Asked by Skyler Compo on Jul 09, 2024
Verified
What would be the Nash equilibrium of this simultaneous game?
A) Hit,Tell
B) Not hit,Tell
C) Hit,Not tell
D) Both B&C
Nash Equilibrium
A concept of game theory where no participant can gain by unilaterally changing their strategy if the strategies of the others remain unchanged.
Simultaneous Game
A game theory scenario where all players make decisions or select strategies at the same time without knowledge of the other players' choices.
- Inspect the effects produced by sequential and simultaneous games.
- Ascertain Nash equilibria in multiple game environments.
Verified Answer
BA
Beree AnayaJul 13, 2024
Final Answer :
D
Explanation :
In a simultaneous game, the Nash equilibrium is reached when each player chooses their best strategy given the other player's choices.
If Tattling Tina tattles, Bratty Brenda's best response is to hit her to avoid losing 10. If Bratty Brenda hits, Tattling Tina's best response is to tattle to avoid losing 10. Therefore, the Nash equilibrium is Hit, Tell.
However, if Tattling Tina chooses not to tattle, Bratty Brenda's best response is to not hit to gain 5. If Bratty Brenda doesn't hit, Tattling Tina's best response is to not tattle to avoid losing 5. Therefore, another Nash equilibrium is Not hit, Not tell.
Lastly, if Bratty Brenda chooses to not hit, Tattling Tina's best response is to tattle untruthfully to gain 5. If Tattling Tina tattles untruthfully, Bratty Brenda's best response is to not hit to avoid losing 5. Therefore, a third Nash equilibrium is Not hit, Tell.
Hence, the best choice is both B&C as they lead to Nash equilibrium.
If Tattling Tina tattles, Bratty Brenda's best response is to hit her to avoid losing 10. If Bratty Brenda hits, Tattling Tina's best response is to tattle to avoid losing 10. Therefore, the Nash equilibrium is Hit, Tell.
However, if Tattling Tina chooses not to tattle, Bratty Brenda's best response is to not hit to gain 5. If Bratty Brenda doesn't hit, Tattling Tina's best response is to not tattle to avoid losing 5. Therefore, another Nash equilibrium is Not hit, Not tell.
Lastly, if Bratty Brenda chooses to not hit, Tattling Tina's best response is to tattle untruthfully to gain 5. If Tattling Tina tattles untruthfully, Bratty Brenda's best response is to not hit to avoid losing 5. Therefore, a third Nash equilibrium is Not hit, Tell.
Hence, the best choice is both B&C as they lead to Nash equilibrium.
Learning Objectives
- Inspect the effects produced by sequential and simultaneous games.
- Ascertain Nash equilibria in multiple game environments.
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