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Nash Equilibrium


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Nash Equilibrium is a game theory concept where in a multi player strategy game, no one player will gain any benefit by changing their strategy while other players keep theirs unchanged. This implies that current strategies and the resulting payoffs are in a state of equilibrium

 

An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Nilesh Gham on 10th January 2020.

 

Applause for all the respondents - Nilesh Gham, Mohamed Asif, Shashikant Adlakha, Sudheer Chauhan, Deepak Pardasani, Ajay Sharma, Saravanan S

 

Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.

Question

Q 225. As per Nash Equilibrium, one cannot predict the result of the choices of multiple decision makers if one analyzes those decisions in isolation. Instead, one must ask what each player would do, taking into account the decision-making of the others.

What is the practical utility of Nash Equilibrium in Organizational Decision Making?

 

 

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"Adam Smith was wrong!! Adam Smith was wrong!! The best result will come, when the individual does what's good for himself, AND the group", a phrase by Russel Crowe portraying John Nash in the lovely movie A Beautiful Mind. And those very words describe everything that there is about the Nash Equilibrium.


At the outset, Game theory tries to look at how individuals (or a collection of individuals) make choices that will, in turn affect other's choices. 
Nash Equilibrium makes reference to a condition in which each individual makes an optimized outcome, based on the expected decisions of others. 
Below are a few popular Game Theory Strategies/ Scenarios each one with of course, much more technical and mathematical workings of various scenarios involving the roles of individuals and the groups. Note that they are called "Games" but are correlated scenarios in the real. Many lab experiments have been conducted and outcomes deduced. 

 

1. The Prisoner's Dilemma:

In the prisoner’s dilemma, two suspected criminals are caught for a crime and are questioned in separate rooms. They cannot talk to each other. each suspect is told individually that if he/ she confesses AND gives a testimony against the other suspect, he/ she can go free, but if the doesn't co-operate, and the other suspect co-operates, he would be sent to prison for three years. 
In case they both confess, they would be given a two year sentence. If non of them confesses, they would be given 1 year in prison. 
Co-operating with each other is the best strategy for the two suspected criminals, when confronted with such a scene, research has shown that most people prefer to confess and give testify against the other, than to remain silent and take the chance that the other suspect would confess. 

 

2. Matching Pennies:
This is a game that has two players A & B, who place a coin on the table at the same time. they result depends on if the coins match. If both coins have heads (or tails), A wins and keeps B's coin too. If the heads/ tails don't match, B wins and keeps A's coin. 

 

3. Deadlock
A very trivial and common example of this game is of two nations have Weapons of mass destruction and are trying to reach agreement with each other on eliminating their stocks of such weapons. Here, co-operation would mean sticking to the agreement, while not agreeing would mean secretly retaining these weapons and not destroying them. The best outcome of such a a deadlock, is in despair, to secretly retain the weapons while the other nation destroys it's stockpile. Clearly, this will give a tremendous, but hidden advantage over the other nation, in case a war breaks out. Thus, sadly, the next best option is for both to retain their status of having Weapons of Mass Destruction 

 

4. Cournot Competition
Assume that two companies A and B manufacture the same product and can produce quantities in large and small numbers. If they both agree with each other to produce small numbers, then an overall lesser supply in the market would give a high price for the product and high profits for both the companies. However, if one of them does not agree and makes larges quantities, the market will be flooded with the product(s) at a low price and thus, reducing profits for both companies. However, if one of them agrees and makes less quantities, and the other makes large quantities, the one making less product would barely break even while the one making large quantities would have a much higher profit than if the both agreed


5. Co-ordination
Assume two tech giants which are choosing and deciding to introducing a dashing new technology in microchip the would help generate millions of dollars in profits, or a revised version of a legacy technical that would generate less profit. If one of giants goes ahead with the new tech, the rate of adoption and use by customers would be much less, and as a consequence, this company would earn much less than if both of them decide on the same course of action.

consider two technology giants who are deciding between introducing a radical new technology in memory chips that could earn them hundreds of millions in profits, or a revised version of an older technology that would generate much lower profits. If only one company decides to go ahead with the new technology, rate of adoption by consumers would be significantly lower, and as a result, it would earn lower profits if the two firms decide on the same course of action. 

 

6. Centipede Game
An extensive-form type of game, in which the two players get an alternating chance to take the bigger portion of a slowly rising pile of cash. The Centipede game happens sequentially, since each player makes his/ her move after the other, rather than at the same time. Every player is also aware of the stratagems chosen by the other players who played and performed this game before them. The game finishes as soon as one of the players take the case pile, with this player having the larger portion and the other player getting the much reduced portion. 


7. Traveler's Dilemma
In this game, a travelling company (say an airline) agrees to give compensation to two passengers with identical damages. The two passengers are separately asked to valuate the damages with a minimum of Rs. 5 and a maximum of Rs. 150. If both estimate the same value, the travelling company will give each of them that amount as reimbursement. However, if the estimates and values are different, the company will pay the lower estimate. with a small bonus of Rs. 5 to the passenger who wrote this lower estimate and a penal fine of Rs. 5 for the passenger who wrote the higher estimate. 

 

8. Battle of the Sexes
This is again a form of co-ordination game as in 5. above, however, with some dissimilarities in the pay offs. This type essential has a couple trying to co-ordinate their night out. They had been in agreement to go either to see the cricket match (the husband's preference) or a drama/ movie (the wife's preference), but, they have forgotten what they decided and to complicate the problem, they cannot communicate with each other. How should they manage this and where should they go? 

 

9. Dictator Game
In this simple game, say with two players A and B, A should decide how he would split a high cash prize with B, who has no inputs in A's decision. This many not be a game theory strategy, but it provides good insights into people's behavior and responses. 


10.Peace-War
This is an interesting variation of the prisoner's dilemma where the "co-operate or non-co-operate" is replaced by a "peace or war". A simple analogy would be to compare two companies who are competing in a price war. If both don't cut the price, they enjoy a prosperity in relation to each other, but a price war would reduce payoffs dramatically. However, if one company reduces prices, and the other does not, the first company would have a much higher profit, since it may be in a position to gain substantial market share, and the large volumes generate give lower production costs. 


11. Volunteer's Dilemma
Here, imagine one has undertaking volunteering work for the common good. The most dreaded outcome would be if none volunteers. Image a company where there are many accounting frauds, and the top management is not aware of it. Many junior workers in this department could be aware of these fraudulent activities but would hesitate to convey to the top management it could result in the employees who are involved in the fraudulent activities to be removed from duty possibly with court proceedings against them as well. 
Also, being a whistle blower could also have it's own repercussions, However, if nobody volunteers, the big fraud could result in the company's eventual demise with everyone loosing their dear jobs. 


Organizations can benefit greatly using these concepts, either individually or in combination with one another. 
The Nash Equilibrium has many applications from evolutionary biology, politics, International Relations, economics, etc. 
 

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Benchmark Six Sigma Expert View by Venugopal R

'Game Theory' relates to study by theoretical framework and mathematical models to comprehend social situation among competing players and provide optimal decision making. In Game theory, Nash Equilibrium refers to a state of decisioning, among two or more players, in which each player understands the ‘equilibrium strategy’ of other players and no player can gain anything by changing their strategies. The idea has been illustrated in most literature on this topic using a popular example on ‘Prisoner’s dilemma’.

 

To see the application of Nash Equilibrium in a business scenario, we may consider two competing companies A and B, trying to fix their pricing strategies for a competing product. However, a relatively higher pricing can pull down the sales and in turn the overall profits for the companies. Let us assume that the strategy of one player is known to the other player.

 

The different scenarios could be as follows:

1.       Player A fixes High price and Player B also fixes High price

2.       Player A fixes High price and Player B fixes Low price

3.       Player A fixes Low Price and Player B fixes High price

4.       Player A fixes Low Price and Player B also fixes Low price

 

The scenarios are represented in the table as below. Let us fix a numerical index of profitability, that is shown inside the cells of the table. The first number represents the profitability index for Player A, and the second one represents the same for Player B.

image.png.367640b336b92c9470fe5805462bc6c7.png

The profitability index is influenced by price and volume. However, a higher price would pull down the volumes thus reducing the overall profitability. Thus from the above table it appears that at lower price has led to improvement of overall volumes from both the players resulting in best profitability index for both.

 

As we can see for scenario 1, both the players have equal profitability index. However, Player A would be tempted to move to scenario 3 to increase its index. Similarly, Player B might shift to scenario 3 to improve its index. Also, in the scenarios 2 and 3, there is a possibility for players A and B respectively to attempt improvement to improve their competitiveness with respect to profitability index. However, in scenario 4, neither of the players will see a benefit in changing their strategies with respect to their competitor’s strategy and hence we can expect the best stability. This state represented by scenario 4 in this example denotes the Nash Equilibrium. In this state, there is a ‘Win-Win’ situation for both the players as well as for the consumers!

 

We may think of another business situation where the players could be the Marketing department and the Product development department. While the Product development’s strategy is to include more innovative features into a newly developed product, the Marketing’s strategy is to time the launch of the product to beat the competition. We can build a scenario to study the effect on the ‘Market success’ of the product and the factors would be the level of innovative features and the time duration for launch. There could be a state of Nash equilibrium, where both the players may not want to alter their strategies, after knowing the other’s strategy. At the Nash Equilibrium state, the Marketing would not want to squeeze the dates any further since, the product competitiveness may be affected. The Product Development would put a freeze on the features to abide by the launch dates, otherwise there is a risk of their future funds getting impacted due to potential loss of revenue opportunity. Again the Nash Equilibrium will get them settle for a Win-Win situation!

 

The above examples have considered only 2 players for simplicity, whereas there could be more in real life scenarios.

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By Definition: Nash Equilibrium is a stable state of a system having interaction of different players were no player can gain by taking independent(in isolation) change of strategy if the strategies of the other player remains unchanged.

 

Below is the Payoff Matrix for Company A & B for their decision for diversifying or not.

NE1(Asif).thumb.png.1b2656f823daa3b6b78d822a4745277a.png

 

In this scenario,
Players” are the firms, Company A and Company B

Moves” are the actions the firms can take: Either Diversify or not diversify
(:unsure:Something like Apple’s strategic decision of getting into Car business)

Payoffs” are the profits the firms will earn:

(Diversifying increases firm’s operational costs, but in long run can increase revenues)

 

NE2(Asif).thumb.png.9bad3853c206947c3233acf86b11bdf5.png

 

Here we have the equilibrium outcome, which is both companies will diversify.

Even though both A & B will perform better if they do not diversify, however such decisions are highly unstable as each company will have upper hand to diversify (extra +30), when competitor is not diversifying.

 

The result referred is called as “Nash Equilibrium”

A “Win Win Situation”

Here Neither Company A nor Company B has anything to gain by modifying its own decision separately.

 

Simply, Nash Equilibrium position is most equitable solution (most stable state), though not the most obvious solution when there is Multi – Party Conflict

 

Nash Equilibrium is one of the fundamental concepts in Game Theory and it provides the base for rational decision making.

It can be used to predict company’s response to competitor’s prices and decision.

In 2000, advice from economists raised £22.5 billion for UK government from an auction of 3G Bandwidth license for mobile phones.

Source: UKRI Economic and Social Research Council 

 

In Oligopolistic market condition, if one organization reduces its service prices, the other competitor must reduce the prices, so that they can retain customers.

Classical Indian examples:

> Bharti Infratel & Jio striking Nash Equilibrium for Telecom Infrastructure sharing

> Dilemma of Shiv Sena whether to support or scoot BJP from the alliance, while forming government in Maharashtra  

 

Organizational decision making involves deciding between alternatives, uncertainty, complexity, Interpersonal Issues & High-Risk consequences. Organizations can follow the application of Game Theory by changing the Payoffs.

 

Even though it is difficult to shift/switch from an competitive to cooperative strategy with any degree of success. It is better for organizations, cooperating with rivals/competitors which would leave everyone better off.

 

Quote

"Let's not do it your way or my way; let's do it the best way." - Greg Anderson 

 

Applying the concept in organizations helps narrow down the number of possible outcome, and therefore strategic decisions that would be taken.  

 

Take Away:

A Lose-Win and Win-Lose situations usually in any kind of relationship does not last and it is temporary and can easily turn to be a Lose-Lose situation later.
To make strong, long term relationship to be sustainable, we will have to rely upon Win-Win Situation.

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Nash equilibrium is a classical example of game theory named after a famous mathematician John Nash and has wide application in the real world micro and macroeconomics and strategic decision making. It implies that favorable outcome of a game is where, each player does not deviate from the intended strategic decision, even after knowing other player's moves/strategic decisions. There is no change in the decision of the player, as there is no reward associated with it and the original strategic decision is the best one.  There may be a single/multiple/no Nash equilibrium at all in a game/scenario. It is one of the best and widely applicable concept of gaming theory, which helps to substantiate the decision-making ability by mathematical calculations and logical application. The Nash equilibrium has applications in different streams like social, economical and strategical.
Example of Nash equilibrium In the real world:
Imagine there are two strategic decisions/ moves- A, B  for two biggest players of soft drinks-Pepsi and Cola (We are all aware of the famous Pepsi and Cola War). In this example, both Pepsi and Cola can choose strategy A, to receive $5 bn, or strategy B, to lose $1 bn. It is explicit and logical that both of them will go for move A and get the reward. Now per se,  Pepsi becomes aware of the intention of Cola and Cola becomes aware of Pepsi's move, It is highly unlikely that any of the two big giants will change their strategy and loose hefty money. This choice represents a Nash equilibrium.  

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Nash Equilibrium: -

Nash equilibrium was invented by John Nash an American mathematician. It is a very important concept of game theory.

  1. Nash Equilibrium is a decision-making theorem in game theory by which a player can achieve the desired outcome without not disturbing or change in their initial strategy.

  2. In Nash equilibrium, each player wins because each player gets their desired outcome.

Nash Equilibrium provides a solution concept in a noncooperative game. This theory is used in economics and other disciplines. John Nash got Nobel prize for this work.

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Game Theory within the Business World


The classical example of theory of games within the business world arises once Associate in Nursingalyzing Associate in Nursing economic setting characterised by an marketcompetitive firms have the choice to just accept the fundamental evaluation structure approved by the opposite firms or to introduce a cheaper price schedule. Despite it being within the common interest to collaborate with competitors, following a logical thought method causes the companies to default. As a result, everyone seems to be worse off. though this is often a reasonably basic state of affairscall analysis has influenced the overall business setting and may be a factor within the use of compliance contracts.

Game theory has branched bent include several alternative business disciplines. From best selling campaign ways to waging war choices, ideal auction ways, and pick designstheory of games provides a theoretical framework with material implications. for instance, pharmaceutical firms systematically face choices relating to whether or not to promote a product straightaway and gain a competitive edge over rival companies, or prolong the testing amount of the drug. If a bankrupt company is being liquidated and its assets auctioned off, what's the best approach for the auction? what's the most effective thanks to structure proxy pick schedules? Since these choices involve varied parties, theory of games provides the bottom for rational deciding.

Nash Equilibrium
The equilibrium is a crucial construct in theory of games bearing on a stable state in a very game wherever no player will gain a bonus by unilaterally dynamical his strategy, forward the opposite participants conjointly don't modification their ways. The equilibrium provides the answer construct in a very noncooperative game. the idea is employed in social science and alternative disciplines. it's named once John writer WHO received the Alfred Nobel in 1994 for his work.

One of the a lot of common samples of the equilibrium is that the prisoner’s quandaryduring this game, there ar 2 suspects in separate rooms being interrogated at an equivalent time. every suspect is obtainable a reduced sentence if he confesses and provides up the opposite suspect. The vital part is that if each confess, they receive a extended sentence than if neither suspect aforementioned something. The mathematical answergiven as a matrix of attainable outcomes, shows that logically each suspects confess to the crime. as long as the suspect within the alternative room’s best choice is to confess, the suspect logically confesses. Thus, this game encompasses a single equilibrium of each suspects confessing to the crime. The prisoner’s quandary may be a noncooperative game since the suspects cannot convey their intentions to every alternative.

Another vital construct, zero-sum games, conjointly stemmed from the first concepts given in theory of games and therefore the equilibriumbasically, any quantitative gains by one party ar up to the losses of another party. Swaps, forwards, choices and alternative money instruments ar usually represented as "zero-sum" instruments, taking their roots from a thought that currently appears distant.

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Nash equilibrium came from an American mathematician and inventor, John  Nash.

It is a decision making theorem of game theory. This theory determines the actions that participants of a game should take for best results in their favour. The Nash equilibrium can be used in many disciplines viz. Economics, social sciences etc.

 

According to this theorem a player can achieve the best outcome without changing the initial strategy.

One popular example is prisoner’s dilemma which adequately shows  the effect of the Nash Equilibrium.

image.png.6f7f5776d3701f077917fc20a4d12daa.png

The Prisoner’s Dilemma is a common situation of game theory that can showcase the Nash equilibrium. In this situation two criminals are arrested and both are held in solitary confinement with no means of communication with each other. The prosecutors do not have any evidence to convict anyone of them, So they offer both either to betray the other and get free or remain silent.

 

If Prisoner A betrays prisoner B and B remains silent, then A will get free and B will be jailed for 10 years.

If Prisoner B betrays prisoner A and A remains silent, then B will get free and A will be jailed for 10 years.

If Prisoner A betrays B and B betrays A then both will be jailed for 5 years.

If both remain silent then both will be jailed for 1 year.

 

In this example, if both chooses for mutual cooperation then outcome will be better for both and if one chooses to cooperate and other doesn’t then outcome will be worst for one of them.

 

As per Nash equilibrium theorem, Decisions that are good for individuals can sometimes be worst for groups.

In the Practical world, Companies use Nash Equilibrium Theorem in Organizational decision making to predict how companies will respond to their Prices. Two companies will probably squeeze the customers more than they can if  they face thousands of competitors.

 

According to Nash Equilibrium, one company cannot predict the result of the choices of multiple decision makers if one company analyzes those decisions in isolation. Instead, companies must ask other competitor companies what they would do, taking into account the decision-making of the others.

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Nash Equilibruim

 

The problem of decision making is always challenging, because the future outcomes of any particular action is not fully predictable.  Also, this action-outcome relationship is frequently changing, which requires a very dynamic adaptive decision making approaches, which should be based on the previous decision making choices.

 

In this background, Nash Equilibrium takes significance as one of the concepts of game theory, where the optimal outcome of a game is one wherein no player gets any additional incentive to change their original strategy even after they come to know about their opponent’s strategy.

 

Nash Equilibrium is a decision-making theorem within game theory which explains that a player can achieve his desired outcome without changing his choice even after knowing the opponent’s choices.  In other words, each player’s decision is optimal when considering the decisions of other players.  Each player wins and get their desired outcome, by sticking to their own choices, even after knowing their opponent’s choices.

 

Real-time application:

Consider two players are playing a game and there are two strategies, A & B, to be chosen.  If the players choose strategy A, the player wins $1 and by choosing strategy B, the same player loses $1.  During the game, if both the players chooses strategy A, then they will get $1 each and stand gained.  If the choice of player 2 is revealed to player 1, even then we can see that the choices of both the players do not change, and they choose only strategy A.  In summary, knowing the other player’s choice does not influence or change the other player’s choice.  This situation is known as Nash Equilibrium.

 

 

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Great answers to highlight the concept of Nash Equilibrium. 

 

Best answer was provided by Nilesh Gham for giving varied examples where this concept can be applied. 

 

Please have a look at Expert View (Venugopal's response) as well. 

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