Explain the Prisoner’s Dilemma game, the notion of dominant strategy, and the co

Question

Explain the Prisoner’s Dilemma game, the notion of dominant strategy, and the concept of Nash equilibrium and cooperation. Using these concepts, then, analyze the following duopoly game.

Philip Morris and R.J. Reynolds spend huge sums of money each year to advertise their tobacco products in an attempt to steal customers from each other. Suppose each year Philip Morris and R.J. Reynolds have to decide whether or not they want to spend money on advertising. If neither firm advertises, each will earn a profit of $2 million. If they both advertise, each will earn a profit of $1.5 million. If one firm advertises and the other does not, the firm that advertises will earn a profit of $2.8 million and the other firm will earn $1 million.

If the two companies decide to collude to maximize profits, what will each country do? What profit will each country earn?

What is the dominant strategy for each company, and what profit will each company earn if they follow those strategies?

Is the solution you found in the first question a Nash equilibrium?

Is the solution you found in the second question a Nash equilibrium?

Explanation / Answer

The payoff matrix is as follows.

(a) If the firms collude then both will decide not to advertise because they will earn maximum profits.

(b) Dominant strategy is the option that a player will choose irrespective of the other player's strategy.

So,

Reynolds earns highest payoff when it advertises (payoff: 2.8 > 2 > 1). So its dominant strategy is to advertise.

Philips earns highest payoff when it advertises (payoff: 2.8 > 2 > 1). So its dominant strategy is to advertise.

(c) In a Nash equilibrium, both firms takes decisions considering the other's reaction.

When Philips advertises, Reynolds also advertises since it gives him highest profit (1.5 > 1).

When Philips doesn't advertise, Reynold advertises since it gives him highest profit (2.8 > 2).

When Reynolds advertises, Philips also advertises since it gives him highest profit (1.5 > 1).

When Reynolds doesn't advertise, Philips advertises since it gives him highest profit (2.8 > 2).

So, the Nash equilibrium is (Advertise, Advertise) with payoff (1.5, 1.5). The solution to 1st question is not a Nash Equilibrium but solution to 2nd question is a Nash Equilibrium.

Reynolds Advertise Don't Advertise Philips Advertise (1.5, 1.5) (2.8, 1) Don't Advertise (1, 2.8) (2, 2)

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