Imagine two drivers playing chicken, a game where they drive towards one another with their cars. Each driver has two actions: go straight or turn left. For simplicity, we standardize directions according to the perspective of an overhead observer. Thus, if both drivers select the same action, they will crash. At the same time, each driver wants to go straight, to seem tough and fearless. Utilities are given by the following table: Utility Turn Left Straight Turn Left -20, -20 - 5, 10 Straight 10, -5 -10, -10 These are in the format (row player, column player) 1. Does either player have a dominating strategy? If so, identify all of them. 2. What are the pure strategy Nash equilibria of this game? 3. Does the game have any mixed strategy Nash equilibria? If yes, compute all of them.

Frank and Nancy met at a sorority sock hop. They agreed to meet for a date at a local bar the next week. Regrettably, they were so fraught with passion that they forgot to agree on which bar would be the site of their rendezvous. Luckily, the town has only two bars, Rizotti's and the Oasis. Having discussed their tastes in bars at the sock hop, both are aware that Frank prefers Rizotti's to the Oasis and Nancy prefer the Oasis to Rizotti's. In fact, the payoffs are as follows. If both go to the Oasis, Nancy's utility is 3 and Frank's utility is 2. If both go to Rizotti's, Frank's utility is 3 and Nancy's utility is 2. If they don't both go to the same bar, both have a utility of 0. There are two Nash equilibrium in pure strategies and a Nash equilibrium in mixed strategies where the probability that Frank and Nancy go to the same bar is 12/25. This game has two Nash equilibria in pure strategies and a Nash equilibrium in mixed strategies where each person has a probability of 1/2 of…

Q3. Two ice cream trucks operate on a beach and play a simultaneous pricing game. If one of them prices low and the other high it gets all the customers and a pay off of 12 while the other gets zero. If both price high each gets 6, and if both price low each get 5. The best strategy is for both to price high. True/False/Uncertain. Explain.

Question 2. Two students are working together to submit their Microeconomics mid-semester group coursework. Each student i can put in the effort x; that costs c(x;), in which x; E [0, 1]. This gives each student the utility of u(x1, x2). Formu- late this situation as a strategic game.

Maipo and Pisco need to decide how to divide a cake between the two of them. Both like cake and want to get as much cake as they can. They decide to let Maipo cut the cake first and then Pisco gets to pick which piece he wants. For simplicity, assume that Maipo can only cut the cake in two ways: He can either divide it into two pieces that are equal size (i.e., both will get half the cake) or he can divide the cake into two pieces where one piece is twice the size of the other (i.e., one will get a piece that is two-thirds of the cake and the other will get a piece that is one-third of the cake). a. Set up this game as a sequential game and draw the game tree that represents it Note: You can either draw the game tree by hand and then photograph/scan the tree and paste it into the assignment or use the drawing tool in Word to draw the tree. b. Find the sub-game perfect Nash Equilibria to this game. Underline the strategies or highlight the game tree path to show what the Nash Equilibria…

which is the nash equilibrium? small pig does press large pig does press (20, 130), small pig doesn't press large pig does press (140, 10), small pig does press large pig doesn't press (-5, 150), small pig does not press large pig doesn't press (0,0).

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Use the scenario below to answer the question.   Chocolate raisin protein bars are Duc’s favorite dessert. A local bakery sells them for $1.00 each. Duc buys one and eats it at the bakery. Duc decides that he wants another one, but is not willing to pay full price. He knows the owner of the bakery and wants to negotiate. He offers to buy two more protein bars at $0.75 each. He plans to eat one at the store and anther one later. The bakery owner agrees to the deals.   What is the total utility of Duc’s decision? 00 75 50 00

Two supermarkets face the following possibilities.                       Superstore     Advertise Don’t Advertise Megastore Advertise $95, $80 $305, $55 Don’t Advertise $65, $285 $165, $115     47. A Nash equilibrium is Group of answer choices for Megastore to advertise and for Superstore to advertise. for Megastore to advertise and for Superstore not to advertise for Megastore not to advertise and for Superstore to advertise. for Megastore not to advertise and for Superstore not to advertise. There is no Nas equilibrium in this rivalry game.