Game Theory: The prelude (Part 1)
Introductory Notes, Formalism and Intuition
Introduction
Intention to write this series of blogs to introduce game theory without requiring any prior knowledge in advanced mathematics. Game theory have immense applications in fields like diplomacy, economics, trading and conflict handling.
Decision problems confront us every day, We play games of strategy all the time, with parents, friends and even contenders. Some games involve trivial decisions and other are serious, some have insignificant consequences and some have serious repercussions.
Why Game Theory ?
We have instinctive expertise over these decision makings, but the need for formalizing these decision making process in contention and creating a language for this strategic thinking is served by game theorists.
Every field in involves decision making, strategic thinking at some level, let it be war, diplomacy, finance, economics, trading and even rent split among room mates. Game theory provides a general concepts and techniques of analysis to help decision making.
Formalism !
Let's start with formalizing some terms we commonly use, but have subtly different meaning in the game theoretic approach.
1. Game Theory
2. Strategic Thinking
3. Rational
4. Strategic Game
- Game theory is the analysis, or science, if you like, of such interactive decision making. Provide some general principles for thinking about strategic interactions.
- Strategic thinking is about interacting with similar player thinking similarly in similar situation. As we must take into account what the other player is thinking, opponent is also taking into account what we are thinking.
- You are said to be behaving rationally, if you are choosing your actions in a way to do the best according to you own criteria, given your objectives or preferences and of any limitations or constraints on your actions.
Game theory provide some general principles for thinking about strategic interactions in order to behave rationally
4. Strategic game involves interactions between mutually aware players and decisions for action of each person depends on the actions taken by the contender and cross-effects derived from these actions taken by the contender and himself. The assumption is mutual awareness of the cross-effects of actions.
Examples
Let’s discuss few examples, these cases helps motivate the development of many conceptual or theoretical framework of game theory.
Example 1: Guess 2/3 of the Average
Game where several people guess what 2/3 of the average of their guesses will be, and where the numbers are restricted to the real numbers between 0 and 100, inclusive. The winner is the one closest to the 2/3 average.
Alain Ledoux is the founding father of the guess 2/3 of the average-game. In 1981, Ledoux used this game as a tie breaker in his French magazine Jeux et Stratégie. He asked about 4,000 readers, who reached the same number of points in previous puzzles.
Example 2: Keynesian beauty contest
Game in which entrants are asked to choose the six most attractive faces from a hundred photographs. Those who picked the most popular faces are then eligible for a prize.
Concept developed by John Maynard Keynes and introduced in Chapter 12 of his work, The General Theory of Employment, Interest and Money (1936), to explain price fluctuations in equity markets.
These are two popular examples which are used by academia to explain the concepts of game theory. Try to find out the answer for these two cases described above.
** Please note that it's not only about what you think the answer is, its also about what all other contenders think what the answer is.
In the next blog, we state some basic concepts and terminology for decision problems.
Thanks for your time
