Question

1. Two soap producers, Dove and Irish Spring, can either stress social media advertising or television advertising in their forthcoming advertising campaigns. The payoffs associated with each decision are given in the table below:

($ in million)		Irish Spring
		Social Media	Television
Dove	Social Media	Dove: $10 Irish Spring: $7	Dove: $14 Irish Spring: $8
	Television	Dove: $11 Irish Spring: $9	Dove: $10 Irish Spring: $5

1. Does Dove have a dominant strategy. If so, what is it?

2. Does Irish Spring have a dominant strategy. If so, what us it?

3. Assuming that Dove and Irish Spring make their decisions simultaneously, what is the Nash equilibrium of this game? Is it unique?

4. Noe assume that instead of making a decision simultaneously, Dove makes their decision first, and Irish Spring follows. What would be the equilibrium outcome of this sequential game?

5. If instead Irish Spring made their decision first, followed by Dove, what would be the outcome of this sequential game?

Answer 1

We can write the payoff matrix in this simple form.

	Irish Spring (IS)
Social Media	Television
Dove	Social Media	(10,7)	(14,8)
Television	(11,9)	(10,5)

a). Dove doesn’t have a dominant strategy.

  Dominant strategy is when one strategy is better than another strategy for one player, no matter how that player's opponents may play. Here Dove chooses Television When IS choose Social media. And when IS choose TV, Dove takes social media.

b). Irish Spring also don’t have any dominant strategy.

c). Nash equilibrium involves strategic choices that once made, provide no incentive for players to change their behaviour further. So given the others equilibrium strategies, Nash equilibrium provides the best choice for each player.

By underlining the best response payoff, we can find the Nash equilibrium (Nash equilibrium occurs when both payoff gets underlined for a strategy matrix). In order to find it, we have to find the best strategy of a player when the other player selects one particular strategy.

In this game, there are two Nash equilibrium. One at the lower left corner and other at the upper right corner. Payoffs for both players in these strategy matrix gets underlined.

	Irish Spring (IS)
Social Media	Television
Dove	Social Media	(10,7)	(14,8)
Television	(11,9)	(10,5)

d). Now if we consider a sequential game, where Dove takes first decision it will look like the game tree as given below. Here the equilibrium out will be same as that of sequential game [(11,9) and (14,8)], as these strategies provide them high payoff.

e) Sequential game when Irish Spring becomes the first player. For convenience, payoffs are given in the form of (player 2, player1). In this case only, don’t get confused. Here also there is no change in the equilibrium outcome, it is same as the simultaneous game. Since at these strategy combinations [(11,9) and (14,8)], both players are having higher payoff than going for other strategy. Therefore no players will be having an incentive to change their strategy or becoming the first player in the game.