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 *
Solution: In an n n magic square, A aij , there is a number s such that
i aij s for all j , and j aij s for all i. If Player I uses the mixed strategy (1 n ,1 n ,,1 n ) his average payoff isV s n no matter what Player II does. The same goes for player II, so the value is s n and p is optimal for both players. In the example, n 4 and s 34 , so the value of the game is 17/2 and the optimal strategies are both
...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...
...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...
...NEGOTIATION
Negotiation theory
Last updated 9 months ago
The foundations of negotiation theory are decision analysis, behavioral decision making, gametheory, and negotiation analysis. Another classification of theories distinguishes between Structural Analysis, Strategic Analysis, Process Analysis, Integrative Analysis and behavioral analysis of negotiations.
Individuals should make separate, interactive decisions; and negotiation analysis considers how groups of reasonably bright individuals should and could make joint, collaborative decisions. These theories are interleaved and should be approached from the synthetic perspective.
Common Assumptions Of Most Theories
Negotiation is a specialized and formal version of conflict resolution most frequently employed when important issues must be agreed upon. Negotiation is necessary when one party requires the other party's agreement to achieve its aim. The aim of negotiating is to build a shared environment leading to longterm trust and often involves a third, neutral party to extract the issues from the emotions and keep the individuals concerned focused. It is a powerful method for resolving conflict and requires skill and experience. Zartman defines negotiation as "a process of combining conflicting positions into a common position under a decision rule of unanimity, a phenomenon in which the outcome is determined by...
...110976
MOSES NGONE 10
PRESENTED TO: Mr. MORIASI MARANGA
DUE DATE: 29TH OCTOBER 2013
DEPARTMENT OF COMMERCE
SCHOOL OF BUSINESS AND ECONOMICS
ATHIRIVER CAMPUS
Table of Contents
GameTheory 3
History and impact of gametheory 5
Gametheory and information systems 6
Definition of key terms 6
Dominance 8
Nash equilibrium 8
Mixed strategies 9
Extensive games with perfect information 9
Extensive games with imperfect information 10
Zerosumgames and computation 11
Bidding in auctions 12
GameTheoryGametheory is the formal study of conflict and cooperation. Game theoretic concepts apply whenever the actions of several agents are interdependent. These agents may be individuals,
groups, firms, or any combination of these. The concepts of gametheory provide a language to formulate structure, analyze, and understand strategic scenarios.
The object of study in gametheory is the game, which is a formal model of an interactive situation. It typically involves several players; a game with only one player is usually called a decision problem. The formal definition lays out the players, their preferences, their information, the strategic actions available to them, and how these...
...implementation of the equilibrium concepts like gametheory selected for the current strategic framework and predictions will be made. Last section presents the discussion on the importance of results obtained through the implementation of the concept solutions.
Relevance from Strategic Perspective
As stated by the Thomson (2009), the most significant and enforceable resources are directives of the commission that are anticipated by the commission and the members states of the EU adopt these directives by conciliation clarification. These directives are adopted after the concentrated consultation with the commitment to transpose these directives into domestic regulations (Carrubba, 2005). Although the member states of the EU have agreed on the outcomes and the institutional regulations for implementation of these directives including the enforcement capability of the commission to issue a contravention schedule against a non complying member state in the European Court of Justice (McLean and Taehee, 2010). The member states may still have motivations to pursue their interests in the process of implementation of directives at the cost of cooperation clarification. The natural and typical difficulty in the way of the implementation process produces a composite strategic compliance game (Koing and Brooke, 2009). This difficulty is common for the monitoring actor and a group of cooperating actor’s circumstances. In the strategic...
... 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...
...Assignment 2: Planning and Playing a Game
Objectives:
• Learn how individuals contribute to teamwork
• Experience some of the features of group work and teamwork
• Understand what managers and organizational developers do to transform
• groups into teams
• Articulate the tangible benefits (both quantitative and qualitative) of
• highperforming teams
• Finish with an interest in learning more about these concepts and
• techniques to apply what you learn
Background: For this assignment, you will plan and play a game with your family or friends, or at work based on the idea of the classic prisoner's dilemma. If you have had a class on gametheory, you will be well aware of this concept. It forms the basis of many TV game shows. The prisoner's dilemma was illustrated in Truman Capote's book, "In Cold Blood" concerning the 1959 robbery of a Kansas farmhouse by Perry Smith and Dick Hickock, who murdered their victims in order to eliminate the witnesses. After the men were captured, the police interrogated them separately. To get a confession, the police offered the men a reduced sentence for cooperating. Failure to cooperate would result in a death penalty charge for both.
In the prisoner's dilemma, if both parties cooperate they are mildly punished; if one betrays another, one is severely punished while the other goes free; and if both betray...
...Tutor: Xiang Sun∗ August 24, 2011 GameTheory
1
Review
• “Static” means oneshot, or simultaneousmove; “Complete information” means that the payoﬀ functions are common knowledge. • Normalform representation: G = {S1 , . . . , Sn ; u1 , . . . , un }, where n is ﬁnite. • si is strictly dominated by si , if ui (si , s−i ) < ui (si , s−i ), ∀s−i ∈ S−i .
• Rational players do not play strictly dominated strategies, since they are always not optimal no matter what strategies others would choose. • Iterated elimination of strictly dominated strategies. This process is orderindependent. • Given other players’ strategies s−i ∈ S−i , Player i’s best response, denoted by Ri (s−i ), is the set of maximizers of maxsi ∈Si ui (si , s−i ), i.e., Ri (s−i ) = si ∈ Si : ui (si , s−i ) = max ui (si , s−i ) ⊂ Si .
si ∈Si
We call Ri the bestresponse correspondence for player i. • Given s−i , the best response Ri (s−i ) is a set. • In the nplayer normalform game G = {S1 , . . . , Sn ; u1 , . . . , un }, the strategy proﬁle (s∗ , . . . , s∗ ) is a purestrategy Nash equilibrium if 1 n s∗ ∈ Ri (s∗ ), i −i equivalently, ui (s∗ , s∗ ) = max ui (si , s∗ ), −i i −i
si ∈Si
∀i = 1, . . . , n,
∀i = 1, . . . , n.
• {Nash equilibrium(a)} ⊂ {Outcomes of IESDS}.
∗
Email: xiangsun@nus.edu.sg; Mobile: 9169 7677; Oﬃce: S170614.
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