Formulate the situation as strategic game - nash equilibrium, Game Theory

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 by xi the amount of the resource used by individual i (where i = 1, 2). Assume specifically that individual i's output is xi(1 (x1 + x2)) if x1 + x2 < 1 and zero otherwise. Each individual i chooses xi ? [0, 1] to maximize her output.

(a) Formulate this situation as a strategic game.

(b) Find the best response correspondences of the players.

(c) Find its Nash equilibria.

(d) Does the Nash equilibrium value of x1; x2 maximize the total output? (Is there any other output pro le that results in a higher total output than the Nash equilibrium?)

(e) Suppose now there are n individuals and hence the payoff function of individual i (where i = 1; 2;...; n) is given by xi(1 (x1 +x2 + ... +xn)) if x1 +x2 +...+xn 6 1 and zero otherwise. Find the Nash equilibria of this game.

 

Posted Date: 3/23/2013 3:56:31 AM | Location : United States







Related Discussions:- Formulate the situation as strategic game - nash equilibrium, Assignment Help, Ask Question on Formulate the situation as strategic game - nash equilibrium, Get Answer, Expert's Help, Formulate the situation as strategic game - nash equilibrium Discussions

Write discussion on Formulate the situation as strategic game - nash equilibrium
Your posts are moderated
Related Questions
A mixed strategy during which the player assigns strictly positive chance to each pure strategy.Morgenstern, Oskar,Coauthor of Theory of Games and Economic Behavior with John von N

1  A, Explain how a person can be free to choose but his or her choices are casually determined by past event 2  B , Draw the casual tree for newcomb's problem when Eve can't pe

#questi1 A, Explain how a person can be free to choose but his or her choices are casually determined by past event 2 B , Draw the casual tree for newcomb''s problem when Eve ca

Explain oligopoly's structure and use game theory to explain why oligopoly firms tend not to use price to compete. Answer- Oligopoly is an imperfect market where there are

A proxy bidder represents the interests of a bidder not physically gift at the auction. Typically, the bidder can inform his proxy of the most quantity he's willing to pay, and als

A subset or piece of a sequential game starting at some node such {that each that each} player is aware of each action of the players that moved before him at every purpose. Sub ga

A payoff offerd as a bequest for someone partaking in some activity that doesn't directly provide her with profit. Often, such incentives are given to beat the ethical hazard drawb

Consider the Cournot duopoly model in which two firms, 1 and 2, simultaneously choose the quantities they will sell in the market, q1 and q2. The price each receives for each unity


Games with Strat e gic M ov es   The ideas in this chapters can be brought to life and the students can better appreciate the subtleties of various strategic moves an