# 留学生作业代写 Solution Concepts – cscodehelp代写

Solution Concepts

How will a rational agent behave in any given scenario? Play. . .

‚ Dominantstrategy;

‚ Nashequilibriumstrategy;

‚ Paretooptimalstrategies;

‚ Strategiesthatmaximisesocialwelfare.

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Dominant Strategies

Given any particular strategy s (either C or D) agent i, there will be a number of possible outcomes.

We say s1 dominates s2 if every outcome possible by i playing s1 is preferred over every outcome possible by i playing s2.

Thus in this game:

j

DC D

i

1 2

4 2

1 5

4 5

C C dominates D for both players.

c -Trenn, King’s College London

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Dominant Strategies

Two senses of “preferred”

s1 strongly dominates s2 if the utility of every outcome possible by i playing s1 is

strictly greater than every outcome possible by i playing s2. In other words, ups1q ° ups2q, for all outcomes.

s1 weakly dominates s2 if the utility of every outcome possible by i playing s1 is no less than every outcome possible by i playing s2.

In other words, ups1q • ups2q, for all outcomes.

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Dominant Strategies

A rational agent will never play a dominated strategy.

So in deciding what to do, we can delete dominated strategies. Unfortunately, there isn’t always a unique undominated strategy (see later).

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Dominant Strategies

h t t pR

Rps

Game with dominated strategies

LCR U

M

D

%. s

l

O

1

O

3

O

O

1

0

O

O0

0

OO

110

O00

000

115

110

000

040

g

o

2

Can eliminate the dominated strategies and simplify the game Which strategy is dominated?

c -Trenn, King’s College London

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Dominant Strategies

Let’s look at the pay-off matrices A and B

̈ ̊1 1 0 ̨‹

For the column player j we get B “ ̊ ̋1 1 0‹‚ 110

̈ ̊1 ̨‹ ̈ ̊1 ̨‹ ̈ ̊0 ̨‹ We can think of this as three vectors ̊ ̋1‹‚, ̊ ̋1‹‚and ̊ ̋0‹‚

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Dominant Strategies

Let’s look at the pay-off matrices A and B

̈ ̊1 1 0 ̨‹

For the column player j we get B “ ̊ ̋1 1 0‹‚ 110

̈ ̊1 ̨‹ ̈ ̊1 ̨‹ ̈ ̊0 ̨‹ We can think of this as three vectors ̊ ̋1‹‚, ̊ ̋1‹‚and ̊ ̋0‹‚

We can see that every component of R is dominated by L (and actually also C) So we can remove R

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Dominant Strategies

Game with dominated strategies

LC U

M

D

Can eliminate the dominated strategies and simplify the game Remove R (dominated by L).

30 O1O 1

OO

11

11

OO

11

04

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Dominant Strategies

Let’s look at the pay-off matrices A

̈ ̊3 0 ̨‹

For the row player i we get A “ ̊ ̋1 1‹‚

04

– ́ ̄ ́ ̄ ́ ̄] Wecanthinkofthisasthree(row)vectors 3 0 , 1 1 and 0 4

c -Trenn, King’s College London

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Dominant Strategies

Let’s look at the pay-off matrices A

̈ ̊3 0 ̨‹

For the row player i we get A “ ̊ ̋1 1‹‚ 04

We can think of this as three (row) vectors ́3 0 ̄ , ́1 1 ̄ and ́0 4 ̄ No strategy here is dominated by any other …

So we cannot remove anything else

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Dominant Strategies

If we are lucky, we can eliminate enough strategies so that the choice of action is obvious.

In general we aren’t that lucky.

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Dominant Strategies

Consider this scenario:

j

CD A

1 2

4 3

2 3

3 2

i

B Are there any dominated strategies?

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Are there any dominated strategies?

D is dominating!

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