3. Consider the following game. Two players can choose either to hunt a stag, or to...
3. Consider the following game. Two players can choose either to hunt a stag, or to hunt a hare. If a player hunts a stag, then they must have the other player’s cooperation in order to succeed. A player can hunt a hare by themself, but a hare is worth less than a stag. The following payoff matrix depicts this situation. What is the Nash equilibrium? Show your work. (10%
Homework Answers
Under the stag hunting game, cooperating is Pareto optimal course of action. Both players can maximize their profits by cooperating. Their profits will not rise if they defect. Hence, there are no incentives to defect from cooperation.
Thus, there will be Two Nash Equilibrium:
( Hunt Stag: Hunt Stag) , and ( Hunt Hare: Hunt Hare)
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3. Consider the following game. Two players can choose either to
hunt a stag, or to...
3. Consider the following stag hunt game. Two hungry hunters go to the woods with the...
3. Consider the following stag hunt game. Two hungry hunters go to the woods with the aim of catching a stag, or at least a hare. They can catch a stag only if both remain alert and devote their time and energy to catching it. Catching a hare is less demanding and does not require the cooperation of the other hunter. Each hunter prefers half a stag to a hare. Letting S denote the action of going after the stag,...
Exercise 1. Two individuals go out on a hunt. Each can individually choose to hunt a...
Exercise 1. Two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each hunter must choose an action without knowing the choice of the other. The only way of hunting a stag is that both hunters choose to hunt it. An individual can always get a hare by himself, but a hare is worth less than a stag. To be precise, each hunter will get a payoff equal to two for...
Asterix and Obelix go hunting. They can either choose to hunt a boar or hunt a...
Asterix and Obelix go hunting. They can either choose to hunt a boar or hunt a rabbit. Each one chooses their action (to hunt boar or rabbit), without observing the action chosen by the other. If either Asterix or Obelix hunts a boar, they must have the cooperation of their partner in order to succeed. Either Asterix or Obelix can hunt the rabbit by themselves, (i.e., alone, without cooperation from the partner), but a rabbit is worth less than a...
Two hunters must choose simultaneously between hunting a stag or hunting hares. If a hunter hunts...
Two hunters must choose simultaneously between hunting a stag or hunting hares. If a hunter hunts hares, they catch a hare, and get a payoff of 3. If both hunters hunt the stag, they catch it, with a payoff of 5 to each. If a hunter tries to hunt the stag alone while the other hunter hunts hares, they do not succeed, and get a payoff of 0. (a) (2 points) Provide the normal form of this game. (b) (5...
1. Two hunters set out to kill a stag. One has agreed to drive the stag...
1. Two hunters set out to kill a stag. One has agreed to drive the stag through the forest, and the other to post at a place where the stag must pass. If both faithfully perform their assigned stag-hunting tasks, they will surely kill the stag and each will get an equal share of this large animal. During the course of the hunt, each hunter has an opportunity to abandon the stag hunt and pursue a hare. If a hunter...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The tab...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y,...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y, or Z. The payoffs are defined as follows. Each player who selects X obtains a payoff equal to y, where y is the num- ber of players who select Z. Each player who selects Y obtains a payoff of 2a, where a is the number of players who select X. Each player who selects Z obtains a payoff of 3B, where ß is the...
Suppose that two players are playing the following game
Suppose that two players are playing the following game. Player 1 can choose either top or bottom, and Player 2 can choose either left of right. The payoffs are given in the following table Player 2 Left Right top 9,4 2,3 Player 1 Bottom 1,0 3,1 where the number on the left is the payoff to Player 1 and the number on the right is the payoff to player 2. 1) Determine the nash equilibrium of the game. 2) If...
Consider the competitive, static, one-time game depicted in the following figure. If larger payoffs are preferred,...
Consider the competitive, static, one-time game depicted in the following figure. If larger payoffs are preferred, does either player have a dominant strategy? If B believes that A will move A1, how should B move? If B believes that A will move A2, how should B move? What is the Nash equilibrium strategy profile if this game is played just once? What is the strategy profile for this game if both players adopt a secure strategy? What strategy profile results...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
3. Consider the following stag hunt game. Two hungry hunters go to the woods with the aim of catching a stag, or at least a hare. They can catch a stag only if both remain alert and devote their time and energy to catching it. Catching a hare is less demanding and does not require the cooperation of the other hunter. Each hunter prefers half a stag to a hare. Letting S denote the action of going after the stag,...
Exercise 1. Two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each hunter must choose an action without knowing the choice of the other. The only way of hunting a stag is that both hunters choose to hunt it. An individual can always get a hare by himself, but a hare is worth less than a stag. To be precise, each hunter will get a payoff equal to two for...
Two hunters must choose simultaneously between hunting a stag or hunting hares. If a hunter hunts hares, they catch a hare, and get a payoff of 3. If both hunters hunt the stag, they catch it, with a payoff of 5 to each. If a hunter tries to hunt the stag alone while the other hunter hunts hares, they do not succeed, and get a payoff of 0. (a) (2 points) Provide the normal form of this game. (b) (5...
1. Two hunters set out to kill a stag. One has agreed to drive the stag through the forest, and the other to post at a place where the stag must pass. If both faithfully perform their assigned stag-hunting tasks, they will surely kill the stag and each will get an equal share of this large animal. During the course of the hunt, each hunter has an opportunity to abandon the stag hunt and pursue a hare. If a hunter...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y, or Z. The payoffs are defined as follows. Each player who selects X obtains a payoff equal to y, where y is the num- ber of players who select Z. Each player who selects Y obtains a payoff of 2a, where a is the number of players who select X. Each player who selects Z obtains a payoff of 3B, where ß is the...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
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