nilesh.ghm

"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. 
 

I would prefer in the below order
 
1.       Resolution
Resolution represents the measurement system’s capability to detect and indicate small changes in the characteristic measured. Resolution is also known as discrimination. E.g. a tape measure with gradations in cm cannot be distinguish between measurements lesser than 1 cm, like 2mm say.
If an instrument is not able to measure the required attribute in the first place, there is no point in proceeding
 
2.       Bias
Bias can be defined as the difference between the mean or the expected results (say of a standard) and the true/accepted reference value, and can be designated as a systematic error. Bias is checked using calibration.
Once an instrument is able to have the necessary resolution, as above, bias would be the second thing to check.
 
3.       Linearity
The next question to answer would be if the procedure is able to delivery accurate and precise results (established above), over a range of values (higher or lower)?
Linearity answers this question and performs calibration over a range of the measurement.
 
4.  Precision
Precision is also an important parameter necessary to demonstrate that a procedure will provide valid result, and helps in quantifying the random error. There may be a myriad of sources of variability in each measurement and many of them can be transient and cannot be easily identified or controlled. Therefore, a variety of approaches are used: Repeatability, Intermediate Precision and Reproducibility.
Once all systematics errors are noted (and removed), through Bias estimation, Precision would be the next thing to check
 
5.       Stability
Stability, may be interpreted as the change in bias of a measurement over time and usage when such a system is used to measure a master part or standard. One can interpret a stable measurement as one which is in (the variation) is in statistical control.
Once all of the above are established, Stability can be used as an on-going check