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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).