How to read a payoff matrix : Game Theory

Eg – Payoff matrix for a new technology game

Firm B

Firm A

Start a new campaign

Don’t Start

Start a new campaign

10,5

15,0

Don’t Start

6,8

10,2




Explanation
1.There are 2 firms A and B and they want to decide whether to Start a new campaign.
2.each firm will be affected by its competitor’s decision.
3. The above table shows the payoff to both firms. This table is called payoff matrix.
4. (a,b) -The first number in each cell is the payoff(profits) to A and second number in each cell
is the payoff to B.
-(10,5) shows the payoffs when both firms start a new campaign.
Firm A’s profits are 10 and firm B’s are 5.
-(15,0) shows the payoffs when firm A starts a new campaign abd Firm B does not.
Firm A’s profits are 15 and firm B’s are 0.

7 comments:

Anonymous said...

This was helpful to a certain point. What about the second set of numbers on the matrix?

Pkmnisdabomb said...

To answer the comment question above, the author did explain each of the numbers in the matrix. In each of the 4 "quadrants", there are two numbers that represent the results of the four possible decisions.

In the top left quadrant (10,5), the two numbers mean Firm A starts a new campaign with a gain of 10 while Firm B starts a new campaign with a gain of 5.

In the top right quadrant (15,0), the two numbers mean Firm A starts a new campaign with a gain of 15 and Firm B does not start a new campaign.

In the bottom left quadrant (6,8), Firm A does not start a new campaign and therefore their gain is only 6, while Firm B does start a new campaign resulting in a gain of 8.

In the bottom right quadrant (10,2), both firms do not start a new campaign. The result is Firm A has a gain of 10 while Firm B (obviously doing poorly compared to it's competitor) has a gain of only 2.

In conclusion, all 4 numbers are accounted for.

Sanja said...

Thank you very much, it was straightforward and very helpful

Matt said...

Keep in mind, a helpful strategy in solving payoff matrices is solving for each PLAYER'S dominant and dominated strategies.

A dominant strategy is a firm(player)'s optimal strategy with, with dominated being the less preferred strategy.

For example, each firm has two strategies in this example: either start a campaign or not. Dominant strategy for firm A would be to start a campaign as its payoffs are 10 and 15 (compared to 6 and 10 if they don't). For firm b, choosing to start a campaign is also the dominant strategy as payoffs are 5 and 8 (compared to 0 and 2 if they don't).

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Ish C said...

But in reality we do not know what opponent strategies are, then how can it be based on 2 firms? Besides how the numbers are picked? We can choose 1, 2. Is there any specific reason to pick these numbers?

Thanks.

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