Using a Game Theory Matrix
When game theory is used, the most popularly adopted technique is to tabulate the outcomes in a matrix.
This matrix is also known by other names like a normal form or a payoff matrix. Continuing with the above example, let's tabulate a game theory matrix for the production houses.
The strategic options for the first production house are plotted on the Y-axis and those for the second production house are plotted along X-axis. Both production houses have the same three strategic options – release the movie one week earlier, one week later or on a fixed day. Here’s what the initial matrix will look like:
The next step is to fill in the payoffs corresponding to the intersection of the options. For instance, if both the production houses decide to pre-pone the release by one week, the expected outcome will be they may both end up with just half a share of the total audience as in the original situation. The payoff for this intersection will be written as (5,5), where the first payoff is for the first production house and the second one is for the second production house.
In this example there can be typically three types of payoffs, the one where the release date clashes has already been explained above and as for the other two:
- If one of the production house releases the movie on the fixed date, while the other one decides to change its release date, we’re assuming both get a payoff of 8 and 8, and;
- When one production house releases its movie one week in advance and the other one delays it by one week, it creates a two week differential; both the players get to enjoy a maximum payoff of 10 each.
Here’s what the matrix with the payoffs looks like:
In this example, the matrix clearly reveals that the best choice for each of them is to move away from their fixed schedule into opposite directions so as to maximize their gains.
This example was a simple one and every intersection had the same payoff for each of the players, however, in most real situations this may not be the case. So how do you use the game theory matrix to make a business decision? The final choice will depend on the game type.
Cooperative Game: Both the players choose an intersection point where both of them have a maximum gain possibility.
Non-Cooperative or Competitive Game: Each player will choose the intersection where his gains are the maximum, irrespective of the gain or loss for the other player.
Game theory is quite an interesting way of arriving at strategic business decisions, but one must not forget in real situations, the final decisions cannot be fully relied on because of the high number of assumptions made when using this technique.