There were 21 flags and each player had the opportunity to remove 1,2, or 3 flags. The player that removes the last flags will be the winning team. By applying the backwards induction theory, think backwards in time and the optimal winning strategy is to leave the opponent player 4 flags by each step to remove the flags so that the remaining number is divisible by 4.
The player that has the first attempt to remove the 1st flag will control the 100% of whole situation. This is the unbeatable strategy that will lead the whole situation by leaving the opponent player with a multiple of 4 flags. This apply when both player understand the trick of this 21 flags game. By leaving the opponent player with 20 flags at the first attempt, no matter how many flags the opponent player remove, the player that in control could then remove the flags and leave the opponent with 16 flags, then 12 flags, then 8 flags and finally 4 flags which forces the opponent in to a situation where no matter how many flags the opponent player remove, the in charge player will be able to take the last flag. The key of this game is the target number you arrange it so you leave your opponent player with. Then whatever amount of flags the opponent player take, you can remove the remaining 1 to 3 flags that sum up to 4. The first attempt to remove the 1st flag of this 21 flags game has the upper hand.
However, if you lost the first attempt to remove this game, you better hope the opponent player do not know the trick of 21 flags. By this, you may still stand a chance to get back the control of this game by playing randomly to confuse the opponent player and try to get back the target number of 4. Unless the opponent understand well the strategy of this game else they most probably will go to make a mistake and allow you to control back the situation by getting back the situation where flags number able to be divide by 4 before ending the game.
... 2012 
 Application Of GameTheory to Business: Preliminary Findings for Term paper
Saurabh Mandhanya 11p164Rajat Barve 11p157Shashank Gupta 11p166Deepak Bansal 11P133Padmini Narayan 11p152Lizanne Marie Raphael 11P025 
[ The Kargil War: Analysis and Learning Through GameTheory ] 

Introduction
India and Pakistan have been involved in conflict over Kashmir since Independence. It has led to numerous wars and attacks. The relations and wars over Kashmir can be studied using GameTheory. Tit for Tat policy has been practiced by both nations. The pay of for wars for both countries has been changing depending on the context. This context has been based on many parameters –
1. Ally countries – US and China are widely regarded as Pakistan allies. China has been against India due to border issues. USSR has been traditionally supporting India until recently. The situation keeps on changing with changing stance of allies.
2. International support  International communities like UN tries to solve the conflict through negotiations.
3. Military strength – It keeps on changing depending upon development and purchase of weapons on both sides.
4. Resources including financial and others – India has always been in a relatively better position due to more available resources.
5. Leadership of both countries especially of Pakistan (Army Rule) – Army Rulers might...
...Topic 5: GameTheory Applied to the Movie and Aviation Industries
I. Case study: GameTheory Applied to the Movie Business
In the movie business, one of the trickiest decisions producers face is what type of movie to make. Suppose there are 2 movie studios and that their producers are trying to decide whether to make an Action Adventure (AA) or Romantic Comedy (RC) movie. Suppose each of the studios does not know what type of movie the competing studio is planning to make that same year and that they do not trust each other in the least. They face the following payoff matrix.
Studio 1
RC AA
Studio 2 RC (50,50) (90,60)
AA (60,90) (75,75)
(Figures show total estimated box office revenues in $ millions for Studio 1, Studio 2.)
What strategy (make an AA or RC movie) should each of the studios chose?
What is the payoff to each of the 2 studios given the strategies they choose?
Answer:
From Studio 1’s perspective:
Studio 1’s payoff
RC 50
RC
AA 90
Firm 2
RC 60
AA
AA 75
Same result from Studio 2’s perspective.
From studio 1’ s perspective: if studio 2 makes a RC, studio 1’s payoff is $50 million if it also makes a RC and $90 million if it makes an AA. If studio 2 makes an AA movie, studio 1’s payoff is $60 million if it makes a RC and...
...GameTheory
The game begins with a case that occurred on two prisoners. Both prisoners were suspected criminals and their work. Both prisoners were placed in a different room, then to be given the question of whether it is true they are committing a crime or not. Option given is: If the prisoner A prisoner confessed while B does not confess, then A will be free, while B will get a 6 month sentence. If they plead not guilty, then it will get a 1 month prison sentence. And if both confess, they will each get a 3 month prison sentence.
Zerosum game
In gametheory and economic theory, a zero–sum game is a mathematical representation of a situation in which a participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.
Prisoners dilemma game is an archeptypal example of of a nonzero sum game.The distinction between a zero sum game and a nonzero sum game is crucial.In zero sum game,with two players for simplicity,the utilities of players always sum to zero wathever the game’s outcome.On certain simplifying assumption,a zero sum game is equivalent to a zero money sum game.In this circumstances,zero sum...
...Gametheory is defined as “the study of the ways in which strategic interactions among economic agents produce outcomeswith respect to thepreferences of those agents, where the outcomes in question might have been intended by none of the agents” by the Stanford Encyclopedia of Philosophy (Ross 1997). The disciplines most involved in gametheory “are mathematics, economics and the other social and behavioral sciences” (McCain 1997).Gametheory was created to confront the problem and provide a theory of economic and strategic behavior. In gametheory, "games" have always been a metaphor for more serious interactions in human society. But gametheory addresses the serious interactions using the metaphor of a game: in these serious interactions, as in games, the individual's choice is essentially a choice of a strategy, and the outcome of the interaction depends on the strategies chosen by each of the participants (McCain1997).
John von Neumann a great mathematician founded gametheory. The legend of John Von Neumann gives a good insight on who John Von Neumann was and his theory. John von Neumann was a child prodigy, born into a banking family in Budapest, Hungary, “when he was only six years old he could divide eightdigit numbers in his...
...no matter what the other person does this is always better? Will such meek be able to survive when they give an open chance to exploiters to keep defecting and gaining? Will the meek inherit the earth?
The world has been preaching moral philosophy and few have been really practicing them. Many quote versus from the Bible and other religious books like above. Some believe that the world is still going on because of some good left in it and others think it is because people have learnt to punish the defectors. Let us study these philosophies in comparison with Prisoners Dilemma & TitForTat strategy in Gametheory.
Game theorists, like gamblers and children, can become addicted to iterated games. Their classic example is the Prisoner’s Dilemma, whose diabolical simplicity has given rise to thousands of scientific publications. Two players are engaged in the game. They have to choose between two options, which we term Cooperate or Defect. If both cooperate, they can earn three points apiece as reward. If both defect, they get only one point each, which is the punishment for failing to join forces. If one player defects while the other cooperates, then the defector receives five points (this is the temptation) while the trusting cooperator receives no points at all (this is the sucker’s payoff).
How will the rational player act? By defecting, of course. This is the right choice, no matter what...
...GameTheory Term Paper
Anomitra Bhattacharya
ab783@cornell.edu,
Cornell ID – 2316802
What ails Uttar Pradesh?
The states of Uttar Pradesh (UP) and Tamil Nadu (TN) reveal a marked northsouth divide in India. Uttar Pradesh, which was ahead of Tamil Nadu in the 1960s, now lags behind in the same sectors where Tamil Nadu has made significant progress. If one were to study Indian history or politics, UP’s lag would come as a surprise. All but four Prime Ministers of India have come from UP. UP has the famous Taj Mahal, the ancient & holy city of Varanasi and the confluence of Ganga and Jamuna rivers in Allahabad. These sites are of great national and international importance. What then accounts for such a miserable record for UP? The longterm reasons are unclear, but the more recent causes are identifiable. We use gametheory to explain some of these causes.
For roughly two decades until 2007, no government in UP lasted throughout its term and there was no political stability. In the state elections of May 2007, the victory of the Bahujan Samaj Party (BSP), a primarily Dalit (lower caste) party under the leadership of Mayawati, finally terminated the endemic political chaos and promised political stability. BSP won 206 of the 402 seats in the state assembly elections. Mayawati’s victory was based on an unusual social coalition. In 2007, every sixth Brahmin (higher caste) in UP voted for the BSP. Even in...
...MATH 4321 Spring 2013 Assignment Solution 0Sum Games 2 1. Reduce by dominance to 2x2 games and solve.
5 4 4 3 (a) 0 1 1 2 1 0 2 1 4 3 1 2
10 0 7 1 (b) 2 6 4 7 6 3 3 5
Solution: (a). Column 2 dominates column 1; then row 3 dominates row 4; then column 4 dominates column 3; then row 1 dominates row 2. The resulting submatrix consists of row 1 and 3 vs. columns 2 and 4. Solving this 2 by 2 game and moving back to the original game we find that value is 3/2, I’s optimal strategy is p (1 2, 0,1 2,0) and II’s optimal strategy is q (0,3 8, 0,5 8). (b). Column 2 dominates column 4; then (1/2)row 1+ (1/2)row 2 dominates row 3; then (1/2)col 1+(1/2)col 2 dominates col 3. The resulting 2 by 2 game is easily solved. Moving back to the original game we find that the value is 30/7, I’s optimal strategy is (2/7,5/7,0) and II’s optimal strategy is (3/7,4/7,0,0).
2. Reduce by dominance to a 3x2 matrix game and solve:
0 8 5 8 4 6 . 12 4 3
Solution: Note that 5/8xCol2 + 3/8xCol1 uniformly dominates Col3. Therefore, we can delete Col3 to get
0 8 * 8 4 * . Then, we use the graphical method in the following. 12 4 *
1/ 3 2 / 3 0 4 / 12 0 8 5 8 /12 8 4 6 0 12 4 3
Answer: The optimal strategy for I is (4/12, 8/12, 0) The optimal strategy for II is (1/3, 2/3, 0) Value = 16/3
3....
...problem, what is the Nash equilibrium in prices?
p1 = p2 = MC = 6
5. (20 total points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table:
Player 2
Player 1
Left
Right
Top
1 2
5 3
Bottom
2 2
3 1
where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.
a) (2 points) Does player 1 have a dominant strategy, and if so what is it? NO
b) (2 points) Does player 2 have a dominant strategy and if so what is it? NO
c) (2 points each) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:
i) Top/Left FALSE
ii) Top/Right TRUE
iii) Bottom/Left TRUE
iv) Bottom Right FALSE
d) (2 points) If each player plays their maximin strategy, what payoff will each of them receive?
BOTTOM/LEFT (2,2)
e) (2 points) Suppose the game is player where Player 1 chooses its strategy first and then Player 2 chooses its strategy. Using the backward induction method we discussed in class, what will be the outcome of the game?
TOP/RIGHT (5,3)
f) (4 points) This game has a unique Nash Equilibrium in mixed strategies where Player 1 plays Top with...