The Stag Hunt Game - A group of 10 hunters are hunting, where the games includea stag and several (>10) hares. Each hunter can choose whether to hunt the stag orgo after a hare. It takes the joint effort of all 10 players to catch the stag, but eachhunter on their own is able to catch a hare. Suppose that a stag is worth $100 and ahare is worth $9. Suppose also that when all 10 players together catch the stag, theyeach get $10 after the game is sold.(a) Formulate this situation as a strategic game and find the Nash equilibria.(b) Now suppose that there are still 10 hunters, who need to choose to either huntthe stag or catch a hare. However, suppose that only 6 hunters are needed tocatch a stag. Assume further that after the stag is caught, it can still be sold for$100 and the money shall be divided evenly among the hunters who have chosento join the stag hunt only. On the other hand, each hunter can always catch ahare on their own and sell it for $9. Formulate this situation as a strategic gameand find the Nash equilibria. (Hint: when specifying the payoffs, you might findit useful to look at action profiles where k hunters choose Stag, where k ≥ 6 ork < 6.)(c) Now suppose that the stag can only be sold for $60. What are the Nash equi-libria?

Stag or hunt share game cooperates game or assurance game. The game is a prototype of thesocial…

The Stag Hunt Game - A group of 10 hunters are hunting, where the games include a stag and several (>10) hares. Each hunter can choose whether to hunt the stag or go after a hare. It takes the joint effort of all 10 players to catch the stag, but each hunter on their own is able to catch a hare. Suppose that a stag is worth $100 and a hare is worth $9. Suppose also that when all 10 players together catch the stag, they each get $10 after the game is sold. (a) Formulate this situation as a strategic game and find the Nash equilibria. (b) Now suppose that there are still 10 hunters, who need to choose to either hunt

The Stag Hunt Game - A group of 10 hunters are hunting, where the games include a stag and several (>10) hares. Each hunter can choose whether to hunt the stag or go after a hare. It takes the joint effort of all 10 players to catch the stag, but each hunter on their own is able to catch a hare. Suppose that a stag is worth $100 and a hare is worth $9. Suppose also that when all 10 players together catch the stag, they each get $10 after the game is sold. (a) Formulate this situation as a strategic game and find the Nash equilibria. (b) Now suppose that there are still 10 hunters, who need to choose to either hunt

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Alice chooses action a or action b, and her choice is observed by Bob. If Alice chooses action a, then Alice receives a payoff of 5 and Bob receives a payoff of 7. If Alice chooses action b, then Bob chooses action cor action d. If Bob chooses action c, then Alice receives a payoff of 10 and Bob receives a payoff of 5. If Bob chooses action d, then Alice receives a payoff of 0 and Bob receives a payoff of 3. Which of the following are correct statements about the game described in the previous paragraph? (Mark all that are correct.) O This game has imperfect information. O Alice's backward induction payoff is 5. O This is a promise game. O Alice's backward induction payoff is 0. O This is a prisoners' dilemma. O Bob's backward induction payoff is 5. O Bob's backward induction payoff is 3. O This is a threat game.
Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 7 and Deborah will receive a payoff of 6. The only dominant strategy in this game is for ____ to choose ____ . The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses ____ and Deborah chooses ____ .
Make sure you clearly write your name and submission:. 1. Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. • "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. • "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper -1 0 1 rock 0 paper 1 scissors -1 (a) Show that this game does not have a pure Nash equilibrium. 1 X 3 (b) Show that…
Two roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn’t, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn’t, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.What is the Nash equilibrium of this game? Group of answer choices Joe cleans, John doesn’t John cleans, Joe doesn’t Both of them clean the apartment Neither of them clean the apartment
Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…
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2. Consider two players playing a simultaneous moves game. These players can be one of the two states of the world, state 1 or state 2, while playing the game. The payoffs-matrix for the two state games are as follows: State 1 P1 U D P2 L R 1,4 1,0 1,6 2,16 0,0 0,24 M State 2 P1 U D P2 L M R 1,0 1,4 1,6 2,16 0,24 0,0 Each players believes that the two states are equally likely, Derive the BNE of the game.
Two hunters are on a stag hunt. They split up in the forest and each have two strategies: hunt for a stag (S), or give up the stag hunt and instead hunt for rabbit (R). If they both hunt for a stag, they will succeed and each earn a payoff of 9. If one hunts for stag and the other gives up and hunts for rabbit, the stag hunter receives 0 and the rabbit hunter 8. If both hunt for rabbit then each receives 7. Compute all Nash equilibria for this game, called 'The Stag Hunt', depicted below. Which of these equilibria do you think is most likely to be played? Why? S R S 9,9 8,0 R 0,8 7,7
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