Game TheoryAbhijit Mukherjee Chirag Talwar Nachiket Mujumdar Nikhil Saraf

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

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

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

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

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

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

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

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 Game Theory.

▪ Eg : McDonald’s ad campaign impacts the demand for McDonalds but will also affect the demand for Burger King

Nikhil Saraf @ MICA

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

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

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

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

Cigarette advertising on TV

After the 1970 agreement (Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits), cigarette advertising decreased by $63 million but the profits rose by $91 million

Nikhil Saraf @ MICA

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 cease TV advertising in exchange for immunity from federal lawsuits

1964

1970

Nikhil Saraf @ MICA

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

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

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

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, 10

0 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

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

Sequential and Repeated Games

Barista

Barista

Barista

CCD

CCD

CCD

Nikhil Saraf @ MICA

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

“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.”

--Raymond W. Smith (Bell Atlantic Chairman during 1990s)in “Business as war game: a report from the battlefront”,Fortune, Sep. 1996

Nikhil Saraf @ MICA