Game theory is a study of strategic decision making. Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers"

1. Game Theory
Abhijit Mukherjee ChiragTalwar Nachiket Mujumdar Nikhil Saraf

2. Game theory
Study of rational behaviour in situations in which your choices affect
others & their choices affect you.
Bad news?
Knowing game theory does not guarantee winning!
Good news?
Gives you a framework for thinking about strategic interaction
Nikhil Saraf @ MICA

3. Games we play
▪ Driving
▪ Doing the dishes
▪ Group projects
▪ Dating
▪ Price wars
▪ Pollution abatement free-riding
▪ DoT
▪ Coordination
 War of attrition
 Free-riding
 Hidden information
▪ Prisoner’s dilemma
▪ Free Riding
▪ Auctions
Nikhil Saraf @ MICA

4. Why study Game Theory?
▪ Because we can formulate effective strategy
▪ Because we can predict outcome of strategic situations
▪ Because we can select or design the best game for us to be playing
Nikhil Saraf @ MICA

5. Key elements of a game
▪ Players:Who is interacting?
▪ Strategies:What are their options?
▪ Payoffs:What are their incentives?
▪ Information:What do they know?
 Rationality: How do they think?
Nikhil Saraf @ MICA

6. How to anticipate other’s behaviour
▪ Evolution: If non-strategic and adaptive, play repeatedly (or observe
past play)
▪ Dominance: Never play a strategy that is always worse than another
▪ Rational ability :To play optimally given some beliefs about what
others play (and what others believe)
▪ Equilibrium:To play optimally given correct beliefs about others
Nikhil Saraf @ MICA

7. Economic Applications of Game Theory
▪ The study of oligopolies (industries containing only a few firms)
▪ The study of cartels, e.g., OPEC
▪ The study of externalities, e.g., using a common resource such as a
fishery
▪ The study of military strategies
▪ The study of international negotiations
▪ Bargaining
Nikhil Saraf @ MICA

8. Oligopoly
Oligopoly is a market structure featuring a small
number of sellers that together account for a large
fraction of market sales.
Nikhil Saraf @ MICA

9. Oligopoly & Game Theory
▪ In oligopoly, unlike in monopoly and perfect competition, profit
maximization decisions should take into account the competitor’s
action.
▪ Similarly, competitor will take my action into account in its decision.
Hence, I will calculate competitor’s action which will be formed based
on its calculation of my action.
▪ Such situations are analyzed using GameTheory.
▪ Eg : McDonald’s ad campaign impacts the demand for McDonalds
but will also affect the demand for Burger King
Nikhil Saraf @ MICA

10. Nash Equilibrium
A Nash equilibrium is a situation in which economic
actors interacting with one another each choose
their best strategy given the strategies that all the
others have chosen.
Nikhil Saraf @ MICA

11. Dominant Strategy
The dominant strategy is the best strategy for a
player to follow regardless of the strategies chosen
by the other players.
Nikhil Saraf @ MICA

12. Prisoner’s Dilemma
▪ Two suspects arrested for a crime
▪ Prisoners decide whether to confess or not to confess
▪ If both confess, both sentenced to 3 months of jail
▪ If both do not confess, then both will be sentenced to 1 month of jail
▪ If one confesses and the other does not, then the confessor gets
freed (0 months of jail) and the non-confessor sentenced to 9 months
of jail
▪ What should each prisoner do?
Nikhil Saraf @ MICA

13. Payoff Matrix for Prisoner’s dilemma
Confess
(yrs)
No Confess
(yrs)
Confess
(yrs)
-3,-3 0,-9
No confess
(yrs)
-9,0 -1,-1
Prisoner 2
Prisoner 1
Nikhil Saraf @ MICA

14. Cigarette advertising on TV
After the 1970 agreement (Carry the warning label and ceaseTV
advertising in exchange for immunity from federal lawsuits),
cigarette advertising decreased by $63 million but the profits rose by
$91 million
Nikhil Saraf @ MICA

15. Cigarette advertising on TV
- All US tobacco companies advertised heavily on television
- Surgeon General issues official warning
- Cigarette smoking may be hazardous
- Cigarette companies reaction
- Fear of potential liability lawsuits
- Companies strike agreement
- Carry the warning label and ceaseTV advertising in exchange for
immunity from federal lawsuits
1964
1970
Nikhil Saraf @ MICA

16. Strategic Interactions
▪ Players: Reynolds and Philip Morris
▪ Strategies:{ Advertise , Do Not Advertise }
▪ Payoffs: Companies’ Profits
▪ Each firm earns $50 million from its customers
▪ Advertising costs a firm $20 million
▪ Advertising captures $30 million from competitor
▪ How to represent this game?
Nikhil Saraf @ MICA

17. Payoff table
No Ad
(Million $)
Ad
(Million $)
No Ad
(Million $)
50,50 20,60
Ad
(Million $)
60,20 30,30
Philip Morris
Reynolds
Nikhil Saraf @ MICA

18. Traveller's Dilemma
An airline loses two suitcases belonging to two different travellers. Both
suitcases happen to be identical and contain identical items. An airline
manager tasked to settle the claims of both travellers explains that the airline
is liable for a maximum of $100 per suitcase (he is unable to find out directly
the price of the items), and in order to determine an honest appraised value of
the antiques the manager separates both travellers so they can't confer, and
asks them to write down the amount of their value at no less than $2 and no
larger than $100. He also tells them that if both write down the same number,
he will treat that number as the true dollar value of both suitcases and
reimburse both travellers that amount. However, if one writes down a smaller
number than the other, this smaller number will be taken as the true dollar
value, and both travellers will receive that amount along with a bonus/malus:
$2 extra will be paid to the traveller who wrote down the lower value and a $2
deduction will be taken from the person who wrote down the higher amount.
The challenge is: what strategy should both travellers follow to decide the
value they should write down?
Nikhil Saraf @ MICA

19. Payoff Matrix for TD Problem
100 99 98 97 ⋯ 3 2
100 100, 100 97, 101 96, 100 95, 99 ⋯ 1, 5 0, 4
99 101, 97 99, 99 96, 100 95, 99 ⋯ 1, 5 0, 4
98 100, 96 100, 96 98, 98 95, 99 ⋯ 1, 5 0, 4
97 99, 95 99, 95 99, 95 97, 97 ⋯ 1, 5 0, 4
⋮ ⋮ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮
3 5, 1 5, 1 5, 1 5, 1 ⋯ 3, 3 0, 4
2 4, 0 4, 0 4, 0 4, 0 ⋯ 4, 0 2, 2
Nikhil Saraf @ MICA

20. Collusion
A collusive agreement is an agreement between two (or more)
firms to restrict output, raise the price, and increase profits.
Firms in a collusive agreement operate a cartel.
Eg : OPEC
Nikhil Saraf @ MICA

21. Sequential and Repeated Games
Barista
Barista
Barista CCD
CCD
CCD
Nikhil Saraf @ MICA

22. Conclusion
▪ Mimics most real-life situations well
▪ Solving may not be efficient
▪ Applications are in almost all fields
▪ Big assumption: players being rational
Nikhil Saraf @ MICA

23. “As for the firms that want to get their hands on a sliver of the airwaves, their
best bet is to go out first and hire themselves a good game theorist.”
--The Economist, July 23,1994 p. 70
“At Bell Atlantic, we’ve found that the lessons of game theory give us a wider
view of our business situation and provide us a more nimble approach to
corporate planning. We call this system, quite simply, the ‘manage the
business’ process.”
--RaymondW. Smith (Bell Atlantic Chairman during 1990s)
in “Business as war game: a report from the battlefront”,Fortune, Sep. 1996
Nikhil Saraf @ MICA