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 cart (H), the other vendor operates a Thai food cart (T ). The Thai food 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 1003 of the sales. If both show up with small carts the two vendors split sales evenly. When the Thai food vendor shows up with a large cart they will get 753 of the sales (253 to the Hot Dog vendor). The Hot Dog vendor makes a decision of whether or not to operate a cart before the Thai food vendor. The decision of the Hot Dog vendor is observable to the Thai food vendor. (Sequential game where the Hot Dog vendor moves first).
Show the game tree for this game.
Find the Subgame Perfect Nash equilibrium.