Game theory

Game theory studies interactive decision-making, where the outcome for each participant or “player” depends on the actions of all.

If you are a player in such a game, when choosing your course of action or “strategy” you must take into account the choices of others.

But in thinking about their choices, you must recognize that they are thinking about yours, and in turn trying to take into account your thinking about their thinking, and so on.

It would seem that such thinking about thinking must be so complex and subtle that its successful practice must remain an arcane art.

Indeed, some aspects such as figuring out the true motives of rivals and recognizing complex patterns do often resist logical analysis. But many aspects of strategy can be studied and systematized into a science – Game Theory.

Game theory is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes.

While used in a number of disciplines, game theory is most notably used as a tool within the study of economics.

The economic application of game theory can be a valuable tool to aide in the fundamental analysis of industries, sectors and any strategic interaction between two or more firms.

Game Theory Definitions

Any time we have a situation with two or more players that involves known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes.

Let’s start out by defining a few terms commonly used in the study of game theory:

• Game: Any set of circumstances that has a result dependent on the actions of two of more decision-makers (players).
• Players: A strategic decision-maker within the context of the game.
• Strategy: A complete plan of action a player will take given the set of circumstances that might arise within the game.
• Payoff: The payout a player receives from arriving at a particular outcome. The payout can be in any quantifiable form, from dollars to utility.
• Information set: The information available at a given point in the game. The term information set is most usually applied when the game has a sequential component.
• Equilibrium: The point in a game where both players have made their decisions and an outcome is reached.

Assumptions in Game Theory

As with any concept in economics, there is the assumption of rationality. There is also an assumption of maximization. It is assumed that players within the game are rational and will strive to maximize their payoffs in the game.

When examining games that are already set up, it is assumed on your behalf that the payouts listed include the sum of all payoffs associated with that outcome. This will exclude any “what if” questions that may arise.

The number of players in a game can theoretically be infinite, but most games will be put into the context of two players.

Example

Imagine you’re buying a car from a dealership.

The dealer wants to sell the car, and has a fixed price beyond which he cannot drop without making a loss. You want to buy the car, but get the best price. The car dealer bases his negotiating tactics on the fact that you want the car, that he could sell the car to another customer, that he’ll win praise for selling the car, and the break-even point beyond which he cannot negotiate down.

You base your negotiating on the fact that the dealer wants to sell the car, that there is a profit margin into which you can haggle to bring down the car’s price, and are mindful that the dealer knows your presence in his office means you want to buy a car.

Every time we interact with another human being, whether it’s eyeing up the last muffin at the coffee shop counter, or doing a favour for a work colleague that we hope will be repaid in kind, we’re using logic that could be described using the rules of game theory.