Game Theory Question

Question

|

| |Adv| ---------|N\A|

Adv| 300,300 | 900,0 |

N\A| 0,900 | 700,700 |

Player 1= Pepsi

Player 2= Coke

A) Solve for the pure strategy Nash equilibrium

B) Is this game a prisoner's Dilema?

C) Is there a cooperative equilibrium? If so, what is it?

D) Does coke have a dominant strategy? Does Pepsi?

My Attempt

---

| |Adv| ---------|N\A|

Adv| (300),(300) | (900),0 |

N\A| 0,(900) | 700,700 |

A) Nash Equilibrium: (Adv, Adv)

B) Not sure how to answer this

C) Yes. If they both got in contact and made the option to not advertise

D)

I would appreciate some help!

Answer 1

Here are a couple hints for the two that you haven't answered:

The prisoner's dilemma is characterized by the inability to sustain the Pareto optimal payoff as a Nash Equilibrium due to the existence of a profitable deviation for both players. Each player has a dominant strategy to "Defect" and so the unique Nash Equilibrium is one where both players "Defect". Does that hold here?

A (possibly mixed) strategy $a$ (weakly) dominates another strategy $b$ for a given player $i$ if player $i$ (weakly) prefers playing $a$ to $b$ for any strategy vector of the other players. In your case, there is just one other player, $j$, and so $i$ simply has to prefer $a$ to $b$ for any strategy played by player $j$.

You just need to see if that holds for your two players.