One of the basic principles in game theory is that you should look forward and reason back. Essentially, this means that before making a move, you should consider all the possible moves that you and the other players can make, together with the possible outcomes that these moves lead to. Then, consider how desirable each outcome is to each player, and based on this, determine which moves they are likely to make.
In order to think this way, it’s useful to use a game tree (also referred to as a decision tree in cases where there is only one player). In the following example, you will see how this principle works, and how you can implement it in order to make smarter decisions, by taking advantage of game theory.
Example: to Advertise or Not to Advertise?
MegaCorp is currently the only company selling a certain type of high-quality industrial lasers.
Startupo is a new company, which is considering entering the market currently dominated by MegaCorp.
To deter Startupo from taking a part of their market share, MegaCorp can engage in a costly advertising campaign, which would involve significantly reducing their prices.
Since Startupo is a smaller and more flexible company, they can wait and see whether MegaCorp runs their ad campaign before deciding if they should enter the market.
As such, each company has two possible moves: MegaCorp can decide whether or not to run the ads, while Startupo can decide whether or not to enter the market.
Therefore, there are 4 possible outcomes for the game, each ranked differently by the players (1 is the most desirable outcome, while 4 is the least desirable outcome):
- No ads, no entry (of Statupo).
- Ads, but no entry.
- No ads, but entry.
- Ads and entry.
- No ads, yes entry.
- Ads, but no entry.
- No ads and no entry.
- Ads and entry.
Based on this, we get the following game tree:
When making the decision whether to or not advertise, MegaCorp starts by looking at the possible outcomes, and then asking themselves which moves their competitor will make:
- If MegaCorp runs the ads, then Startupo will choose not to enter the market (since it gets them their #2 choice, as opposed to their #4 choice). In this case, MegaCorp also gets their #2 choice.
- If MegaCorp doesn’t run the ads, then Startupo will choose to enter the market, since it leads to a better outcome for them than not entering the market (choice #1 versus choice #3). In this case, MegaCorp get their #3 choice.
- Clearly, MegaCorp should run its ads, to prevent Startupo from entering the market. This way they get their #2 choice (similarly to Startupo), while if they decide not to run the ads, they will get their #3 choice, while Startupo will get their #1 choice.
This rationale is phrased so that it appears we start by considering MegaCorp’s moves. However, in reality we start by considering the outcomes, and then considering which move Startupo will make in each of the two scenarios available to them (ads/no ads). Only then do we consider MegaCorp’s initial move.
This method of backward induction can be used to find the optimal solution of a game when the following conditions apply:
- Sequentiality: the game must be sequential, meaning that the players act one after another (as opposed to a simultaneous game, where the players act at the same time).
- Finiteness: the game must be finite (have a clear endpoint).
- Perfect information: the players must have perfect information regarding the possible moves, outcomes, and the desirability of each outcome.
- Assumption of rationality: the players must make the rational choice (i.e. select the option that is best for them).
Of course, in reality, things are more complicated. Perfect information rarely exists, and the potential moves and motives of each player tend to be more complex. However, this method is nonetheless the best way to approach such scenarios, and these extra factors and consideration can be appropriately incorporated into the model. Similarly, the addition of more players to the game doesn’t change the overall strategy either; rather, it just increases the complexity of the game tree.
This all leads to an important caveat: just because the game has an optimal strategy that you should select, doesn’t mean that it’s easy to find it. (Think about chess, for example)
Summary and conclusions
- When thinking strategically, start by looking forward in order to see the possible moves and outcomes in the scenario.
- Try to predict how desirable each outcome is for each player.
- When you have the game tree mapped out, with all the possible moves and consequent outcomes, reason backward in order to find the best moves for you to make.
- This allows you to find the optimal solution to a game, given that some conditions are met (sequentiality, finiteness, availability of perfect information, and the assumption of rationality).