Nash Equilibrium|Dominant Strategy|Game Theory|Explained with example|Economics for Beginner|Masters

Summary

This video script explores Nash Equilibrium and Dominant Strategy in game theory. It uses a scenario with two firms, A and B, deciding whether to advertise. Firm A has a dominant strategy to advertise, as it always yields higher payoffs. Firm B also prefers advertising due to higher payoffs in that strategy. However, in a modified example where Firm A's payoff for not advertising is higher, there's no dominant strategy for A, leading to a Nash Equilibrium where both firms advertise based on mutual best responses.

Takeaways

• 📊 A dominant strategy is when a player does the best they can regardless of what the other player does.
• 📈 Nash equilibrium occurs when both players are doing the best they can, given what the other is doing.
• 💼 Example: Two firms (A and B) can choose to advertise or not advertise their product, with various payoffs.
• 💰 Payoff refers to the profit a firm receives based on the choices made by both firms.
• 🏢 If both Firm A and Firm B advertise, the payoffs are 10 for A and 5 for B.
• 📉 If Firm A advertises and Firm B does not, the payoffs are 15 for A and 0 for B.
• 📊 Firm A has a dominant strategy in advertising because its advertising payoffs are always higher than not advertising.
• 📈 Similarly, Firm B also has a dominant strategy in advertising since its payoffs from advertising are higher than not advertising.
• 🔄 In a modified example, Firm A does not have a dominant strategy because one payoff (20) from not advertising is higher than the advertising payoff (15).
• 🎯 The Nash equilibrium occurs when both firms advertise, as each is doing the best it can given the other's actions.

Q & A

What is a Nash equilibrium?

A Nash equilibrium occurs when each player in a game is doing the best they can, given what the other player is doing. In this situation, no player has an incentive to deviate from their chosen strategy because they are maximizing their payoff based on the other's actions.

What is a dominant strategy?

A dominant strategy is a strategy that provides a better outcome for a player, regardless of what the other player does. If a player has a dominant strategy, they will always choose it because it yields the highest payoff in all possible scenarios.

What is the difference between a Nash equilibrium and a dominant strategy?

The key difference is that a dominant strategy is the best choice for a player no matter what the other player does, while a Nash equilibrium is a situation where both players are making the best decision given the other's actions. In a Nash equilibrium, players may or may not have dominant strategies.

In the example involving Firm A and Firm B, what are the possible payoffs when both firms choose to advertise?

When both Firm A and Firm B choose to advertise, Firm A receives a payoff of 10, and Firm B receives a payoff of 5.

Does Firm A have a dominant strategy in the first example?

Yes, Firm A has a dominant strategy in the first example. Advertising provides higher payoffs for Firm A (10 and 15) compared to not advertising (6 and 10), so Firm A will always choose to advertise.

Does Firm B have a dominant strategy in the first example?

Yes, Firm B also has a dominant strategy in the first example. Advertising yields higher payoffs for Firm B (5 and 8) compared to not advertising (0 and 2), so Firm B will always choose to advertise.

What happens when one value is changed in the second example, and how does it affect Firm A's strategy?

In the second example, the value 10 is replaced with 20 for Firm A’s payoff when neither firm advertises. This change means Firm A no longer has a dominant strategy because while advertising gives higher payoffs in some scenarios, not advertising provides a higher payoff (20) in one case.

Does Firm B still have a dominant strategy in the second example?

Yes, Firm B continues to have a dominant strategy in the second example. Advertising still provides better payoffs (5 and 8) compared to not advertising (0 and 2), so Firm B will always choose to advertise.

What is the Nash equilibrium in the second example?

The Nash equilibrium in the second example occurs when both firms choose to advertise. Firm B has a dominant strategy to advertise, and given that Firm B advertises, Firm A’s best response is also to advertise.

Why does the game lead to both firms advertising in the Nash equilibrium?

Both firms end up advertising because Firm B has a dominant strategy to advertise, and Firm A, in response to Firm B’s choice to advertise, maximizes its payoff by also advertising. This situation creates a Nash equilibrium where neither firm can improve their outcome by changing their strategy.