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Short introduction to Game Theory

Salvator Vella

Salvator Vella

on 4 September 2013

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Transcript of Short introduction to Game Theory

Short introduction to Game Theory
and decision-making

Game theory is a vast domain of the mathematics and social science.
This 90' presentation will not make you an expert in any way.
The only aim is to make you aware of the shortcomings of the traditional way of making decisions...
... and to have fun.
Why a Game Theory?
"No man is an island"

Study of rational behavior in interactive or interdependant situations.

Bad news: Knowing game theory does not guarantee winning

Good news: Framework for thinking about strategic interaction
Example of the important of game in real life
Gore vs Bush before the US Supreme Court
No Majority in one round
4 judges prefer:
Bush to Gore to Remand (B>G>R)
3 judges prefer:
Gore to Remand to Bush (G>R>B)
2 judges prefer:
Remand to Bush to Gore (R>B>G)

No majority for any of the 3 options
Decision in 2 rounds and importance of agenda setting
3 possibilities:
1° B vs G then winner vs R
2° R vs B then winner vs G
3° G vs R then winner vs B
Recall member preferences:
4 B>G>R 3 G>R>B 2 R>B>G
Winner depends on agenda:
1° => Winner is R
2° => Winner is G
3° => Winner is B
Chief Justice selected 3° and the face of the world changed dramatically!
Strategic Thinking & Game Theory
Like the general, you must recognize that business rivals, prospective spouse and even your child are intelligent and purposive people. Their aims often conflict with yours. Your own choice must allow for the conflict and utilize the cooperation.

Strategic thinking is the art of outdoing an adversary, knowing that the adversary is trying to do the same to you.

The science of strategic thinking is called game theory.
Decision Theory vs Game Theory
Decision Theory
"You are self-interested and selfish"
Game Theory
"So is everyone else"
Golden Rule
Never assume that your opponents' behavior is fixed.

Predict their reaction to your behavior.
10 of you go to a restaurant

If each of you pays for your own meal ... This is a decision problem

If you all agree to split the bill...
This is a game!
The structure of a game
The strategic environment
Who are the players? (Decision makers)
What strategies are available? (Feasible actions)
What are the payoffs? (Objectives - can differ per player, reflecting their interest)

Rules of the game
What is the time-frame for decisions?
What is the nature of the conflict and interaction?
What information is available? For who?
Are the agreements or contracts enforceable?

Rationality: players aim to maximize their payoffs
Common knowledge: each player knows the rules and each plays knows that all the other players know the rules.

2 kinds of strategic interactions
The essence of a game of strategy is the interdependence of the players' decisions. These interactions arise in 2 ways:

1. The first is sequential: The players make alternative moves, fully knowledgeable of the preceding moves by other players.

2. The second is simultaneous: The players act at the same time, in ignorance of the others' current actions.
1. Simultaneous Game
2 companies, Coca-Cola & Pepsi-Cola, have to decide on their advertising budget.
What is your advice for each of them considering the EBIT outcome:
Full transcript