Am Introduction to Game Theory

Using games in marketing planning and behaviour prediction

PhD. Lecturer Loredana Ivan loredana.ivan@comunicare.ro

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Game theory refers to:

Describing Explaining PredictingIndividuals’ behavior in interdependency

situations

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Game theory is based on:

Rational behavior Rational choice theoryRational behavior= to choose the best

ways in order to achieve a particular outcome (result)

We predict what decisions people might take by assuming they will act rational

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Examples of rational behavior

1.In businesses, people are guided mainly by profits

2. In education, people are guided mainly by achieving social status

3. In politics, people are guided mainly by the democratic rule of majority

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Another approach to rational behavior

Choosing a specific object (person) that satisfy a specific criteria (formally imposed)

Ex. The criteria for marriage: a person closer to your age

Rational behavior: choosing such person

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Rational choice theory

A larger approach over rationalityTo choose between different outcomes

based on a set of preferences and set of opportunities (possible alternatives)

You analyze the cost of the chosen alternative/ of giving up to other alternatives

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Brief history of GT

1980- GT a topic in the economy

Neumann & Morgenstern (1944). The Theory of Games and Economic Behavior

John Forbes Nash (1950, 1951) – Nash equilibrium

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What e actually do?

We create a model based on some simple assumptions

No-fat modeling – using examples to illustrate the theory

We predict what would happen when the involved players would maximize their utility

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To maximize their utility means….

Taking into account the constraints of the situations

Taking into account their preferences, abilities, information

Players choose specific strategies and maximize the payoffs in an interdependency situation

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Concepts that we use in GT

1. Players2. Information (situational constraints)3. Actions (of players)4. Strategies5. Payoffs6. Total outcome7. Equilibrium – the best strategy for all

players involved

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Concepts that we use in GT

8. Dominant strategy: the best strategy of the player X (with maximum payoff) no matter what kind of strategy the others are choosing

9. Dominant strategy equilibrium: equilibrium when both players choose their dominant strategy

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Prisoner Dilemma GamePrisoner2 Prisoner1

Deny Confess

Deny -1, -1 -10, 0

Confess 0, -10 -8,-8

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Prisoner Dilemma Game

Dominant strategy for Prisoner 1 and Prisoner 2 is Confess

Dominant strategy equilibrium is (Confess, Confess) wit the outcome (-8, -8)

Theoretic equilibrium is (Deny, Deny) with a better outcome (-1, -1)

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Types of games

Simultaneous games Non-simultaneous gamesIn Prisoner Dilemma, the equilibrium is

the same no matter if the game is simultaneous or successive

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Types of games

Cooperative: the players are establishing trusting connections. They make promises and are interested in fairness

Non-cooperative

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Types of games

With conflict Without conflict

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Examples

1. Cooperative without conflict: members of a team that coordinate their actions

2. Cooperative with conflict: 2 trade unions negotiate bigger salaries

3. Non-cooperative without conflict: two companies having the same product but with no communication

4. Non-cooperative with conflict: Prisoner Dilemma

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Bismark Sea Battle Game

Battle in 1943: general Kimura versus general Kennedy - players

Actions:Going North - shorter way = 2 daysGoing South – longer way =3 daysKennedy can switch the route by going

back but loosing days

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Modeling Bismark Sea GameKennedy Kimura

N S

N 2, -2 2,-2

S 1, -1 3,-3

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Week Dominant strategy The weakest strategy of a player in

that sense that they will be other strategies with higher payoffs

We eliminate the week dominant strategies

We obtain the new equilibrium: (North, North)

What is happening when the game is not simultaneous?

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Guinea Pigs Game

Two pigs in a Skinner box (B.F. Skinner 1904-1990)

Player 1: big pig Player 2: small pigPressing the pedal – 10 units of food

with a cost of 2 units.

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Actions:

1) Big pig gets fist, he eats 9 units, 1 unit small pig

2) Small pig gets first, he eats 4 units, 6 units- big pig

3) They get together, small pig 3 units, big pig – 7 units

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Modeling Guinea Pigs GameBig Pig Small Pig

Press Wait

Press 5,1 4,4

Wait 9, -1 0,0

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Dominant strategies

For Big Pig – PressFor Small Big – WaitEquilibrium when eliminate the week

dominant strategy:(Press, Wait) with payoffs – (4,4)

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Nash equilibrium

A situation when no player is motivated to change his strategy, du to the fact that the other players would not change their strategy

The equilibrium from Guinea Pigs game is a Nash one

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Another example

Players: teacher and studentsAction1: they can accept a course with

large number of participants – payoff 1

Action2: they can reject it – payoff 2 (the course+ the quality)

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Modeling

Students TeacherAccept Reject

Accept 1,1 (Nash) 0,0

Reject 0,0 2,2

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Modeller Dilemma(modified prisoner Dilemma)

Prisoner2 Prisoner1Deny Confess

Deny 0, 0 (week Nash) -10, 0

Confess 0, -10 -8,-8 (strong Nash)

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Nash equilibrum

No player can win if he change only his strategy

A player chooses a strategy (the best one for him) taking into account the fact that the other player would not change his strategy

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Pareto Efficiency – Pareto optimum

No individual can increase his situation without decreasing other’ situation

Pareto improvement: a situation when a player gets into a better position without making the other player worse

Pareto optimum – when we can no longer do more Pareto improvements

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New example: Romanian worker versus German worker

Information: 5 computers per day – 8 Euro per hour

Actions:If one goes beyond the norm, the other

one is loosing his jobIf both go beyond the norm, the same

salary but more working hours

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ModelingGerman Romanian

Go beyond No

Go beyond 6,6 8, -8

No -8,8 8,8

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Bibliography

Osborne, Martin G. (2000). An Introduction to Game Theory. Toronto: University of Toronto

pp. 1-51 !!!On the CD