What are the payoffs associated with a dominant strategy equilibrium and a Nash equilibrium?

Steps to Solve

1. Identify the Players and Strategies
   We have two players: Prairie Glen and Mountain View. The strategies for Prairie Glen are to set a high or low price, and Mountain View can choose to advertise or not.

2. Construct the Payoff Matrix
   From the game matrix, we list the possible outcomes based on different strategy combinations:

   • If Prairie Glen sets a high price and Mountain View advertises: $(1000, 1000)$
   • If Prairie Glen sets a high price and Mountain View doesn't advertise: $(2500, 500)$
   • If Prairie Glen sets a low price and Mountain View advertises: $(500, 2500)$
   • If Prairie Glen sets a low price and Mountain View doesn't advertise: $(2000, 2000)$

3. Determine Dominant Strategies
   A dominant strategy is one that yields a higher payoff regardless of the other player's action.

   • For Prairie Glen:

     • If Mountain View advertises: High price gives $1000$, low price gives $500$ — High price is better.
     • If Mountain View doesn’t advertise: High price gives $2500$, low price gives $2000$ — High price is better.

   • Hence, Prairie Glen’s dominant strategy is to set a high price.

   • For Mountain View:

     • If Prairie Glen sets a high price: Advertising gives $1000$, not advertising gives $500$ — Advertising is better.
     • If Prairie Glen sets a low price: Advertising gives $2500$, not advertising gives $2000$ — Advertising is better.

   • Hence, Mountain View’s dominant strategy is to advertise.

4. Identify the Dominant Strategy Equilibrium
   Both players have dominant strategies:

   • Prairie Glen: High price
   • Mountain View: Advertise
   • The payoff for this combination is $(1000, 1000)$.

5. Find Nash Equilibrium
   A Nash equilibrium occurs when both players choose strategies where neither has an incentive to deviate unilaterally:

   • The dominant strategy combination is $(1000, 1000)$, which is also the Nash equilibrium because neither player can improve their payoff by changing their strategy given the other's choice.