Nash equilibrium.
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- 3. Consider this game in an extensive form (there are 2 players, A and B): right left B B (2, 3) (4, 2) (6, 6) (1, 9) (1, 9) (7, 7) (5, 3) a. Find the subgame-perfect equilibrium. (1) b. Explain why the players cannot reach the outcome with the payoffs circled in orange (which they both would prefer to the equilibrium outcome). (1) gauche milieu gauche milieu gauche milieu droitThe Chinese government has created a fund worth more than 20 trillion won to foster the semiconductorindustry. Although there is a large technological difference between memory semiconductors, systemsemiconductors can be developed in a short period of time. The number of companies producinghomogeneous quality products has increased.■Question (a) In the Cournot game, when the number of firms increases from 2 to n, compare the output,total output, and profit of each firm with N.E. in the Cournot model. ■Question (b) If the number of companies participating in the semiconductor market increases to infinity,that is, in a perfectly competitive market, what will be the equilibrium point?2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors rock 0 -3 1 paper 1 -1 scissors -1 0 0 3 (a) Show that x¹ = (3) and y¹ = (3) together are not a Nash equilibrium for this modified game.
- 2. Two friends are playing poker with one another and need to decide on how to play their next tum. The payoffs in this game are as shown in the following payoff matrix: Player 2 Fold All-in Fold (-20,-30) (-20,100) Player 1 All-in (120,-30) (-80,-150) Determine the mixed-strategy Nash Equilibrium for this game.Consider the following game in extensive form. a В В В d f h i e (3, 2z) (9, 5) (6, 32) (2z, 19) (15, 7) (2, 20) (7, 32) Z=7 (a) How many pure strategy profiles exist in this game? (b) In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs to the two players?Model the situation as a strategic game assuming that both ‘James’ and ‘Robert’ are altruistic, ranking outcomes according to the other person’s comfort and, out of politeness, prefer to stand than to sit if the other person stands. Model the situation as a strategic game and find any Nash equilibrium (equilibria) if it exists. Does a dominant strategy exist for either ‘James’ or ‘Robert’ with these preferences? Show all steps and working in support of the answerContext:The London Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘James’ and ‘Robert’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing. consider james as "Row Player" and Robert as "Column Player"
- How does a Nash Equilibrium affect consumers? It makes some customers travel farther than necessary to purchase product. It eliminates the possibility of a socially optimal solution. (c ) It enables customers the ability to compare the products (price, variety, etc.) with ease. (D All of the aboveWhen it comes to customs clearance of goods, customs officers and smugglers try to prevent the otherparty from predicting their respective intentions. Their respective profit metrics are as follows:■There is no general Nash equilibrium (pure strategy).■Question: What is the mixed strategy equilibrium? – find out x and yA seller would like to sell a painting using second price (Vickrey) auction. The seller knows that there are three buyers and each buyer is equally likely to have High (H), Medium (M), or Low (L) valuation for the painting. The valuations of the buyers are independently distributed. Assuming that the buyers will play the Nash equilibrium in the second price auction, how much revenue will the seller make?
- can we find nash equilibrium through mixed strategy as well?Let's consider the following game: Player 1 chooses a (potentially negative) number x, and player 2 chooses a (potentially negative) number y. The payoff for player 1 is given by U1 = 100x - x2 - 2xy. The payoff for player 2 is given by U2 = 130y - 2y2 - 2xy. Solve for the Nash equilibrium in pure strategies. What is Player 1's payoff in the equilibrium? Enter a numerical answer below. You may round to the second decimal if necessary.Exercice 1: In the following table i) by describing precisely your reasoning, find the balance(s) of the game ii) Justify that the equilibrium(s) found is/are nash equilibria