To obtain the Nash equilibrium you must analyze what is the best response for each strategy from the other player.
Let’s start with player 1:
- If player 2 chooses to keep, the possibilities for player 1 is to keep (10) or No tariff (5). Player 1 will choose to keep tariffs because is the highest payoff in this situation. Player 1 decision is circle in red.
- If player 2 chooses No Tariff, player 1 will choose again to keep (15) which gives him a higher payoff that if he chooses to No Tariff.
We can also note that player 1 dominant strategy is to KEEP
Now, player 2:
- If player 1 chooses to keep, the best response for player 2 is to keep too (10). Player 2 decision is circle in blue.
- If player 1 chooses no tariff, the best response for player 2 is to keep(15)
Therefore, player 2 dominant strategy is to Keep
This game has just one Nash equilibrium (KEEP, KEEP), in this game all players play their dominant strategy. Just like in the prissioners' dilema, they would be better off if both choose their dominated strategy.
b) If I undestood correctly, the problem is asking you to change two payoff boxes (no tariff, no tariff) to (keep, no tariff) ONLY for player 1, everything else ramains the same.
Your new payoff table should look like this:
In this case the Player 1 doesnt have a dominant strategy. Only player 2 has the dominant strategy to keep.
If both decide based on their best strategy, Nash equilibium will remain at (keep, keep). As you can see, both will get better payoff if they chooses no tarrif.
Player2 keep15.5 10,10 No Tariff 15,5 14,14 Keep Player No Tariff 5,1
Player2 keep 10,10 No Tariff 14,5 Keep Player1 No Tariff 5,15 15 14