= - Five players must simultaneously choose a number from the interval [0, 9]. Let x; denote the number chosen by player i; x = (x1, ..., x5 ) all selected numbers; x_{ x\x; all selected numbers except the number chosen by player i. If player i chooses the number x; Є [0,9], while the others choose the numbers _, then the utility of player i is u; (xi, x_i) = 4(9 − xi) + 2-1 xj. Find the Nash equilibria of the game and the corresponding utilities. Would all players be better off if they signed a binding contract before the game requiring them to choose the number 9?

You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…

Which of the following is a significant difference in the outcomes between the dictator game and the ultimatum game? Multiple Choice O O O O Self-interest is revealed more strongly in the ultimatum game than in the dictator game. The ultimatum game tends to result in a more even split of the money. There is little difference, as fairness considerations lead to similar splits of the money in both games. The dictator game tends to result in a more even split of the money.

A new government lottery has been announced. Each person who buys a ticket submits an integer between 0 and 100. The winner is the person whose submission is closest to four-fifths of the average of all submissions. If ties​ occur, the price will be shared. If Chloe expects other players to select numbers​ randomly, what number should she​ choose?   Chloe should choose the number (a)_____   if you expect all other players to exhibit the same depth of reasoning as Chloe, what number would you choose?   you should choose the number (b)______

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(a) In the extensive form below, player 1 moves first, and player 3 moves last. (3) Note the two information sets including the nodes where player 3 moves: P1 L R P2 P2 A B P3 P3 d 2,3.2 2,1,1 3,0,4 3.4,0 3,1,1 Ennio Stacchetti December 17, 2021 (a) Find all subgame perfect equilibria in pure strategies. (b) Find a Nash equilibrium that is not a subgame perfect equilibrium.

Need within 1 hour 30 minutes i need only part 2 do it correectly and neatly

Let's say we have a game called "guess 2/3 of the average," where players can choose any number x ∈ [0, 100]. 5% of players are at level N0, 40% at level N1, 35% at level N2, 15% at level N3, and 5% at level N4. Players at level N0 choose a number randomly, while players at higher levels choose a number according to their beliefs, which are as follows: players at higher levels believe that all other players are one level lower than themselves. (a) What will be the winning number and which level players will be the winners? (b) Under the assumptions of classical game theory, the mentioned version of the game "guess 2/3 of the average" has exactly one equilibrium, in which everyone chooses the number 0. Prove that this outcome is indeed a Nash equilibrium of the game.

There is a project for which player 1 can exert effort e ≥ 0 that costs her c(e) = 0.5e2. If player 1 and player 2 can come to an agreement, then a total value of v(e) = e is produced, which can be allocated between the two players. Effort also produces a value y(e) = ke, where k = [0, 1], that player 1 can obtain for herself if player 1 and 2 fail to agree. The game has three stages: (I stage) Player 1 chooses effort e ≥ 0; (II Stage) Player 2 observes e and chooses and effort level a € [0, 1]; (III stage) Player 1 observes a and either agrees (a) or rejects (r) the offer. If player 1 accepts the offer, then her payoff is ae - 0.5e² and player 2's payoff (1 − a)e. If she rejects the offer, then player 1's payoff is ke - 0.5e² and player 2's payoff is zero. • What is the subgame perfect equilibrium effort choice? •Suppose that player 2 can choose k = [0, 1] before the above game is played. What would he choose? What would be the equilibrium effort? Suppose now that the government,…