Game Theory and Conflict Mohammad Tawfik
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Game Theory and Conflict
Based on: “Games People Play”
By Prof. Scott Stevens
The Teaching Company
Game Theory and Conflict Mohammad Tawfik
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Game Theory
Game Theory and Conflict Mohammad Tawfik
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What is game theory?
• Game theory is a branch of applied mathematics that studies strategic situations where participants choose different actions in an attempt to maximize their returns.
Game Theory and Conflict Mohammad Tawfik
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It may be used to explain …
Game Theory and Conflict Mohammad Tawfik
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… Predict …
Game Theory and Conflict Mohammad Tawfik
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… Evaluate …
Game Theory and Conflict Mohammad Tawfik
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… Human Behavior
Game Theory and Conflict Mohammad Tawfik
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Game Theory and Conflict Mohammad Tawfik
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Attention!
• Bad news:
Knowing game theory does not guarantee winning
• Good news:
Framework for thinking about strategic interaction
Game Theory and Conflict Mohammad Tawfik
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Why game theory?
• Because we can formulate effective strategy…
• Because we can predict the outcome of strategic situations…
• Because we can select or design the best game for us to be playing…
Game Theory and Conflict Mohammad Tawfik
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Classical Games!
2x2 Simultaneous Games
Game Theory and Conflict Mohammad Tawfik
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Definition
• 2 players
• One of two moves
• Neither of the players know what the other is doing before he/she decides
Game Theory and Conflict Mohammad Tawfik
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Game Theory and Conflict Mohammad Tawfik
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The coordination game!
• YOU prefer one of two choices
• YOU prefer to have same choice as OTHER
• Luckily, OTHER prefers the same choice!
Game Theory and Conflict Mohammad Tawfik
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Example
• YOU prefer developing software using Windows
• YOU and OTHER are developing software to the same customer
• YOU and OTHER prefer developing using the same operating system
• Operating system choices are Windows or Linux!
Game Theory and Conflict Mohammad Tawfik
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Payoff Matrix
Payoff YOU
Windows Linux
OTHER Windows 2+2 0+1
Linux 1+0 1+1
Sometimes, the solution is not obvious! 1- If you BOTH do not think in the same way! 2- If OTHER is Irrational!!!
Game Theory and Conflict Mohammad Tawfik
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Game Theory and Conflict Mohammad Tawfik
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The battle of the sexes game!
• YOU prefer one of two choices
• YOU prefer to have same choice as OTHER
• Unfortunately, OTHER prefers the other choice!
Game Theory and Conflict Mohammad Tawfik
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Same Example
• YOU prefer developing software using Windows, while, OTHER prefers Linux
• YOU and OTHER are developing software to the same customer
• YOU and OTHER prefer developing using the same operating system
• Operating system choices are Windows or Linux!
Game Theory and Conflict Mohammad Tawfik
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Different Payoff Matrix!
Payoff YOU
Windows Linux
OTHER Windows 2+1 0+0
Linux 1+1 1+2
NO GOOD SOLUTION!
Game Theory and Conflict Mohammad Tawfik
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Solutions!
• Communicate both ways
• Send a message one way communication
• Select your preference and guarantee at least one point!
• Guess based on previous experience of OTHER preferences
• The use of a focal point
Game Theory and Conflict Mohammad Tawfik
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Game Theory and Conflict Mohammad Tawfik
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The Chicken game!
• YOU prefer one of two choices
• YOU prefer that OTHER have opposite choice
• Unfortunately, OTHER prefers the same choice!
Game Theory and Conflict Mohammad Tawfik
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Same Example
• YOU and OTHER prefer developing software using Windows
• YOU and OTHER are developing software to the same customer
• YOU and OTHER prefer developing using the different operating systems so that the customer remains dependent on you only!
• Operating system choices are Windows or Linux!
Game Theory and Conflict Mohammad Tawfik
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Different Payoff Matrix!
Payoff YOU
Windows Linux
OTHER Windows 0+0 1+3
Uniux 3+1 1+1
You both end crashing into Windows!
Game Theory and Conflict Mohammad Tawfik
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Solution!
• One player has to commit to a choice!
Game Theory and Conflict Mohammad Tawfik
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Game Theory and Conflict Mohammad Tawfik
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The Prisoners’ Dilemma game!
• If YOU and OTHER choose choice A, you both win 3 points
• If YOU choose A and OTHER chooses B, you win 1 point, and OTHER wins 4 points
• If YOU choose B and OTHER chooses A, you win 4 points and OTHER wins 1 point
• If you both chose B, you both get 2 points
Game Theory and Conflict Mohammad Tawfik
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Same Example
• If YOU and OTHER develop using Windows, you get paid 3 M$ each
• However, if only one of you develops for Linux, he gets 4 M$ for being distinguished, while the other only gets 1 M$ for being so old fashioned
• If you both develop for Linux, you get paid only 2 M$ each as there is no distinguishing and you probably used open source code!
Game Theory and Conflict Mohammad Tawfik
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Different Payoff Matrix!
Payoff YOU
Windows Linux
OTHER Windows 3+3 4+1
Linux 1+4 2+2
What would you do?
Game Theory and Conflict Mohammad Tawfik
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Solutions!
• The only RATIONAL solution for both of us is to develop using Linux! … It is safer!!!
• We both reach the less than best solution
• UNLESS we cooperate!
Game Theory and Conflict Mohammad Tawfik
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Bidding Example!
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Two-Tiered bidding
• In 1988 “Bloomingdales” had a market price of 100$ per share … it is being sold out!
• “Macy’s” offered 102$ per share provided that they get majority of stocks (50% +1)
• Robert Campeau offered a two-tiered offer of 105-90$ per share for the first 50% of shares, he pays 105$ per share for all shares and for the rest he pays an extra 90$ per share for all shares!
Game Theory and Conflict Mohammad Tawfik
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Let’s use numbers
• If there are only 10 shares … the total share price is 1000$
• If Macy’s took over, they will pay 102$ for each of the first 5 shares and the rest remains for 100$, the total price will be 1010$
• If Campeau gets the first 5 shares, he will pay 525$ for them, for the other 5 shares, he will; pay 450$ for a total of 975$ !!!
Game Theory and Conflict Mohammad Tawfik
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Every body loses except Campeau!
• Campeau created a prisoners’ dilemma