Dominant Strategy

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Definition of Dominant Strategy:

A dominant strategy is a term used in game theory to describe a decision that always leads to the best payoff for a player, no matter what the other players do. A rational player will always play his dominant strategy.

Detailed Explanation:

Suppose you own a taxi company, Reliable Taxi. You have one competitor, Best Taxi. An advertising salesman is trying to convince you that you can increase your market share by advertising. Should you? How will Best Taxi respond? Your profit is affected by Best's decision. There are four possible combinations, each resulting in a different profit.

  1. Both Reliable Taxi and Best Taxi advertise.
  2. Neither company advertises.
  3. Reliable Taxi advertises and Best Taxi chooses to save money and not advertise.
  4. Best Taxi advertises and Reliable Taxi chooses not to advertise.

Table 1 provides the expected profits for each company with every possible outcome. Reliable Taxi's payoffs are purple and the payoffs for Best are green. Presently, both companies earn $175,000. Neither you nor Best Taxi advertises and each of you serves 50 percent of the market. This is represented in the bottom right box. The advertising salesman tries to convince you that your profits would jump to $200,000 if you advertise. Best, would suffer a drop in its profits to $100,000 resulting from a loss of market share. This is represented by the lower left box. How would Best respond? You are concerned. What if Best advertises and you do not? This case is displayed in the upper right box. Your profits would fall to $100,000 while Best's profits would jump to $200,000. But, advertising is expensive and your community's total number of taxi users would not increase much if both of you advertise. In fact, if both you and Best advertise, both companies would see a decrease in profits to $150,000. Is your dominant strategy to advertise or not advertise? What is Best's dominant strategy?

Table 1

Table 2 helps answer the questions above. You believe Best will advertise. Your payoffs are shown on the top line in purple. $150,000 exceeds $100,000, so your best choice is to advertise if you believe Best will also advertise. This choice is underlined in Table 2. The second row provides payoffs if Best chooses not to advertise. Again, advertising has the highest payoff and is underlined in purple. $200,000 is preferable to $175,000. Advertising is your dominant strategy because it has a higher payoff regardless of Best Taxi's decision. 

Does Best have a dominant strategy? Its dominant strategy is also to advertise. Best's payoffs are recorded in green. The first column provides Best's payoffs if Reliable chooses to advertise. $150,000 exceeds $100,000 so Best would earn a higher profit if it advertises. Advertising is also the more profitable option if Reliable chooses not to advertise. These payoffs are in the second column and $200,000 is greater than $175,000. Advertising is also Best's dominant strategy.

Table 2

The most likely outcome is that both companies advertise and earn $150,000 since both Reliable Taxi and Best Taxi have a dominant strategy to advertise. Economists refer to this as a Nash equilibrium named after John Nash. This outcome is circled on the table. It is interesting to note that each would earn more if they colluded and chose not to advertise ($175,000 vs $150,000). However, both advertise because they fear losing market share if one advertises and the other doesn’t.

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