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

Assignment Help:

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.

 


Related Discussions:- Formulate the situation as strategic game - nash equilibrium

Paired prisoners'' dilemma, Paired Prisoners' Dilemma Students can be p...

Paired Prisoners' Dilemma Students can be paired off and instructed to play several ver-sions of a particular game with a prisoners' dilemma structure.Provide each pair with a

Find the quantities that firm is selling – equilibrium price, 1. Two firms,...

1. Two firms, producing an identical good, engage in price competition. The cost functions are c 1 (y 1 ) = 1:17y 1 and c 2 (y 2 ) = 1:19y 2 , correspondingly. The demand functi

Case study - rock-scissors-paper, Case study GAME 1 Rock-Scissors-Pap...

Case study GAME 1 Rock-Scissors-Paper This game entails playing three different versions of the children's game rock-scissors-paper. In rock-scissors-paper, two people si

English auction, A type of sequential second worth auction during which an ...

A type of sequential second worth auction during which an auctioneer directs participants to beat the present, standing bid. New bids should increase the present bid by a predefine

What terms are included in the monopolistic competition, What terms are inc...

What terms are included in the monopolistic competition? Product Differentiation: 1. The meaning of monopolistic competition and product differentiation 2. Why monopolist

Yankee auction, Yankee auction typically implies a multiunit discriminatory...

Yankee auction typically implies a multiunit discriminatory English auction. not like a Vickrey auction where every winning bidder pays identical worth for every unit, in a very ya

Battle of the sexes, scenario A wife and husband ready to meet this even...

scenario A wife and husband ready to meet this evening, but cannot remember if they will be attending the opera or a boxing match. Husband prefers the boxing match and wife pref

Game playing in class, GAME PLAYING IN CLASS There are several games t...

GAME PLAYING IN CLASS There are several games that are appropriate for use on the first or second day of class. These games are simple but can be used to convey important poin

Bidder''s choice, A multiunit auction mechanism for assigning heterogeneous...

A multiunit auction mechanism for assigning heterogeneous (different) objects. The highest bidder in the first round selects one item among those offered for sale. Then, a second r

Volunteer''s dilemma , Scenario As described by William Poundstone, imag...

Scenario As described by William Poundstone, imagine that you just notice that electricity has gone out for your entire neighborhood. the electrical company can send somebody to

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd