Masdar Wireless Businessman, Computer Scientist, Blogger

Game Theory Essentials

This post is based mainly on the free on-line course at Coursera, named Game Theory which is provided by Stanford University and University of British Columbia.

A Brief Introduction to the Basics of Game Theory

The basic elements of performing a noncooperative game-theoretic analysis are (1) framing the situation in terms of the actions available to players and their payoffs as a function of actions, and (2) using various equilibrium notions to make either descriptive or prescriptive predictions.

In framing the analysis, a number of questions become important. First, who are the players? They may be people, firms, organizations, governments, ethnic groups, and so on. Second, what actions are available to them? All actions that the players might take that could affect any player’s payoffs should be listed. Third, what is the timing of the interactions? Are actions taken simultaneously or sequentially? Are interactions repeated? The order of play is also important.

Ascertaining payoffs involves estimating the costs and benefits of each potential set of choices by all players. In many situations it may be easier to estimate payoffs for some players (such as yourself) than others, and it may be unclear whether other players are also thinking strategically. This consideration suggests that careful attention be paid to a sensitivity analysis.

Games in Normal Form

Normal form games are often represented by a table. Perhaps the most famous such game is the prisoners’ dilemma, which is represented in Table 1. In this game there are two players who each have two pure strategies, where ai = {C, D}, and C stands for “cooperate” and D stands for “defect.” The first entry indicates the payoff to the row player (or player 1) as a function of the pair of actions, while the second entry is the payoff to the column player (or player 2).