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)....
... 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...
...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 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...
...scenario. After that the solution concepts are selected in order to acquire a prediction about the possible behavior of the players and outcomes of their actions. These results will be obtained through 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....
...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...
...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
•...
...Solution to Tutorial 1
2011/2012 Semester I MA4264 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...
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