Asked by Angela Mejias on Jul 12, 2024
Verified
Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough.If both pigs choose Wait at the Trough, both get 2.If both pigs choose Press the Button, then both pigs get 5.If Little Pig presses the button and Big Pig waits at the trough, then Big Pig gets 10 and Little Pig gets 0.Finally, if Big Pig presses the button and Little Pig waits at the trough, then Big Pig gets 3 and Little Pig gets 2.In Nash equilibrium,
A) both pigs will wait at the trough.
B) Little Pig will get a payoff of 2 and Big Pig will get a payoff of 3.
C) Little pig will get a payoff of zero.
D) Little Pig will get a payoff of 5 and Big Pig will get a payoff of 5.
E) the pigs must be using mixed strategies.
Nash Equilibrium
A concept in game theory where no player can benefit by changing their strategy if the strategies of the other players remain unchanged.
Payoff
The return or reward from an investment or decision, often evaluated in terms of profit or benefit gained.
- Understand the concept of Nash equilibrium and how it applies to various strategic games.
Verified Answer
NA
Neema AbrahamJul 17, 2024
Final Answer :
E
Explanation :
In this game, there is no dominant strategy for either player. If Big Pig chooses to wait at the trough, Little Pig can either choose to press the button and get a payoff of 2, or wait at the trough and get a payoff of 2. Similarly, if Little Pig chooses to wait at the trough, Big Pig can either choose to press the button and get a payoff of 3, or wait at the trough and get a payoff of 2.
Therefore, the best strategy for both pigs is to use mixed strategies, meaning they should sometimes choose to press the button and sometimes wait at the trough. By using mixed strategies, the pigs can ensure that they receive the highest expected payoff over the long run.
The exact probabilities for each strategy depend on the payoffs and the players' preferences. In general, the probabilities of each strategy being played depend on how close the payoffs are for each strategy. For example, if the payoffs for pressing the button and waiting at the trough are very close, the pigs may choose to play each strategy with roughly equal probability.
Therefore, the best strategy for both pigs is to use mixed strategies, meaning they should sometimes choose to press the button and sometimes wait at the trough. By using mixed strategies, the pigs can ensure that they receive the highest expected payoff over the long run.
The exact probabilities for each strategy depend on the payoffs and the players' preferences. In general, the probabilities of each strategy being played depend on how close the payoffs are for each strategy. For example, if the payoffs for pressing the button and waiting at the trough are very close, the pigs may choose to play each strategy with roughly equal probability.
Learning Objectives
- Understand the concept of Nash equilibrium and how it applies to various strategic games.