Game Theory and Negotiations

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



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.



It may be used to explain …



… Predict …



… Evaluate …



… Human Behavior





Attention!

• Bad news:

Knowing game theory does not guarantee winning

• Good news:

Framework for thinking about strategic interaction



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…



Classical Games!

2x2 Simultaneous Games



Definition

• 2 players

• One of two moves

• Neither of the players know what the other is doing before he/she decides





The coordination game!

• YOU prefer one of two choices

• YOU prefer to have same choice as OTHER

• Luckily, OTHER prefers the same choice!



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!



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!!!





The battle of the sexes game!


• YOU prefer to have same choice as OTHER

• Unfortunately, OTHER prefers the other choice!



Same Example

• YOU prefer developing software using Windows, while, OTHER prefers Linux


• YOU and OTHER prefer developing using the same operating system




Different Payoff Matrix!

Payoff YOU

Windows Linux


Linux 1+1 1+2

NO GOOD SOLUTION!



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





The Chicken game!


• YOU prefer that OTHER have opposite choice

• Unfortunately, OTHER prefers the same choice!



Same Example

• YOU and OTHER prefer developing software using Windows


• YOU and OTHER prefer developing using the different operating systems so that the customer remains dependent on you only!





Payoff YOU

Windows Linux


Uniux 3+1 1+1

You both end crashing into Windows!



Solution!

• One player has to commit to a choice!





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



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!




Payoff YOU

Windows Linux


Linux 1+4 2+2

What would you do?



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!



Bidding Example!



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!



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$ !!!



Every body loses except Campeau!

• Campeau created a prisoners’ dilemma

Education

Game Theory and Negotiations