Answers for VA7 - Drawings for Bi-Matrix Price Games

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You can upload your drawing for question 2 by clicking on the 'reply' to this post and posting the file. To attach a file click on the little paper clip picture after you click 'reply'. To add an image click on 'reply' then choose from the top menu pane to 'embed image'. I don't care if you upload a picture from your phone or word document, or some other type of file, as long as I can open the file and see your bi-matrix clearly.

HERE ARE THE INSTRUCTIONS AGAIN.

This chapter touches upon the importance of game theory for analyzing the behavior of oligopolies. Why is game theory important here? When only a small number of firms sell to a market what one firm decides to do (advertise or not, lower price or not, etc) affects the profit of the other firms. So when each firm is deciding on which strategy to pursue, it has to anticipate how the other firms will react to that strategy with its own strategy. The profits that the firms make will depend jointly on the entire set of strategies chosen by all of the firms.

Game theory is a study of how to behave in such situations. Example: poker or chess. What is the best way to play poker? In any situation, at any point in the game, your best next play must anticipate the reaction of the other players to what you do. Everyone's outcome will depend jointly on how everyone plays.

What does this have to do with oligopoly? Here is another example: If Verizon wants to charge less for its phone plans then it will attract a giant share of the market and that hurts AT&T's profit and helps there own profit. If AT&T counters by lowering their own prices, this would lower Verizon's profit. So how AT&T reacts is important for Verizon to anticipate, and vice versa. When Verizon makes a decision it has to take into account what AT&T will do in response, and vice versa.

For this video assignment you will learn from the video how to draw and solve a so-called 2x2 bi-matrix game. In these games there are 2 players, each has 2 strategies and both players choose their best strategy at the same time without any collusion or cooperation between each other.

1. Watch the following video closely to see how to draw the bi-matrix game, and how to solve for the Nash Equilibrium of the game. As explained in the video, the Nash Equilibrium occurs when every player is playing a best response to every other player's best response.

2. I want you to draw the bi-matrix for the following game, and solve for it's Nash Equilibrium.

players: Heartland Airlines (HA), Cosmopolitan Airline (CA)

strategies: each can charge a high price, or a low price

payoffs:

^If HA and CA both charge a high price they are colluding and they each get a payoff of 100

^If HA charges a high price while CA charges a low price then HA gets the low payoff of 60 while CA gets a high payoff of 120. CA was able to lure customers away from HA.

^If HA charges a low price while CA charges a high price then HA gets the high payoff of 120 while CA gets a low payoff of 60. HA was able to lure customers away from CA.

^If both CA and HA charge low prices they each get a payoff of 70. The two companies are competing against each other with their prices.

Solve for the Nash Equilibrium and draw the bi-matrix. Take a picture of you drawing and upload it here. Or you can make the bi-matric using something like the drawing program in Word, or Dia draw (free). Let

3. There can be more than one Nash Equilibrium or no Nash Equilibrium at all. In the following game HA and CA are trying to decide which segment of the market to appeal to with advertising, prices,special promotions, etc. Each firm has two strategies available: appeal high income customers, or appeal to lower income customers.

^If both try to appeal to high income customers they will directly compete against each other and each firm gets a payoff of 50.

^If both try to appeal to lower income customers they will, again, directly compete against each other and each firm gets a payoff of 50.

^If HA appeals to high income customers, and CA appeals to lower income customers, then each firm gets a payoff of 80.

^If CA appeals to high income customers, and HA appeals to lower income customers, then each firm gets a payoff of 70.

Does this firm have more than one Nash Equilibrium or no Nash Equilibrium? If it has more than one, what are the equilibria? You don't have to send me you picture for this one, but you will want to draw one fro yourself so you can solve the game.