds food and the other doesn't) as long as in every past period in which one of them found food but the other didn't, the one who found food shared it. If at any point in the past a vampire found food but didn't share, they act as in part a.

(c) At the beginning of any particular night, before the vampires know whether they will find food, what is Spike's expected payoff if both he and Anya follow the agreement?

(Hint: with probability 1/4 both find food. With probability 1/2 at exactly one vampire finds food. With probability 1/4 neither vampire finds food.)

(d) Suppose Spike found food in period k but Anya didn't. What is his expected payoff from following the agreement in that period? (Hint: his payoff is composed of two pieces. First Spike experiences today's payoff of sharing food with Anya. By doing so, he also preserves the agreement forever after)

(e) What is Spike's expected payoff if he doesn't share his food with Anya? (Hint: he does better in the current period, but destroys the agreement from tomorrow on)

(f) For which values of is the agreement self-sustaining? (That is, acting according to the agreement is a sub-game perfect Nash Equilibrium)

(g) Speculate about what would happen if the probability of finding food were close to 1 or close to 0. Would the agreement be easier or more difficult to sustain?

(h) Now suppose that the telepathic link between Spike and Anya does not always operate. Thus, neither vampire knows for certain whether the other one has found food. Of course, if the other shares, the receiver learn that the other one found food. However, if a vampire finds food but chooses not to share, the other vampire only finds out through the telepathic link with probability 2/3. For which values of is the agreement self-sustaining? Explain the difference with f.

Posted Date: 2/25/2013 2:47:24 AM | Location : United States







Related Discussions:- Calculate expected payoff, Assignment Help, Ask Question on Calculate expected payoff, Get Answer, Expert's Help, Calculate expected payoff Discussions

Write discussion on Calculate expected payoff
Your posts are moderated
Related Questions
Write a bouncing ball video game. The game is similar to the one described and depicted in The balls bounce within the screen where the two horizontal walls are fixed. The two v

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

A market mechanism during which an object, service, or set of objects is being purchased, instead of sold, to the auctioneer. The auction provides a selected set of rules which wil

Equilibrium payoffs are (4, 5). Player A’s equilibrium strategy is “S then S if n and then N if n again.” Player B’s equilibrium strategy is “n if S and then n if S again and then

A strategy defines a collection of moves or actions a player can follow in a very given game. a method should be complete, defining an action in each contingency, together with peo

For the section on dynamic games of competition, you can begin by asking if anyone in the class has played competi- tive tennis (club or collegiate or better); there is usually one

Consider a game in which player 1 chooses rows, player 2 chooses columns and player 3 chooses matrices. Only Player 3''s payoffs are given below. Show that D is not a best response

Tower defense - is a subgenre of real-time strategy games. The goal of tower defense games is to try to stop enemies from crossing a map by building towers which shoot at them as t

a) This you just have to list all the attributes for the program. i.e. unique id's for puzzle pieces, attributes for the puzzle like a data field for the number of edges, methods t

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