Phillip Morris and R.J. Reynolds have spent huge sums of money each year to adve

Question

Phillip Morris and R.J. Reynolds have spent huge sums of money each year to advertise their tobacco products in an attempt to capture customers from each other. Suppose that each year Phillip Morris and R.J. Reynolds have to decide wheather or not they want to spend money on advertising. If neither advertises, they will both earn a profit of $2million. If they both advertise, each will earn a profit of $2.8 million in profits and other will earn only $1 million. Construct the payoff matrix to illustrate this problem. Is this a zero sum game Explain (one sentence- look up the definition of zero sum games before you start) Suppose that this is a non-cooperative game. Does either firm have a dominant strategy What is it Explain why this is or is not a dominant strategy. Now suppose that the firms can write an enforceable contract about what they will do. Does this change the outcome What is the cooperative solution to this game Why

Explanation / Answer

(a) Pay-off matrix is as follows –

R. J. Reynolds

Advertise

Do not advertise

Philip Morris

Advertise

$1.5 m, $1.5 m

$2.8 m, $1 m

Do not advertise

$1 m, $2.8 m

$2 m, $2 m

(b) Zero-sum game is the game in which gain by one player results in equivalent loss for another player. For example, if one player gains $1 and other player loses exactly $1 then game is said to be zero-sum game as net wealth remains same.

In the given game, suppose that initially both firms do not advertise and thus are earning $2 million each as profit. Net wealth is $4 million.

Now, Philips Morris decides to advertise while R.J. Reynolds still does not advertise. Pay-off will be - $2 million for Philips Morris and $1 million for R.J. Reynolds. Net wealth is $3.8 million.

As we can see that this change in strategy has resulted in a gain of $0.8 million for Philips Morris while a loss of $1 million for R.J. Reynolds.

As gain by one player is not equivalent to loss by other player, this game is not zero-sum game.

(c) If Philips Morris chooses to advertise then R.J Reynolds will earn a profit of $1.5 million if it advertises and $1 million if it does not advertises. As pay-off is higher in case of advertise, it will advertise.

If Philips Morris chooses not to advertise then R.J Reynolds will earn a profit of $2.8 million if it advertises and $2 million if it does not advertises. As pay-off is higher in case of advertise, it will advertise.

It can be seen that R.J Reynolds chooses to advertise irrespective of the strategy adopted by Philips Morris. When a player chooses a strategy irrespective of the strategy adopted by other player that strategy is said to be dominant strategy of the respective player.

So, R.J Reynolds has a dominant strategy and that is to advertise.

If R.J. Reynolds chooses to advertise then Philips Morris will earn a profit of $1.5 million if it advertises and $1 million if it does not advertises. As pay-off is higher in case of advertise, it will advertise.

If R.J. Reynolds chooses not to advertise then Philips Morris will earn a profit of $2.8 million if it advertises and $2 million if it does not advertises. As pay-off is higher in case of advertise, it will advertise.

It can be seen that Philips Morris chooses to advertise irrespective of the strategy adopted by R.J. Reynolds. When a player chooses a strategy irrespective of the strategy adopted by other player that strategy is said to be dominant strategy of the respective player.

So, Philips Morris has a dominant strategy and that is to advertise.

(d) Part (c) shows that if they do not cooperate and plays their dominant strategy (to advertise) then they will both get pay-off of $1.5 million each.

However, pay-off matrix in part (a) shows that if they both do not advertise then in that case each one can have profit of $2 million.

So, if firms can write an enforceable contract about what they will do then it is beneficial for them to not to advertise as it results in higher profits.

Thus, the outcome of game changes once the firms cooperate.

The cooperative solution is (not advertise, not advertise).

This is cooperative solution because they are deviating from their dominant strategy (to advertise) and are accepting a strategy that they would not have chosen if the cooperation does not happen.

R. J. Reynolds

Advertise

Do not advertise

Philip Morris

Advertise

$1.5 m, $1.5 m

$2.8 m, $1 m

Do not advertise

$1 m, $2.8 m

$2 m, $2 m

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