Game theory is often used as a systematic decision making tool that relies on understanding the strategic interactions that come about as a result of competition or cooperation. This theory is used in strategic situations where there are two or more decision makers but none of them has absolute control over the final outcome. This final outcome depends on the autonomous decisions taken by all the involved parties. This theory is used widely in social sciences as well as in formal sciences, however here we’ll restrict the discussion to how game theory is used in making business decisions.
What is Game Theory?
To help you get a better understanding of what game theory is and how it works, we’ll explain it with an example. Let’s assume that there are two movies, based on a similar subject, that are to be released on the same date. Each of the production houses is now left with three options – to pre-pone the release, postpone the release or stick to the schedule. Both have a common interest and the outcome depends on what each production house decides. Both the production houses can signal each other about their intentions and thus adjust their release schedule so their interest doesn’t collide. This is an example of a cooperative game. Now if the two decide not to disclose their intention to each other and play a non-cooperative game, the outcome will be – gains for one and losses for the other. In both cases, game theory can be used by the production houses to find an optimal solution.
To use game theory for business decision making, the situation must have:
- Two or more, but definitely a finite and known number, of autonomous decision makers.
- There should be a complete set of known outcomes, resulting from different strategic selections made by individual players.
- Every decision maker has a certain preferential order for these outcomes, which can be assigned a numeric payoff.
- It should be known how each player will react to every eventuality.
- In case of a cooperative game, every player must have complete information about their as well as the other players’ strategies and payoffs. Also, each player should be aware of the selections made by the other players.
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.
Images by – Sidharth Thakur