The Book of Five Rings – The Water Book

Miyamoto Musashi’s Book of Water from the Book of Five Rings is about the ideas of form-ability, fluidity of water. The way we live and control our lives, the decisions we make, the actions we do are solely based on the behaviors and the routines we follow. It is really an understatement to call this book as a Guide for Sword-Fighters.

Miyamoto Musashi’s philosophy for 21st century

Ancient combat strategies for the modern competitions  

After understanding the Ground Book which builds the foundation of the Book of Five Rings by Miyamoto Musashi, we will deep dive into the next book called the Water Book. The general idea is to understand how water behaves, how it tries to bring in consistency throughout, how it tries to level even in disturbances, how a drop to drop creates an oceanic impact, how it flows and remains unobstructed of the challenges. The Water Book is about the the spirit of the warrior, the attitude, the way of looking at things and handling them, making decisions about them.  

“The principle of strategy is to have one thing, to know ten thousand things.

In short, know the ocean from single drop. Miyamoto Musashi wants to highlight the effectiveness of his strategy of Water by showing the consistency in these principles. Once a warrior understands a consistent idea, it becomes very easy for him to implement it everywhere effectively. Thus, by learning this consistent way of water if a warrior defeats his single enemy, he thereby also gains the ability to defeat the thousands of enemies singly. That is how effective these ideas from the Water Book are!

Language does not extend to explaining the Way in detail, but it can be grasped intuitively. Study this book; read a word and then ponder on it. If you interpret the meaning loosely you will mistake the Way.

This is exactly what has been already established in modern philosophy as the Language Theory of Philosophy by Ludwig Wittgenstein. An ancient, age-old warrior already understood this knowledge way ahead of his time. Miyamoto-san knew that a novice self-learner will take every word literally and hence will fail to actually grasp the depths of the wisdom he has shared. He wants readers to inculcate every word in their own lives. These are not ideas just for battling, killing and fighting. These are the ideas to handle any type of situations, people, systems in your everyday lives.    

The principles of strategy are written down here in terms of single combat, but you must think broadly so that you attain an understanding for ten-thousand-a-side battles.

The wisdom is so distilled and ubiquitous that it can be used in any battle, any problem solving.

If you merely read this book, you will not reach the Way of Strategy.

Again, this Book of Water rather the Book of Five Rings is not to be taken literally.

Spirituality – The Way of Life

In strategy your spiritual bearing must not be any different from normal. Both in fighting and in everyday life you should be determined though calm. Meet the situation without tenseness yet not recklessly, your spirit settled yet unbiased. Even when your spirit is calm do not let you spirit slacken. Do not let your spirit be influenced by your body, or your body be influenced by your spirit. Be neither insufficiently spirited nor over spirited. An elevated spirit is weak and a low spirit is weak. Do not let your enemy see your spirit.”

One has to now understand that Miyamoto-san even though explicitly talks about sword fights it is not only about sword fights. He wants readers to understand that the true greatness does not come from following special regime or following some trick or knowing some secrets. Actually, the secret to a great life is that there is no secret!

Miyamoto-san doesn’t want a warrior to force things. He wants everyone to be at their optimum, neither less nor more, neither in excess nor in scarce – just the perfect amount. Once this happens in a person’s daily routine then it becomes part of him, his way of life. Then even an extraordinary situation, a bad event doesn’t affect him. This is what discovering spirituality is!  

With your spirit open and un-constricted, look at things from a high point of view. You must cultivate your wisdom and spirit. Polish your wisdom: learn public justice, distinguish between good and evil, study the Ways of different arts one by one. When you cannot be deceived by men you will have realized the wisdom of strategy.

Miyamoto-san though promotes his “Way of Strategy” in the Book of Five Rings, he wants the readers to expand their vision, their perspectives to different arts too. The idea is that when you become aware of many things, many arts it becomes really difficult to fool you, to trick you. That is also a superpower in a way.    

Stance

Please mind that it is not just about how a warrior should stand in a fight. Stance here also means about your attitude in the situations of hardships and challenges. Here it goes:

  1. Adopt a stance with head erect, neither hanging down, nor looking up, nor twisted – Don’t project yourself as too proud or too peasant and helpless. Be at peace with yourself.
  2. Your forehead and the space between your eyes should not be wrinkled – Control and hide your anger and project it effectively when and where required
  3. Do not roll your eyes nor allow them to blink – Don’t fiddle, observe your surrounding with a calm and focused mind
  4. With your features composed, keep the line of your nose straight with a feeling of slightly flaring your nostrils – Be in the moment. Breath.
  5. Hold the line of the rare of the neck straight: instill your vigor into your hairline, and in the same way from the shoulders down through your entire body – Concentrate all your energy to your torso, your vital organs in order to handle what is to come next
  6. Lower both shoulders and, without the buttocks jutting out, put strength into your legs from the knees to the tips of your toes. Brace your abdomen so that you do not bend at the hips – Don’t tighten your body, don’t be stressed from the fear of your enemy. Loosen up your body to make it pliable to respond enemy attacks effectively.
  7. Wedge your companion sword in your belt against your abdomen, so that your belt s not slack – this is called “wedging in” – Prepare yourself to attack, tighten your core body, your weapons, your tools/ equipment to face any situation

“In all forms of strategy, it is necessary to maintain the combat stance in everyday life and make your everyday stance your combat stance.

Here you must understand that these are not the recommendations to warriors only. Miyamoto-san wants these to be the way of life. One has to really appreciate the depths of his wisdoms through these teaching.

Gaze – Don’t just look, have a vision

In strategy it is important to see distant things as if they were close and to take a distanced view of close things.

While doing all of these stances Miyamoto-san suggests to not get fooled by the appearances only. He recommended these mentioned stances in order to project strong warrior in front of his opponent. But what if the enemy also projects the same stances nevertheless, he is strong in reality? At these moments, Miyamoto-san guides to understand the big picture and the details to decide effective strategies based on the enemy’s behavior.  

Holding the Long Sword

Miyamoto-san beautifully explains the role of each finger on the grip of sword. It can only be experienced on personal level of reader and cannot be expressed in words only. But the overall idea is not just grab the sword with all five fingers rather make it an extension of your body which has its own reflexes.

Fixedness means a dead hand. Pliability is a living hand.

It is again a reminder to not blindly and mechanically follow the rule, tricks, or techniques. Become agile and formless, shapeless like water (..my friend!)

Be water my friend!
Footwork

Whether you move fast or slow, with large or small steps, your feet must always move as in normal walking.

Miyamoto-san here again says that there is nothing like “special technique” to defeat any enemy. When you are not forcing things to be there, you break the patterns, mechanical nature of your moves. Your moves, decisions become natural.   

You should not move on one foot preferentially.

If you have preferences, then it becomes easy to defeat you by attacking on your preferences, your preferences will make you more predictable.

“If you try to wield the long sword quickly you will mistake the Way. To wield the long sword well you must wield it calmly.

Any big responsibility, any big authority, any big decision, any big power should be handled wisely, calmly with a focused mind.

Way of the Long Sword

Miyamoto-san then exactly points out each and every technique to the student. The details with which everything is explained deserves great attention of every reader. The information is clear, concise and just enough.

a. The Five Attitudes

The great thing about a true master is that he is the ultimate simplifier. A true master knows how to teach complicated and intertwined knowledge points in simplified ways without losing the essence of the concept. Miyamoto-san thus incorporates his exact learning into small chunks of wisdom where every word is just enough to grasp the whole concept.

Miyamoto-san at the very beginning makes clear as to where exactly the sword is supposed to be used. The five attitudes he describes seem very simple. The five attitudes are:

  1. The Middle attitude – it is about hitting (and killing) the enemy by striking on torso and vital organs with sword against his face  
  2. The Upper attitude – it is about exactly striking upper blow of sword when enemy attacks and when he escapes this cut Miyamoto-san guides to follow the flow on line and scoop from below
  3. The Lower attitude – it is about hitting the hands of enemy from below, Miyamoto-san also suggests that this is the most encountered stance from enemy
  4. The Left-side attitude – it is about hitting the hands of enemy from below and parrying the same attack to cut from his left side
  5. The Right-side attitude – it is about crossing enemy’s sword attack from below and swinging it further and using upper strike from the right side

These are in simple and no-nonsense words, the five directions in which you can swing a sword to kill your enemy. You really have to understand that the reader of this book especially the pupil learning swordfight are supposed to have that innate natural excitement of learning something special from the great master – his tricks and secrets to become invincible. But the great Sword-master Miyamoto-san delivers his wisdom in the ways of common sense. And believe me it is not sarcasm, rather Miyamoto-san is very serious while discussing the five attitudes here. The whole idea of five attitudes is that, there are mere five vital regions where one has to focus to defeat his enemy. And in those five the Middle Attitude is the most vital. (Logically, the middle region, the torso of human body consists most of the vital organs in human body so it already makes more sense)

“To understand attitude, you must thoroughly understand the middle attitude. The middle attitude is the heart of the attitudes. If we look at strategy on a broad scale, the Middle attitude is the seat of the commander, with the other four attitudes following the commander. You must appreciate this.

The attitudes are not there only to explain the parts of human body, it also represents the whole organization of the enemy’s battalion. All the vital weaponry, the best of the best soldiers, the best diplomats, the best strategists are the middle part of every commander on battle-field. Miyamoto-san suggests to focus on this middle part while defeating enemies in masses. Such hidden and smart instructions are hidden and scattered all over the Book of the Five Rings.     

b. The “Attitude No-attitude” teaching

Miyamoto-san gives five attitudes to fight at first and then instructs to forget about them here.  Please understand that the five attitudes are not just “A Guide to Basic Human Anatomy” for the sword-fighters. There is deeper meaning in Miyamoto-san’s advice.

Whatever attitude you are in, do not be conscious of making the attitude; think only of cutting. Your attitude should be large or small according to the situation.

One can understand it like this – Do not get overwhelmed by the thought of deciding which approach to select to kill the enemy. Actually, if one gets tangled and confused in selecting the right approach, he will immediately loose his life to his opponent as the enemy has already stricken him.

One should only focus on intent to kill the enemy and let the right attitudes come out of those attitudes. Even though five attitudes are defined that does not mean that they are supposed to followed mechanically. This way of mechanistic selection and confusion from it disappears when one does enough practice which is what Miyamoto-san focuses and instructs everywhere.

Fixed formation is bad

Again, Miyamoto-san suggests to be fluid, non-fixated, agile, flowable like water.

c. To Hit the Enemy “In One Timing”

The idea is to not hesitate to act on right opportunity with the full intent of killing the enemy

d. The “Abdomen Timing of Two”

Don’t spare your enemy even when you see him retreating, when you see him relaxing follow him up with a cut

e. No Design, No Conception

Go fully “in” when you see enemy going fully “in”. Use everything you have, don’t follow the structuredness and rigidity of some tricks you learned elsewhere. Again, be fluid in nature, respond accordingly.

f. The Flowing Water Cut

When your strike fails, when you fail (in anything in your real life too) widen your perspective, expand your spirit and this time strike your next blow slowly but decisively, thoughtfully. Miyamoto-san understands that when the enemy sees his strike winning, the true warrior must make a conscious effort to not let his enemy’s morale raise high with this small win. Miyamoto-san call it like “Stagnant water”, when you blow fails, pause-think-come back with full intent of focus.

g. Continuous Cut

When you realize that the enemy- opponent is equivalent to you and it is difficult to defeat (kill) him; then you should attack in such way that it will harm the enemy at multiple locations. Try to hit as many birds as possible in single stone when you are fighting an equal opponent. It is about effectiveness and efficiency of your single stroke.

h. The Fire and Stones

When fight goes one-to-one make sure that it hits different parts of the enemy.

i. The Red Leaves Cut

Force the enemy to lose his sword, his vital and important tools, weapons like a falling and dying red leaf of fall. Disable the enemy by capturing his resources.

j. The Body in Place of the Long Sword

Don’t just be too focused on your weapon, your sword, your tools and resources. Use your body to attack the enemy. If you can focus on getting the control of enemy’s sword, he can think of you similarly. So, with sword use your body too.

k. Cut and Slash

Miyamoto-san here clarifies that cutting is about cutting with full intent of killing but slashing is just touching the enemy, injuring him.

Be decisive about your moves before attacking and be ready to accept the consequences.

Miyamoto-san explicitly clarifies additional thing here:

“Even if you slash strongly, and even if the enemy dies instantly, it is slashing.

I would like to highlight one very important bias that every learner every, student faces in their learning process, especially when they are leaning on their own which is the “Outcome Bias”. Many a times we make some hypothesis on the inner working of the things which we are trying to understand and it eventually happen in the end but in somewhat different ways- in a way we didn’t expect but it happens. Does that mean that we have completely understood everything? The answer is “No”. This is known as the “Outcome Bias” where you decide whether a certain action is right or wrong based on the outcome and the outcome might be just luck. So, it might be a possibility that your hypothesis is wrong.

The outcome bias is dominant in self-learners which Miymoto-san expertly points out here.

l. Chinese Monkey’s Body

Don’t extend yourself partially in enemy’s territory just like Chinese Monkey’s body in Miyamoto-san’s words. If you extend your arms towards the enemy, the enemy will grab you by your arms and pull you in completely.

m. Glue and Lacquer Emulsion Body

When you engage with the enemy make sure that you engage fully. As in do not lose the contact with your enemy when you are really in the fight. Otherwise, you will be unable to anticipate and react to your enemy’s next blows.

n. To Strive for Height

Once engaged with enemy in fight, establish dominance in every possible way, don’t let your enemy’s morale rise up and take the high ground. (That’s exactly what Obi-Wan Kenobi did)

o. To Apply Stickiness

When fully engaged, stick with the enemy; don’t lose touch of him and his sword. Reduce the strength of the strike but keep in touch with his blade, that will help you to gauge his moves immediately.

p. The Body Strike

Find the weakness of the armor and directly attack the body through that weakness.

q. Three Ways to Parry His Attack

When enemy blows attack, target his important areas first for counter attack. First way is to attack on his eyes-his vision; second on his neck, the part which connects the mind and the tools of any organization, any battalion; third on his face, on the image and perception of the organization, the battalion.

r. To Stab at the Face

Stabbing at face means to destroy the senses and the mind of the opponent. Face as in head is eyes, ears, nose, tongue, skin and mind all in single spot which is another vital region of the body. Once you drive the head, the complete body will follow thereby making enemy predictable to attack and kill effectively.

Try to control enemy’s moves by explicitly targeting his most important parts with full intent.

s. To Stab at the Heart

When you are tired, just blow single and focused strike on the vital part of the enemy.

t. To Scold “Tut-TUT!”  

Make sure that your enemy understands that your counterattack was intended to hurt, kill him. Try to bring down his morale. Don’t let him think that he has won.

u. The Smacking Parry

If you develop a rhythm of attacks in your fight, you can still handle the coming blows from enemy and simultaneously hurt him with counterattacks. It’s about developing a sense of timing.

v. There are Many Enemies

When you are alone and surrounded by many, don’t hesitate and wait; attack with the intent to kill many in single strikes. Don’t attack and strike from front or head on; approach and attack from sides.

Whatever you do, you must drive the enemy together, as if tying a line of fishes, and when they are seen to be piled up, cut them down strongly without giving them room to move.

w. The Advantage when Coming to Blows

Go out, practice, and implement your truths, your learnings in reality.

x. One Cut

Become a master in such way that it looks effortless to others. (like Saitama!!!)

While actually reading all these ways to kill the enemy with sword, you will feel like you are actually witnessing these iconic sword strikes in a sword fight or like an intense sword fight in an anime. Miyamoto-san creates a live picture of strokes of sword in his writing while writing all this, which itself is a great experience for readers.

Closing remarks of the Book of Water

In the closing remarks of the Book of Water, Miyamoto-san instructs to make these ideas the way of life. He wants these ideas to become part of your habits. When they will get reflected in your habits the body will react naturally to the challenges as if these techniques are second nature for it. Miyamoto-san expects a flow, a harmony like water in the rhythm, spirit of the readers while handling sword or any situation in their life.

“Step by step walk the thousand-mile road

Miyamoto-san is aware that the novice will get overwhelmed by the details and the number of the teachings from the Book of Water alone. He wants the student, the warrior, the reader to learn one by one, one at a time and imbibe it in their lives.

“Study strategy over the years and achieve the spirit of the warrior. Today is victory over yourself of yesterday; tomorrow is your victory over lesser men.

It is about practicing, relearning and distilling down the wisdom over the period. This is only possible by discipline. Only discipline will bring out the best version of you from your personality of times gone, once you become something different and greater from your previous version nobody can stop you. Discipline is the way.

Even if you kill an enemy, if it is not based on what you have learned – it is not the true Way.

In the end of the Book of Water, Miyamoto-san explains the only way to develop wisdom. Knowledge can be transferred, can be taught from one person to another but wisdom always develops from inside. And as it develops from inside, there is very high possibility that it will be full of biases as these are self-truths. Hence clearing the biases in your learning process by continuously practicing them with reality is the way. One must be always be sure about the hypotheses in their knowledge building process in order to create the real wisdom.

Miyamoto Musashi’s Book of Water from the Book of Five Rings is about the ideas of formability, fluidity of water. The way we live and control our lives, the decisions we make, the actions we do are solely based on the behaviors and the routines we follow. The ideas expressed in the Book of Water are can also be connected to Game theory, Corporate Strategies, Principles of War Strategies and Diplomacy, Human psyche, Competitiveness, Lifestyle, Resources and Manpower Management, Spirituality and nonetheless Philosophy of Life and Knowledge. It is really an understatement to call this book as a Guide for Sword-Fighters.

What is special about water? That it is so omnipresent that it is not that special. It is so formless, shapeless that it takes shape of anything. Water has ability to make impact even when it is in drop and even when it in the form of ocean. The specialty of water is that it is not special, or at least no specialty can be assigned to it. It is water’s fluidity, pliability to the situations which enables it to take their forms which is what makes water so special. That is exactly what Miyamoto-san establishes here for the ways to live life thereby with the battles and fights in it.  

Links for further Reading:

  1. The Book of Five Rings – The Ground Book
  2. The Book of Five Rings – The Water Book
  3. The Book of Five Rings – The Fire Book
  4. The Book of Five Rings – The Wind Book
  5. The Book of Five Rings – The Book of the Void

Game Theory – Minding our decisions

“All stable processes we shall predict.

All unstable processes we shall control.”

– Jon von Neumann

Human relationships are more of multiple complex interactions. The interactions with living or non-living bodies create some actions and these actions have some favorable or unfavorable outcomes. The word “relationship” here is not used just as in parents, siblings, in-laws or acquaintances but as a connection to everything around us, mostly living things. The awareness of our actions and their consequences- that visualization of cascade is one of the major parts of our knowledge building, relationship development, behavior management, personality development.

As a sane creature (most of the time) we try to calculate the consequences of our actions, have a thought about it and then decide our strategy while acting on something. This is what some people call the motivation or habit or trait of that person, that character. Important thing to understand is that every action always has multiple outcomes which brings the complexity in the expected outcomes of the scenarios. Different people have different motivations/ habits/ traits so they react and decide in different way adding further complexity to the scenario.

Take a simple example:

Many a times when you are trying to call your friend this happens. You call him, his phone rings but he doesn’t pick up. Then he notices the missed call and tries to call you while you are already calling him. The call remains engaged from both sides. Then you both wait for exactly the same time oping that the one on other side will call.

This goes for some time, and after some trial and error your call gets connected.

What should be an optimal strategy for such simple scenarios?

There is a rigorous field of mathematics and economics (not limited to these only and rather a wide field) which can deal with such problems and far more complex problems in our day-to-day interactions.

“Game theory is the study of mathematical models of strategic interactions among rational agents.”

 Simply put, game theory can give answers to have the best strategy for the interactions which can be business interactions, economical interactions, national interactions, war strategies or competitor strategies. The idea of Game theory was developed by famous mathematician Jon von Neumann and economist Osker Morgenstern. Let us dive in deeper.

Basic Definitions in Game Theory

Game– A game is any situation in which players (the participants- the agents) make strategic decisions—i.e., decisions that take into account each other’s actions and responses.

Agents– The participants, the players of the game.

Rational Agents– This is the most important idea in Game theory where the rationality of agent is the idea of welfare of the agent. The agent will always try to achieve its own welfare. In economics this is known as maximizing the utility.

A rational agent always tries to maximize its utility.

Strategy– Rule or plan of action for playing the game.

Payoff/ Outcome– The value of utility, extent of welfare from certain strategy. It is numerical, quantified measure of the benefit from a strategy.

Optimal Strategy– A strategy which maximizes the utility of an agent.

Please note that the clear definition of utility, rational agent, optimal strategy defines the boundaries of the problems in Game theory thereby making it mold-able into the mathematical models (although mathematical models can consider the factors beyond boundaries but it will make the problem unnecessarily complicated). Mathematical models as in the mathematical equations which can be solved using general techniques to get the maximized outcome for the agents.

Please note that the word “Game” in game theory can be any situation which requires strategic decision making involving more than one agent. The game can be simple like Stone-Paper-Scissors, Tic-Tac-Toe or a Chess game to more complex game like launching a new smart phone in the market or taking over a company or setting up a war with a nation or even winning the general elections of the country.

The Prisoner’s Dilemma

The Prisoner’s Dilemma is the most common and famous example to understand the basics of Game Theory. Consider a scenario:

Two persons are arrested by Police under the crime of armed robbery. The Police know that they have committed this robbery together but they don’t have enough proof to justify that. They can only charge the persons under the theft of the car used for robbery due to lack of evidences. Police think that if both persons confess the armed robbery, then they can easily jail them under the proper charges of armed robbery. So, they lock each of them in separate cell and ask them to either confess or deny the crime.

The police inspector tells each one of them separately in their cell the following:

If only one of you confesses the crime and the other doesn’t, then the one who confesses will be freed but the another one refusing will be sentenced for 10 years. If you both confess, you’ll each get 5 years. If neither of you confess, then you’ll each get two years for the car theft.

Now, if we see the overall scenario, the best thing for both the prisoners is to deny the crime and set themselves free at first, but if you think properly of all the consequences and the information available to both the prisoners, that is not the best strategy.

The common information of three possible cases given to both the prisoners by the policeman is known as Information Set in Game theory.

So, the outcomes of such scenario can be arranged in a table to form a matrix which is also known as the Normal Form in game theory.

If we assign a number to each the payoff of each strategy,

  1. 0 for the worst case- 10 years of jail
  2. 2 for 5 years of jail
  3. 3 for 2 years of jail
  4. 4 for becoming free, no jail

then the normal form can be given as follows:

Decision Matrix

 It becomes very easy to see as an agent of this game- the prisoner will try to maximize his utility by refusing the crime thereby setting him free. But the catch here is that he doesn’t know what another prisoner has done- whether he confessed or refused the crime.

Now, we need to understand that the final outcome is not dependent on only one prisoner decision. Hence, the decision making of second prisoner will affect the decision making of first prisoner. Let us see from the perspective of Prisoner 1:

  1. Refusing should be the best idea, but if Prisoner 1 refuses and the Prisoner 2 confesses then it will lead to 10 years of imprisonment (zero utility) for Player 1 more risky operation as he is not sure about Prisoner 2’s decision.
  2. If Prisoner 1 confesses the crime, then there are two possibilities:
    • Prisoner 2 also confesses thereby both will get 5 years of sentence (utility of two)
    • Prisoner 2 denies thereby prisoner 1 getting freed and Prisoner 2 gets sentenced for 10 years (utility of 4 for prisoner 1 and zero for prisoner 2)

 So, confessing becomes the best strategy for both the prisoners when they are in an isolated cell.

Which is why the optimal strategy for both the prisoners of this game is to confess. In any possible decision by another prisoner, it will give the best possible outcome.

The one thing important to notice here is that they both could have refused simultaneously. Because, if they both refuse it would have maximized the utility of both (2 years of jail for both, utility of 3 for both). The thing is that the risk associated with refusing is more than the risk associated with confessing. Thus, even if the utility is highest in some cases the interaction of other players forces a player to choose optimal strategy which will yield the best irrespective of other players decisions.

The Nash Equilibrium

Mathematician John Nash took the Game theory developed by Neumann and Morgenstern and provided mathematical background for finding the strategy where the solution will be optimal irrespective of the decision made by the other players. For that we need to understand the two types of games – Cooperative and non-cooperative games

If the prisoners in above examples are supposed to have a word with each other before presenting their opinion to the police they surely would have understood that refusing will benefit them both, which when exploited is a collusion – a foul play, here in the prisoner’s game it is exploited.

But as we know in reality, even if they are given a meet to discuss before presenting their opinion there is still that risk of changing the statement at the last minute (!) thereby making the game a non-cooperative game. Nash Equilibrium exists in such non-cooperative games.

A cooperative game represents the game where players agree to work towards a common goal. It’s like splitting your restaurant bill with your friends. Here the main focus remains on the contribution from each player, like Coalition of Countries to reduce carbon footprint, to stop Global Warming. Shapley value is used in cooperative games instead of Nash Equilibrium. Shapley value distributes the payoff based on the contribution a player makes in the game.

Shapley value simply decides the fairness of payoff for each player in cooperative game whereas Nash equilibrium decides the best decision to maximize the payoff in a non-cooperative game.   

“In non-cooperative games there exists an equilibrium at which no side has any rational incentive to change the chosen strategy even after running through all the choices available to the opponent”

In short, Nash Equilibrium is like a law which needs no punishment to enforce to the rational people, because the people understand that breaking that law will not benefit them.

It is like following a traffic signal properly. If all will rush at the crossing all will be late in their journey maybe possible deaths due to accidents. Following the time-based signal will give opportunity to everyone, thereby zeroing the risk of accidents and saving the travel time. (And still some people break the signal, hence the word “rational agent” is of highest importance in Game theory!)

John Nash – a mathematician received Nobel Prize in economics for his work of Nash Equilibrium. The development of mathematical tools further for game theory revolutionized the economics. The movie on his life called “A Beautiful Mind” depicts his original thought process in a beautiful way.

“I can observe the game theory is applied very much in economics. Generally, it would be wise to get into the mathematics as much as seems reasonable because the economists who use more mathematics are somehow more respected than those who use less. That’s the trend.”

– John Forbes Nash Jr.

Assumptions of Game Theory

  1. All players are utility maximizing rational agents that have full information about the games, rules and the outcomes/ payoffs. (So that the mathematical models will fit)
  2. Players are not allowed to communicate – no coalition in a bad way – no collusion- no foul play (hence the reason Governments also establish anti-collusion, antitrust laws, anti-monopoly laws in real world)
  3. Possible outcomes are known in advance and cannot be changed (Deterministic models, hence the reason many equity traders try to find some trends in the equity indices based on certain assumptions)
  4. The number of players can be infinite but most of the games will contextualize in terms of two players only (thereby simplifying the model).

Strategies of Game theory

  1. Pure and mixed strategies:
    • PURE- Players follow same strategy in the game- All the companies may increase the product prices of their products to increase the profit. (Actually, it not that simple)
    • MIXED- Different players follow different strategy in the game. (One company will try to sell less but expensive units, the another one will try to market the best-in-class after-sales services) 
  2. Dominant and dominated strategies:
    • A dominant strategy leads to the best of all alternative payoffs
    • a dominated strategy leads to the worst of all alternative payoffs
    • Say, there are two companies A and B both have two products – consumer and professional. The market has 80 % of consumers and 20 % of professionals. What can A and B do.
    • Company A and B both will enter both the consumer and professional market hence each will get 50% of the share from total market (half of consumer i.e., 40% consumer and half of professional i.e., 10% of professional market to each company), thereby maximizing the utility which is Dominant Strategy
    • Company A and B both will enter only professional market (which is already 20% of whole market- smaller market share) so both will get only 10% each of the total market thereby getting the least amount of market share which is Dominated strategy
    • Only company A can enter in consumer market and company B can enter professional market thus one will get complete consumer market and the another will get complete professional market. Reverse is also possible here.
    • The example i) here is called as Strictly Dominant Strategy, example ii) is called as Strictly Dominated strategy.
  3. Maximin strategy – A strategy which will maximize the profit, the utility in the game
  4. Minimax strategy- A strategy which will minimize the loss in the game

Game Theory for Life- The Concept of Finite and Infinite Game

The applications of Game theory are uncountable in real world. The complexity of real-life problems projects an impression as if Game theory has just started developing like a new born baby. The problems Game theory can solve and the promises it provides can add great value to humanity.

In order to understand the depths of the contributions of the Game Theory, we must understand the idea of Finite and Infinite Game.  

The finite game has known players, fixed rules, has an end point where there is one winner and there in one loser- a zero sum game. Like the game of chess, the game has two players, all the rules are fixed and cannot be changed by some external influence, either one of the kings gets the checkmate or the match becomes draw- no win or no lose- the game ends.

The infinite game is an eternal game- it goes on. The resources are infinite, the rules keep on changing, the players come and go. The infinite game is similar to what our life is. If one knows how to win an infinite game, then he/she can also win a life.

Simon Sinek has a beautiful book called “The Infinite Game” where he has explained how to win at an infinite game and thereby possibly at life. The insight from the idea of an infinite game is that the main goal of the game is to keep it playing. As the resources are infinite, players are infinite, rules are changeable- there is no endpoint for such game which will justify the worth of the winner. There is no winner.         

Most of the games in economics, finance may seem finite games for once but deep down, when explored further are the infinite games, our life is the best example of it. Simon Sinek has given many lectures, talks about the mindset for infinite game which are beautiful. They are beautiful because they reflect the philosophical nature of Game theory and its synergy to human decision making which is not rational all the times. Simon Sinek highlights on five headers while discussing the infinite games.

  1. Just cause- A Specific vision for the future which is yet to exist. It is powerful enough to motivate people, make sacrifice for it.
  2. Trusting teams- Creating room for improvements, improvements will lead to evolution, development. This will truly lift the human spirit. It is about the creation of psychologically safe environment where people can demonstrate who they are and improve over it to last longer in the game.
  3. Worthy rival- As the game is infinite- won’t end, the rival should always inspire one to elevate the game thereby strengthening both the sides. If the rival is not strong- worthy the game will end to some part but still new player will enter and perpetuate the game, thus the sustenance demands worthy rival.
  4. Existential Flexibility- Disruption for more effective development leading to evolution
  5. Courage to lead- Given the uncertainty of the outcome, a risk-taking attitude for the unknown but good future dependent upon the just cause is important to live through the infinite game.

Such ideas given for the infinite game can help build better organizations, better teams, better institutions.

“An infinite mindset embraces abundance whereas a finite mindset operates with a scarcity mentality. In the Infinite Game we accept that “being the best” is a fool’s errand and that multiple players can do well at the same time.”

– Simon Sinek, The Infinite Game

The Game theory itself represents an institution which has proved to become useful in not only economics but also in philosophy of humanity.

(We can deduce the optimal strategy for the engaging phone call game using Game theory. The optimal strategy is to do what both sides were doing before initiating the call. Thus, the one who tried calling first should continue calling whereas the one receiving the call should wait for the call rather than calling back! Please assume the rationality of your friend, willingness of your friend to accept the call, strong signal strength for the game!)

References and Further Readings:

  1. The Infinite Game by Simon Sinek
  2. Ross, Don, “Game Theory”, The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), Edward N. Zalta (ed.)
  3. Game Theory: Definition, Role in Economics, and Examples by investpedia.com
  4. What game theory teaches us about war | Simon Sinek – TED Archive
  5. The Infinite Game for New York Times
  6. Strategic Dominance: A Guide to Dominant and Dominated Strategies by effectivology.com
  7. Photo of Jon von Neumann from Wikimedia and www.lanl.gov
  8. Photo of John Nash from Wikimedia and Peter Badge
  9. Photo of Simon Sinek from Wikimedia
  10. Memes from