Econ 431 Solution to Problem Set #4
(a) Consider the following Table: Cows in field Yield per cow Total Yield 1 8 8 2 5 10 3 3 9 4 2 8
To maximize total milk production (social optimum) the men should graze 2 cows total. But consider the following payoff table: Mr. Two x2=1 0,8 5,5 6,3
Mr. One
x1=0 x1=1 x1=2
x2=0 0,0 8,0 10,0
x2=2 0,10 3,6 4,4
Grazing two cows is a dominant strategy for each farmer. In equilibrium they each receive 4 quarts, even though it is possible to obtain 5. If Mr. One grazes two cows he can pay Mr. Two not to graze any, but he must pay him at least 4 quarts per day, that being what Mr. Two could get by grazing his own cows. Paying 5 or 6 quarts will work as well. But if the price for Mr. Two to graze no cows were 7 quarts, then Mr. One would prefer to make no deal, since he can be assured of getting 4 quarts with 2 cows rather than just getting 3 quarts. Alternatively, Mr. Two can graze the cows and pay Mr. One not to. Finally, each can agree to graze only one cow. This is probably the most sensible outcome. Each gets 5 quarts of milk and no transfers are necessary. (b) There are two possible kinds of equilibria, cooperative and noncooperative. If the men make no deal, then each will graze two cows and get 4 quarts per day, since grazing 2 cows is a strongly dominant strategy. But this equilibrium is unlikely, since it is easy to do better. Transfer payments of milk are possible. Communication is easy (since they are on the same field). It is easy to enforce a contract by withholding milk and easy to observe when the contract is broken (when the other guy grazes cows even though he promised not to.) So a cooperative equilibrium where one farmer grazes two cattle and pays the other to graze none or where each promises only to graze one cow is most likely, particularly in a situation where the men are repeating the game day in and day out.
(c) Mr. i gets Qi=(250  X)xi = (250  X i  xi )xi , where X i is the total...
...Cows are Fat cowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcowcow
Entrepreneurship
Date Task Hours
Oct. 5th Tacked, lounged, mounted, and walked on 3 year old 1
Oct. 6th Tacked, lounged, and walked mounted 1
Oct. 7th Tacked, lounged, walk, and a little trot 1
Oct. 8th Tacked, lounged, walk, and trot 1
Oct. 9th Tacked, lounged, walk, and trot 1
Oct. 10th Tacked, lounged, walk, trot, and a little canter 1
Oct. 11th Tacked, lounged, walk, trot, and canter 1 ½
Oct. 13th Tacked, lounged, walk, trot, canter, move to big arena 1 ½
walk, and trot
Oct 14th Tacked, lounged, walk, trot, canter, move to big arena 1
walk, trot, and canter
Oct. 15th Phasing out lounging, walk, trot, canter, big arena walk 1 ½
trot, and canter
Oct. 16th Tacked, walk, trot, canter, big arena walk, trot, canter 1...
...Beauty Contest Experiment
The experiment executed in the seminar was very simple. Players had to choose a number between 0 and 100. The objective is to choose a number based on your guess of the mean guesses of the group and multiply it by 2/3. It is called the Beauty contest Experiment because it was based on a theory John Maynard Keynes proposed on the relationship of the stock market with beauty contests conducted in newspapers of his time. In this report I will examine the logic behind choosing the best response strategy in theory and compare it with the actual results of the experiment conducted. From the comparison I will provide justification for why the theory is different from reality by also comparing it to examples in real life.
To understand the underlying logic of the game’s strategy one must understand the Nash Equilibrium. Princeton University’s Website (an excellent source since John Nash the person who came up with the Equilibrium attended that university) defines Nash Equilibrium as “a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices...
...GameTheory
International Business Management
Preface
Since GameTheory is a tool used to analyze strategic behavior by taking into consideration how participants expect other to behave I thought about an everyday example in my life. I wanted to analyze my job at the bar and take into account some independent parties that compete with me. Since it’s not my choice who my boss will hire or fire I was interested in how each decisions outcome would be for the corresponding parties. What would be my benefits, considering different situations?
The game begins:
To finance my studies I work as a waitress in a bar. Usually, the bar is very crowded and it is difficult to serve all the guests. It is a tough job and sometimes very exhausting but serving all the guests is still doable. Nevertheless my boss realized that doable doesn’t mean high quality service. Due to the delay in receiving their order, customers sometimes complain to the boss. My boss is now in dilemma what to do. He could either replace me with a new waitress, hoping for better quality service with her, or he could hire a new waitress to support me in serving the customers and therefore have 2 waitresses serving. However, he knows the delay is most probably due to crowded bar and not due to lack of knowledge and skills form my side, he is having in mind to get a second waitress and have two waitresses, which will...
... 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...
...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...
...GameTheory and Business
Gametheory emerged as a scholarly field of study in the first half of the 20th century. Since that time, it has significantly affected various academic disciplines, such as economics, political science and biology. Although the term "gametheory" may suggest a certain frivolity, the concepts underlying it have many realworld applications and offer a structured and logical method of considering strategic situations.
The parallels between competitive games and strategic business situations should be fairly obvious. Consider the game of chess. There are two players, each of whom makes moves in sequence. After observing the move made by the first player, the second player makes a counter move. Then the first player, having observed the first two moves, makes the third move and so on.
Compare this to the business situation of gas stations competing for customers through strategic pricing. (The players in this case are station A and station B.) Suppose, for instance, that station A starts by choosing a new pricing strategy. Given station A's decision, station B decides how it will set its prices. Given station B's response, station A can choose to revise its pricing strategy and so on. The objective of each gas station in this "game" is to maximise its own profit. For each to do so, it must be continually acting and...
...GAMESTHEORY
In gametheory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute Nash equilibrium.
Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phil's decision, and Phil is making the best decision he can, taking into account Amy's decision. Likewise, a group of players is in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others. However, Nash equilibrium does not necessarily mean the best payoff for all the players involved; in many cases, all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium: e.g., competing businesses forming a cartel in order to increase their profits.
The prisoner's dilemma is a fundamental problem in gametheory that demonstrates why two people might not cooperate even if it...
...In creating a game theoretical model to try and better understand the quandary in our kitchen, we will use repeated prisoners’ dilemma games, collective action analysis, and finally, a two species evolutionary game.
We begin by applying a Repeated Prisoners’ Dilemma I (PDI) model to our situation. The rules for a PDI game are simple; the two players can either cooperate (wash) or defect (not wash). The players can fully observe each other’s move to wash their dish or to not wash. They will move in sequential order where player one moves first and the second player observes the move (see fig. 1). Then the second player carries out a move. The strategy called titfortat (tft), where player one cooperates on the first play and then does what the other player did the previous period, will be used to model the behavior of our players. The probability of continuing the game (p) is less than one, and so we have a finite game of unknown length. In our model, (p) is set at .9 showing that there is a ninety percent chance of continuation. We believe there is a ten percent chance that one player will not be using the kitchen to cook on the following day, which would end the current game. Using the tft strategy will help us to understand when a player’s payoffs make sense to cooperate, defect once, or defect forever on dish duty given the discount rate (r) and the...