game theory

posted by .

Two companies, A and B, produce widgets. Each can produce 0, 1, 2, 3, or 4 widgets (they can’t
produce fractions of widgets). Let X be the number of units produced by A, and Y be the number of
units produced by B. Given X and Y, widgets will sell at a price equal to $(14-X-Y). Every widget costs
$5 to produce. The companies choose X and Y simultaneously, each trying to maximize profits.

a) (2 points) Derive an expression for A’s profits.
b) (2 points) Derive an expression for B’s profits.
c) (8 points) Draw a table representing this one-stage game, showing the players’ strategies and
payoffs.

In class we defined dominated strategies as those strategies that are never a best response. This
definition actually refers to strictly dominated strategies (i.e., for any action that the opponent might
take there is always another strategy that gives a higher payoff). There is a second type of dominated
strategies called weakly dominated strategies. These are strategies that give the same payoff as other
strategies for some actions that the opponent might take and give a lower payoff than other strategies
for all other actions the opponent might take (i.e. when a weakly dominated strategy is a best response
there is another strategy that is also a best response to the same opponent’s action)

d) (3 points) Does either company have a strictly dominated strategy?
e) (3 points) Draw the reduced game once strictly dominated strategies have been removed.
f) (3 points) In the reduced game, does either company have weakly dominated strategies? What are
they?
g) (3 points) If companies did not exclude the possibility of playing their weakly dominated strategies,
what are the possible Nash equilibriums of the reduced game?
h) (3 points) Looking at the payoffs of the reduced game, does it make sense for either company to
play their weekly dominated strategies? Why or why not?
i) (3 points) Based on your answer to (h), what would be your prediction of the game?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Econ

    The demand for widgets (QX) is given by the following equation: QX = 425-PX¡V1.5PW¡V1.25PG+0.8PY+0.1 M where QX= number of units of widgets sold per week PX = the price of widgets = 400 PW = the price of woozles = 50 PG = the price …
  2. economics

    Two companies, A and B, produce widgets. Each can produce 0, 1, 2, 3, or 4 widgets (they can’t  produce fractions of widgets). Let X be the number of units produced by A, and Y be the number of units produced by B. Given X …
  3. Math

    The revenue R from selling x number of phone widgets is given by , and the cost C of producing those widgets is given by . Find the number of widget it requires to break even.
  4. statistics

    Three percent of the widgets produced by machine 1121 are defective. what is the probablity that a box of 30 widgets produced by that machine contains two or more defective widgets?
  5. economics

    Suppose the price of widgets falls from $7 to $5 and consumption of widgets rises from 15 widgets a month to 25 widgets. Calculate your price elasticity of demand of widgets. What can you say about your price elasticity of demand of …
  6. Calculus

    A company manufactures widgets. The daily marginal cost to produce x widgets is found to be C'(x) = 0.000009x^2 - 0.009x + 8 (measured in dollars per unit). The daily fixed costs are found to be $120. a. Use this information to get …
  7. econmics

    Suppose the price of widgets rises from $7 to $9 and consumption of widgets falls from 25 widgets a month to 15 widgets. Calculate your price elasticity of demand of widgets. What can you say about your price elasticity of demand of …
  8. math

    A machine produces 75 widgets an hour.How many widgets does it produce in 6 minutes?
  9. Math

    1. An assembly line produces widgets with a mean weight of 10 and a standard deviation of 0.200. A new process supposedly will produce widgets with the same mean and a smaller standard deviation. A sample of 20 widgets produced by …
  10. word problems

    The revenue R from selling x number of phone widgets is given by R = 32 x R=32x, and the cost C of producing those widgets is given by C = 22 x + 1830 C=22x+1830. Find the number of widgets it requires to break even.

More Similar Questions