Game Theory: An Overview

The Basics Of Game Theory

Game theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology (most notably evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. 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 attempts to mathematically capture behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others. While initially developed to analyze competitions in which one individual does better at another’s expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria. Today, “game theory is a sort of umbrella or ‘unified field’ theory for the rational side of social science, where ‘social’ is interpreted broadly, to include human as well as non-human players (computers, animals, plants)” Here, we’ll take an introductory look at game theory and the terms involved, and introduce you to a simple method of solving games, called backwards induction.

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
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 that are 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. One of the simplest games is a sequential game involving two players.

Solving Sequential Games Using Backwards Induction
Below is a simple sequential game between two players. The labels with Player 1 and two within them are the information sets for players one or two, respectively. The numbers in the parentheses at the bottom of the tree are the payoffs at each respective point, in the format (Player 1, Player 2). The game is also sequential, so Player 1 makes the first decision (left or right) and Player 2 makes its decision after Player 1 (up or down).

Conclusion
By using simple methods of game theory, we can solve for what would be a confusing array of outcomes in a real-world situation. Using game theory as a tool for financial analysis can be very helpful in sorting out potentially messy real-world situations, from mergers to product releases.