Презентация Evolutionary games. (Lecture 7) онлайн
На нашем сайте вы можете скачать и просмотреть онлайн доклад-презентацию на тему Evolutionary games. (Lecture 7) абсолютно бесплатно. Урок-презентация на эту тему содержит всего 31 слайд. Все материалы созданы в программе PowerPoint и имеют формат ppt или же pptx. Материалы и темы для презентаций взяты из открытых источников и загружены их авторами, за качество и достоверность информации в них администрация сайта не отвечает, все права принадлежат их создателям. Если вы нашли то, что искали, отблагодарите авторов - поделитесь ссылкой в социальных сетях, а наш сайт добавьте в закладки.
Презентации » Математика » Evolutionary games. (Lecture 7)
Оцените!
Оцените презентацию от 1 до 5 баллов!
- Тип файла:ppt / pptx (powerpoint)
- Всего слайдов:31 слайд
- Для класса:1,2,3,4,5,6,7,8,9,10,11
- Размер файла:1.06 MB
- Просмотров:127
- Скачиваний:0
- Автор:неизвестен
Слайды и текст к этой презентации:
№2 слайд
![Classic game theory Lectures](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img1.jpg)
Содержание слайда: Classic game theory
Lectures 1-6: “Classic game theory”, rational players:
Players aim to maximize their payoffs, and they never make mistakes.
Critiques of CGT:
The assumption that players never make mistakes is unrealistic. To determine the optimal strategy may be difficult in many situations.
How do we choose between the different equilibria? (e.g. coordination games have 2 PSNE and 1 MSNE)
№3 слайд
![Evolutionary game theory An](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img2.jpg)
Содержание слайда: Evolutionary game theory
An Alternative approach
Evolutionary game theory is an alternative approach:
players are not fully rational, they make mistakes.
Players’ behavior evolves overtime, systematic mistakes are eliminated in the long-run.
What EGT achieves:
Helps select between several Nash equilibria
Provides an interpretation to the concept of mixed strategy
№4 слайд
![Evolution in biology](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img3.jpg)
Содержание слайда: Evolution in biology
Principles of evolution
Animal behavior may be genetically predetermined, e.g. degree of aggressivity.
Heterogeneity: different members of a group behave differently.
Fitness: Some types of behavior are more successful.
Selection: Animals pass their genes to the next generation. Animals with most successful types of behavior reproduce more quickly.
e.g. if aggressive types are more successful, they will spread and eventually all animals within that species will be aggressive.
№5 слайд
![Evolution in game theory](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img4.jpg)
Содержание слайда: Evolution in game theory
Animal = Player
Behavior = Strategy (not a choice variable)
Behavior success = Payoff of strategy
Successful strategies will spread by imitation or learning
Firms observe which business practices work, and adopt them.
e.g. if TFT dominates defect, then defectors will not survive in the long-term; and they will be replaced by TFT players.
№7 слайд
![Price competition Review of](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img6.jpg)
Содержание слайда: Price competition
Review of the pricing game
Prisoner’s dilemma situation. A unique PSNE: (D,D).
If the game is not repeated, cooperation cannot be sustained.
If the game is repeated infinitely or indefinitely, cooperation may be sustained as long as the rate of return r is not too high.
Classic game theory assumes that players make an informed choice to play cooperate (C) or defect (D) based on the payoffs.
№8 слайд
![Player types EGT assumes that](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img7.jpg)
Содержание слайда: Player types
EGT assumes that players have no choice between C and D. Each player is born with a predetermined trait.
Suppose that there are two types of players:
Cooperators (probability x).
Defectors (1-x).
Cooperators always cooperate; defectors always defect.
Each player is “born” with a type.
Suppose that players are randomly matched.
The “other player” could be a cooperator or a defector.
№10 слайд
![ESS evolutionary stable](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img9.jpg)
Содержание слайда: ESS (evolutionary stable strategy)
Thus, defectors are fitter than cooperators.
This leads to an increase in the proportion of defectors from one “generation” to the next.
E.g. suppose that x=0.4 initially. The proportion of defectors will increase gradually, as defection is more successful. At some point all players will adopt defection.
The evolutionary stable strategy is the long-run outcome of the evolution process. The ESS is that all players defect. Only one type will remain.
When a strategy is strictly dominant, it is the ESS.
№13 слайд
![Repeated prisoners dilemma](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img12.jpg)
Содержание слайда: Repeated prisoners’ dilemma
Suppose the game is repeated three times.
Each pair of players plays the games 3 times in succession.
Is cooperation possible?
When the game is repeated, players can have more complex strategies. Suppose there are two types of strategies:
Always defect (probability 1-x)
Tit-for-tat (probability x)
Players are randomly drawn against each other.
№15 слайд
![Repetition Nash equilibrium](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img14.jpg)
Содержание слайда: Repetition: Nash equilibrium
Classic game theory. Suppose that players must decide in advance either T or A. Two pure strategy NE: {A,A}, {T,T}
One mix strategy NE:
Play A with probability p=1/3:
864p+936(1-p)=792p+972(1-p)
Play T with probability 1-p=2/3
3 possible outcomes.
№16 слайд
![Repetition performance EGT](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img15.jpg)
Содержание слайда: Repetition: performance
EGT expected payoffs:
π(A)= 936x+864(1-x) = 864+72x
π(T)= 972x+792(1-x) = 792+180x
π(T)> π(A) if x>2/3
π(T)< π(A) if x<2/3
The performance of each type depends on the composition of the population
Large % of type A A is more successful
Large % of type T T is more successful
№18 слайд
![Repetition ESS If more than](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img17.jpg)
Содержание слайда: Repetition: ESS
If more than 2/3 of the population is T type, then T players are more successful, and their proportion will grow until it reaches 100%
If less than 2/3 of the population is T type, then A players are more successful, and their proportion will grow until it reaches 100%
Two ESS: All A or all T
№19 слайд
![Repetition ESS Monomorphic](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img18.jpg)
Содержание слайда: Repetition: ESS
“Monomorphic” outcome: all of the type.
If everyone else is type A, types that don’t defect will not survive. If everyone else is type T, types that do defect will not survive.
EGT can help select from a multiplicity of NE.
In this example, only the PSNE are evolutionary stable, the MSNE is not.
Thus, we can eliminate the MSNE on the ground that it is not evolutionary stable.
Importance of the initial population mix of types.
№22 слайд
![n-repetitions There are two](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img21.jpg)
Содержание слайда: n-repetitions
There are two ESS, one all T, one all A.
The cut-off point depends on n: the higher n, the more likely that T types prevail.
As n very large, the cut-off point converges to x=0.
Intuition:
when the game is repeated more times, the long term benefits of cooperation outweigh the short term benefit of defection.
Cooperation is more likely to be evolutionary stable if the
game is repeated many times.
№24 слайд
![ESS vs. Nash equilibrium](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img23.jpg)
Содержание слайда: ESS vs. Nash equilibrium
Backdoor justification for the NE
Even if players are not rational, if the more successful strategies spread in the population, then the outcome must be the same as that resulting from consciously rational play.
Thus, the NE can be reached even if players are not rational. Players who don’t play the successful strategy will die out.
№27 слайд
![Chicken game H gt L if x lt H](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img26.jpg)
Содержание слайда: Chicken game
π(H)> π(L) if x<1/2
H is successful if the proportion of H is less than ½
L is successful if the proportion of L is less than ½
Each type is fitter when it is relatively rare!
If most firms produce less, I am better off producing more.
If most firms produce more, I am better off not producing less.
№30 слайд
![Chicken game EGT provides an](/documents_6/c90182ae035ea3f8d08d9e9f1d6a9b13/img29.jpg)
Содержание слайда: Chicken game
EGT provides an alternative interpretation of mixed strategies:
With rational players, the 50-50 result suggest players randomize each time they play.
In the evolutionary game, each player uses a pure strategy, but different players use different strategies. The distribution of those playing L and those playing H is 50-50.
Скачать все slide презентации Evolutionary games. (Lecture 7) одним архивом:
Похожие презентации
-
Repeated games. (Lecture 6)
-
Sequential games. Empirical evidence and bargaining. (Lecture 5)
-
Sequential games. (Lecture 4)
-
Simultaneous games. Oligopoly. (Lecture 2)
-
Relational algebra. Lecture 8
-
Evolutionary algorithms
-
Mathematics for Computing. Lecture 2: Logarithms and indices
-
Mathematics for Computing 2016-2017. Lecture 1: Course Introduction and Numerical Representation
-
Auctions. (Lecture 10)
-
Mechanism design. (Lecture 9)