(c) best responses 4. A particular street corner is a popular location for food
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Question
(c) best responses 4. A particular street corner is a popular location for food carts to sell lunch to people working in the area. Two vendors must each decide in the morning whether to operate carts on a particular day or stay at home. One vendor operates a small size Hot Dog car m, the other vendor operates a Thai food cart (T). The Thai fod vendor can choose to bring either a large cart or a small cart. There is a higher cost of operating the large cart (additional person), but the Thai food vendor will serve a larger share of the customers. There is fixed demand for 40 lunches at $10- each (Total market sales/revenue will be $400). The cost of operating a small cart is $100 (for both H and T), while the cost of operating the large Thai food cart is $150. When only one vendor shows up to the street corner they will get 100% ofthe sales. If with small carts the two vendors split sales evenly. When the Thai food vendor shows up with a large cart they will get 75% of the sales (25% to the Hot Dog vendor). Note: decisions are made simultaneously. both show up (a) Can this economic interaction be modeled as a game? If so, identify all the ele- ments that make this a wall.dofinnd (b) Show the game matrix for this interaction. (c) Does either player have any strictly dominant strategies? (d) Does either player have any strictly dominated strategies? (e) Identify all Nash equilibria to this game.Explanation / Answer
Solution:
a) Yes, it is possible to present this in a game.
For the Hot Dog vendor, there are 2 strategies namely, not operating (NO) and operating with small cart (OSC). Similarly, for the Thai food vendor, there are 3 strategies namely, not operating (NO), operating with small cart (OSC), and operating with big cart (OBC).
b) Notice that the vendor that is not operating earns 0 profit.
When HD vendor (TF vendor) operates with small cart, and TF vendor (HD vendor) doesn't operate, entire market share is for HD vendor (TF vendor). In this case HD vendor (TF vendor) makes profit = 400 - 100 (cost of cart) = $300.
If both operate with small cart, evenly distribution results in sales = 400/2 = $200 for each. Since, each undergo cost of $100 as well, profit for each vendor = 200 - 100 = $100
Lastly, if TF vendor operates with big cart, and1) HD vendor doesn't operate, profit = 400 - 150 (cost of big cart) = $250
2) HD vendor also operates, TF makes sales = 75% of 400 = $300, profit = 300-150(cost of big cart) = $150, and HD vendor makes sales = 25% of 400 = $100, and profit = 100 - 100(cost of small cart) = $0
Accordingly, out matrix form game is as follows:
Row player : Thai Food (TF) vendor, column player : Hot Dog (HD) vendor
c) For Hot dog vendor :
If TF vendor chooses NO, HD vendor chooses OSC (as 300 >0)
If TF vendor chooses OSC, HD vendor chooses OSC (as 100 >0)
If TF vendor chooses OBC, HD vendor is indifferent between NO and OSC. Clearly, for any strategy chosen by TF, HD always chooses OSC. So, operating with small cart is the dominant strategy for Hot dog vendor.
Similarly, for Thai food vendor :
If HD vendor chooses NO, TF vendor prefers OSC
And when HD vendor chooses OSC, TF vendor prefers to choose OBC. Clearly, for any strategy chosen by HD, there is no particular strategy that TF vendor always chooses. So,there is no dominant strategy for Thai food vendor.
d) Dominated strategies are the ones which are not chosen under any scenario (i.e, irrespective of what the other player chooses, player i will never choose that strategy). We have already seen from part c), that both, hot dog vendor and thai food vendor, never choose NO strategy, under any strategy chosen by another player. So, for both, hot dog vendor and thai food vendor, dominated strategy is of not operating.
e) Finding the pure strategy Nash equilibrium to this game:
When Thai food vendor chooses OSC, we have already seen that Hot dog vendor would choose OSC as well. When Hot dog vendor chooses OSC, Thai food vendor chooses OBC (and not OSC), so this is not the Nash equilibrium here.
When Thai food vendor chooses OBC, we have already seen that Hot dog vendor would choose OSC still. When Hot dog vendor chooses OSC, Thai food vendor chooses OBC, so this is required the Nash equilibrium.
Thus, there exists a unique pure strategy Nash equilibrium to this game that is Hot dog vendor chooses to operate using small cart and Thai food vendor operates using big cart.
NO OSC NO ($0,$0) ($0,$300) OSC ($300,$0) ($100,$100) OBC ($250,$0) ($150,$0)Related Questions
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