Juan Pablo and Zak are competitors in a local market. Each is trying to decide if it is better to advertise on TV, on radio, or not at all. If they both advertise on TV, each will earn a profit of $8,000. If they both advertise on radio, each will earn a profit of $14,000. If neither advertises at all, each will earn a profit of $20,000. If one advertises on TV and other advertises on radio, then the one advertising on TV will earn $12,000 and the other will earn $10,000. If one advertises on TV and the other does not advertise, then the one advertising on TV will earn $22,000 and the other will earn $4,000. If one advertises on radio and the other does not advertise, then the one advertising on radio will earn $24,000 and the other will earn $8,000. If both follow their dominant strategy, then Juan Pablo will

Question

BlackTom AI · Accepted Answer

We start by restating the scenario and the answer choices to set the stage for evaluation.
Question: Juan Pablo and Zak are deciding between TV, radio, or not advertising. Payoffs depend on both choices as described. If both follow their dominant strategy, then Juan Pablo will which option?
Answer options:
- advertise on TV and earn $8,000.
- advertise on radio and earn $14,000.
- advertise on TV and earn $22,000.
- not advertise and earn $20,000.

Now, analyze each option by considering how each player’s payoff changes with the other player's possible actions, to identify any dominant strategy for Juan Pablo.
Option 1: Juan Pablo advertises on TV and earns $8,000.
- If Zak also chooses TV, the outcome is both on TV with payoff $8,000 for each. Here TV yields $8,000, but we must check other scenarios to see if TV is ever better for Juan Pablo.
- If Zak chooses radio, the scenario is TV vs radio, where the TV player earns $12,000 and the radio player earns $10,000. For Juan Pablo, TV would give $12,000 in that case, which is higher than $8,000. So TV is not consistently best.
- If Zak chooses none, TV yields $22,000, which is much higher than $8,000. Thus TV can be attractive when the other does not advertise.
- If Zak also chooses TV, TV yields $8,000; if Zak chooses radio, TV yields $12,000; if Zak chooses none, TV yields $22,000. This inconsistency shows TV is not the best across all possibilities, so TV is not a dominant strategy for Juan Pablo.
Conclusion for Option 1: There is no reason to single out TV as the consistent best choice given all possible rival actions.

Option 2: Juan Pablo advertises on radio and earns $14,000.
- If Zak chooses TV, the outcome is TV vs radio with the TV player earning $12,000 and the radio player earning $10,000. As Juan Pablo is the radio player in this scenario, he would earn $10,000, which is less than $14,000, so radio is not worse here; but we must compare across all possibilities.
- If Zak chooses radio, both advertise on radio and each earns $14,000. This matches the option value.
- If Zak chooses none, radio vs none yields the radio advertiser $24,000 while the non-advertiser gets $8,000; since Juan Pablo is the radio advertiser, he would earn $24,000, which is greater than $14,000.
Thus, when Zak chooses none, radio still yields a higher payoff than $14,000, showing radio is advantageous in that case.
- If Zak chooses TV, as noted, radio yields $10,000 in the TV-radio mismatch, which is below $14,000.
Overall, although radio is not strictly best in every single rival action, it provides higher payoffs than some alternatives in multiple scenarios and, crucially, in the matching scenario with Zak on radio it yields $14,000. The key check is to see if radio dominates TV or not; as shown in the other options, radio yields higher payoffs in most cases and, in particular, when the rival chooses TV or none, radio (and its resulting payoffs) tends to be favorable. This aligns with the idea that Juan Pablo should choose radio.

Option 3: Juan Pablo advertises on TV and earns $22,000.
- If Zak chooses none, TV yields $22,000 for Juan Pablo, which is beneficial in that case.
- If Zak chooses radio, TV yields $12,000, which is far less than the $14,000 he could earn by choosing radio.
- If Zak chooses TV, TV yields $8,000, which is also worse than radio’s payoff of $14,000 in that same scenario.
Thus TV does not provide the best outcome across all possible actions by Zak; many scenarios favor radio or even none, so TV is not a dominant strategy.

Option 4: Juan Pablo not advertise and earns $20,000.
- If Zak chooses TV, the TV vs none scenario gives the TV advertiser $22,000 and the non-advertiser $4,000; Juan Pablo would earn $4,000 if he does not advertise, which is far less than $20,000, so not advertising is not robust here.
- If Zak chooses radio, the radio vs none scenario gives the radio advertiser $24,000 and the non-advertiser $8,000; Juan Pablo would earn $8,000, again less than $20,000, so not advertising is not robust.
- If Zak chooses none, both not advertising yields $20,000 for each, which matches this option, but since other rival actions yield lower payoffs for not advertising, not advertising is not a dominant strategy.

Putting these assessments together, only the second option consistently aligns with the concept of a dominant strategy for Juan Pablo in the given payoff structure, especially when considering the best responses to the rival’s potential actions and the fact that both players end up choosing radio in the dominant-strategy outcome.

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