The Idea Of Promoting Non-zero Sum Games: How Winning With Others Helps You Win Bigger

Game theory is a branch of both Economics and Mathematics. 


When you start considering

  • your opponents 
  • possible action choices and respective outcomes of actions of both you and your opponents

you have entered the realm of Game Theory.

The field has found applications in areas as diverse as Artificial Intelligence, Evolutionary BIology and Politics.

A game where a player wins 5 points and his opponent loses 5 points is a zero-sum game.
5+(-5)=0.

On the other hand, in a non zero-sum game, the outcome is not zero.
For example, if a player wins 5 points and his opponent wins 2 points, the overall outcome is 5 + 2 = 7. So here we have a win-win, non-zero sum game – both wins.

Non-zero sum game doesn’t mean that you have to lose in order to make others win. The idea is not to think solely in terms of your profit but to develop business plans so that you win bigger by including others as “co-winners”. Here are some practical examples.

  • Lets consider Google’s Android Platform. Google could develop a mobile operating system and develop all the apps themselves. If that happened then we would have far less apps and more importantly, less innovative apps. But Android is an open platform. Anyone can develop apps for the Android platform. So in this case, Google didn’t want to win only by themselves. Google saw you – the app developer – as a co-winner. That is the reason why we have so many App developers making great money. Of course, Google is winning. Google is taking 30% cut. And Google is winning bigger by helping you win. As more apps are available, Android Phone / Tablet sell is on the rise. So just as Google and App Developers are winning, companies who advertise on Android are reaching more customers through the apps and winning bigger. And last but not least, don’t forget the customers whose lives are getting easier and richer with all these apps that app developers are developing. They are winning too!
  • As the economic condition of the developing and undeveloped nations rises, their purchasing power rises, which in turn creates opportunities for developed countries in our increasingly interconnected and interdependent world. Developed countries have more exports and imports among themselves. Why not plan for a future where all the countries have more to export and more to import? Won’t the citizens have a better and richer life? 
  • Google and Facebook have taken initiatives to increase Internet penetration, targeting “the next billion” or so they say, which in turn increases the number of users of their services. So here is the win-win scenario. 
    • Users learn more, communicate better, use better tools [apps] and as a result earn more + living condition goes up.
    • Marketers, App developers reach more of their customers and sell more of their products.
    • Google and / or Facebook get more cut.
  • Taking initiative to reduce Climate change should be win-win.
  • Here is how mobile 
    • fights poverty
    • bypasses poor infrastructure which could have been a roadblock to development 
    • makes companies get rich.

Organization Of The Study And Application Of Algorithms

Computational Abstractions

  • Control Abstractions
    • Loop 
    • Recursion
  • Data Abstractions 
    • Data Abstraction Components
      • Structure of Data
      • Operations on Data
    • Linear Data Abstractions 
      • Array
      • Stack 
      • Queue
      • Linked List 
    • Tabular Data Abstractions 
      • Hashing
    • Recursive Data Abstractions
      • Binary Search Tree 
      • Red Black Tree
      • Heap
    • Graph Abstraction
      • Model: Objects with binary relation defined on pairs


Computational Complexity

  • Time Complexity
  • Space Complexity  


    Algorithmic Paradigms

    • Dynamic Programming
      • Recursively define solution to problem in terms of solution to limited number of subproblems.
        • What could be the penultimate subproblems? (Work backwards.)
        • Subproblems having same structure as the original problem, only being smaller in size. 
        • Prove – defining solutions in terms of solutions to subproblems is optimal.
      • Compute and store the results of subproblems in memory so that you don’t have to recompute them. Then use the stored results to compute solution to the problem. 
    • Divide & Conquer
      • Divide the problem into subproblems (dividing up inputs into parts) and solve the subproblems recursively. 
      • Combine the results of solutions of subproblems.
    • Greedy
    • Backtracking
      • If you can define the space of all possible solutions, you can search the space for solutions systematically through backtracking. 
      • In backtracking, you generate one element at a time towards the solution and backtrack whenever you meet a dead-end.  


    Application Domains


    Design algorithms using 

    • Domain Knowledge
    • Computational Abstractions & Algorithmic Paradigms 

    Number Theory

    • Domain Knowledge: Prime, GCD etc.
    • Computational Abstractions & Algorithmic Paradigms: Loop, Recursion etc.

    Combinatorics

    • Domain Knowledge: Binomial Co-efficient, etc.
    • Computational Abstractions & Algorithmic Paradigms: Loop, Table, Dynamic Programming etc.

    String Processing

    Linear Programming


    Matrix Algorithms

    Computational Geometry

    • Domain Knowledge: Properties of geometric objects
    • Computational Abstractions & Algorithmic Paradigms: Stack, etc.

    Polynomials & Fast Fourier Transform

    Areas Of Mathematics I Am Working On

    Probability & Statistics

    • Probability.
      • Bayes. Bayesian Network.
      • Hidden Markov Model
    • Statistics
    • Stochastic models & processes

    Algebra

    • Classical Algebra
      • Polynomials
      • Inequalities
      • Series & Sequences
      • Functional Equations
    • Linear Algebra. Matrix. 
      • Eigenvalue. Eigenvector.
      • Latent Semantic Indexing.
    • Abstract Algebra
      • Group Theory 
    • Algebraic Geometry
    • Representation Theory
    • Category Theory
    • Quaternions 

    Analysis

    • Calculus
    • ODE
    • PDE
    • Real Analysis
    • Complex Analysis
    • Vector Analysis
    • Tensor Analysis
    • Fourier Analysis
    • Laplace Transform
    • Harmonic Analysis

    Geometry

    • Euclidean Geometry
    • Co-ordinate Geometry
    • Trigonometry
    • Topology
    • Manifold
    • Differential Geometry
    • Dynamical Systems

    Discrete Mathematics

    • Combinatorics
    • Combinatorial Geometry
    • Graph Theory
    • Automata & Language Theory. Boolean Algebra.
    • Number Theory
    • Cryptography
    • Mathematical logic

    Applied Mathematics

    • Algorithm
    • Game Theory
    • Concrete Mathematics
    • Operations Research
      • Optimization
    • Numerical Analysis. Scientific Computing
    • Network Science
    • Mathematical Economics
    • Mathematical Physics
    • Mathematical Biology
    • Theoretical Computer Science 


    And of course Mathematical Problem Solving and the study of heuristics.

    Anyone want to join me?