# 程序代做 Competition between agents – cscodehelp代写

Competition between agents

(groups.msn.com/artofjimlee)

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Multi-party decision making

(xkcd.com/1890/)

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In the real world

(U.S. Army Military History Institute)

Strategic analysis.

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In the real world

( /citylimits.org)

School admissions

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In the real world

(froedtert.com)

Kidney exchange

Longest chain involved 28 donors and recipients.

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The grade game

( ’s Report Card, US National Archives)

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The grade game

Imagine in this module we assign grades as follows

You are randomly paired with a partner (you do not know who!)

You have to write X or Y on the piece of paper

You will get a grade based on the following rules:

If both you and your partner write X, then you both get a B

If you write X and your partner writes Y then you get D and your partner gets A If you write Y and your partner writes X then you get A and your partner gets D

If both you and your partner write Y then you both get C

PCD

” 3¥27

(The Grade Game, )

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The grade game

What would you do?

What you get depends also on the choice of your partner. This is the blueprint of strategic interaction.

There is a poll on KEATS to find out …

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Choose the side

Which side of the road to drive on?

(haulagetoday.com)

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Choose the side

Which side of the road to drive on?

(businessinsider.com)

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Choose the side

Which side of the road to drive on?

Any fule kno that.

( / )

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Choose the side

Which side of the road to drive on?

Same side as everyone else

(berkshireeagle.com)

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Choose the side

How do you choose when you don’t know what “everyone else” is doing.

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Game theory

Game theory is a framework for analysing interactions between a set of agents. Abstract specification of interactions.

Describes each agent’s preferences in terms of their utility.

‚ Assumeagentswanttomaximiseutility.

Give us a range of solution strategies with which we can make some predictions

about how agents will/should interact.

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Payoff Matrices

We can characterise the “choose side” scenario in a payoff matrix j

left right left

i

right

we have two agents, each player picking a (pure) strategy

Agent i is the row player

gets the lower reward in a cell.

Agent j is the column player gets the upper reward in a cell.

1 1

0 0

0 0

1 1

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Payoff Matrices

We can characterise the grade game scenario in a payoff matrix

j

YX Y

i

X

Payoffs are the US grade points that correspond to the problem statement. From the game earlier: Grade A is 4, Grade B is 3 etc.

2 2

1 4

4 1

3 3

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Outcomes

An outcome is what we get when we combine the actions of all the players. An outcome corresponds to an element of the payoff matrix

j

left right up

i

down

We identify outcomes by the moves the players make:

pwhat i plays, what j playsq Thus pup, rightq identifies the outcome in which

i plays up and j plays right

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1 1

0 0

0 0

1 1

Payoff Matrices

Actually there are two matrices here, one (call it A) that specifies the payoff to i and another B that specifies the payoff to j.

jA

Sometimes we’ll write the payoff matrix as pA, Bq in recognition of this.

̈1 0 ̨

A “ ̋3 1‚is the payoff matrix for i from the following table

‘

“i l

left right : up 0

1

o :2

0

oooh

i0

down

Note that ai1,j1 is the payoff if i picks action i1 and j picks action j1

1

O

O

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