Coevolution of Cooperative Strategies under Egoism

Speaker: Ta-Chun Lien

References

Outline

• Game Theory Review• Motivation• Resource-bidding game• Implement methods and Experimental Results• Discussion• Conclusions

Game Theory Review

• Games• Extensive form and normal form• Nash equilibrium• Iterated eliminate dominated strategies(IEDS)• Mixed Nash equilibrium

Games

• Who is playing – the group of players that strategically interacts

• What the are playing with – the alternative actions or choices

• When each player gets to play (in what order)• How much they stand to gain (or lose) form

the choices made in the game

Extensive form

Normal form

Nash equilibrium

Examples

IEDS

Mixed Nash equilibrium

p

1-p

q 1-q

Motivation

• Cooperation and competition in Mother Nature

• Nurse scheduling problem

Cooperation and competition in Mother Nature

"the greatest improvement in the productive powers of labour, and the greater part of the skill, dexterity, and judgment with which it is anywhere directed, or applied, seem to have been the effects of the division of labour."

Chapter 1, Wealth of Nations

Selfish gene

• “a predominant quality to be expected in a successful gene is ruthless selfishness.”

• “This gene selfishness will usually give rise to selfishness in individual behaviour.”

• “a gene might be able to assist replicas of itself that are sitting in other bodies. If so, this would appear as individual altruism but it would be brought about by gene selfishness.”

Egoism

• Egoism means that an individual’s utility function would depend only on its fitness (interests in game theory), whereas altruism means that utility function depends on all individuals’ fitness.

G. S. Becker. Altruism, egoism, and genetic fitness: Economics and sociobiology.Journal of Economic Literature, 14(3):817–26, 1976.

Auction-based nurse scheduling

• Auction stage: nurses bid for their preferred working shifts and days off using “points”.

• Scheduling completion stage: allocates remaining unfilled shifts to nurses who have not yet met their minimum required working hours.

Resource-bidding game

• Four assumptions• Definition• Three examples

Four assumptions

• The seal bid, single run auction is adopted.• Players receive fixed and equal points at the

beginning of each turn.• Players have to bid all points in each turn.• For equal bids, we use the seniority for tie

break — the most senior player wins the bid.

Definition

Definition(cont’d)

P R

p1

p2

p3

r1

r2

f1

f2

f3a1j=(2,3)

bid