Game Theory: Game Strategy
The easiest way to get started with thinking about Game Theory to make decisions is to realize we already started last week! When we covered Decision Theory we were really just talking about a game with a single player – you.
Let’s work with an example. Let us say you are considering raising the price on your product from $100 to $200 to improve your margins and raise revenue. If you model it like a decision (using what we learned last week) it would look as follows:
The outcomes here make it clear we should raise the price and make more revenue!!
However, selling a product is not a single player game as there are at least two players: the seller and the buyer. We need a new way to think about this, which is where Game Theory modeling starts to become useful. Below is the same decision but framed with the decisions for both the buy and the seller at the same time:
This table describes the different decisions faced by the two players, the Seller on the left side and the Buyer across the top. Each cell of the table contains the payoff to each player for the corresponding pair of decisions (the Seller’s payoff is in the lower left corner and the Buyer’s in the upper right). If the Seller raises the price but the Buyer doesn’t buy, the Seller gets nothing but the Buyer saves $200. If the Seller keeps the price and the Buyer buys, the Seller gets $100 and the Buyer spends $100. The payoffs are measured in whatever form of utility best represents the benefit to the players. In the above example, using dollars makes it easy to understand but doesn’t capture the benefit the buyer gets from the product after buying it so it not a very good measure of utility.
In Game Theory, decisions (e.g. “Raise Price”, “Keep Price”) are referred to as strategies. Your job is to choose the strategy that will give you the best payoffs based on what your opponents might do. I’ve updated our example (below) with arrows which represent the path from worse payoffs to better payoffs:
If you have properly modeled the strategies and payoffs, it should be clear which strategies are better than others.
As you can see, Game Modeling is a much more powerful way of thinking about decisions involving more than one person as the incentives become easy to analyze. Tomorrow we will jump into how to do that analysis to choose strategies and win the game!
Quote of the Day: “We do not stop playing because we grow old, we grow old because we stop playing!” ― Benjamin Franklin