Evolutionary games. (Lecture 7) - презентация, доклад, проект скачать

Нажмите для полного просмотра!

Evolutionary games. (Lecture 7), слайд №1

Evolutionary games. (Lecture 7), слайд №2

Evolutionary games. (Lecture 7), слайд №3

Evolutionary games. (Lecture 7), слайд №4

Evolutionary games. (Lecture 7), слайд №5

Evolutionary games. (Lecture 7), слайд №6

Evolutionary games. (Lecture 7), слайд №7

Evolutionary games. (Lecture 7), слайд №8

Evolutionary games. (Lecture 7), слайд №9

Evolutionary games. (Lecture 7), слайд №10

Evolutionary games. (Lecture 7), слайд №11

Evolutionary games. (Lecture 7), слайд №12

Evolutionary games. (Lecture 7), слайд №13

Evolutionary games. (Lecture 7), слайд №14

Evolutionary games. (Lecture 7), слайд №15

Evolutionary games. (Lecture 7), слайд №16

Evolutionary games. (Lecture 7), слайд №17

Evolutionary games. (Lecture 7), слайд №18

Evolutionary games. (Lecture 7), слайд №19

Evolutionary games. (Lecture 7), слайд №20

Evolutionary games. (Lecture 7), слайд №21

Evolutionary games. (Lecture 7), слайд №22

Evolutionary games. (Lecture 7), слайд №23

Evolutionary games. (Lecture 7), слайд №24

Evolutionary games. (Lecture 7), слайд №25

Evolutionary games. (Lecture 7), слайд №26

Evolutionary games. (Lecture 7), слайд №27

Evolutionary games. (Lecture 7), слайд №28

Evolutionary games. (Lecture 7), слайд №29

Evolutionary games. (Lecture 7), слайд №30

Evolutionary games. (Lecture 7), слайд №31

Содержание ▲

Вы можете ознакомиться и скачать презентацию на тему Evolutionary games. (Lecture 7). Доклад-сообщение содержит 31 слайдов. Презентации для любого класса можно скачать бесплатно. Если материал и наш сайт презентаций Mypresentation Вам понравились – поделитесь им с друзьями с помощью социальных кнопок и добавьте в закладки в своем браузере.

Слайды и текст этой презентации

Слайд 1

Описание слайда:

LECTURE 7 EVOLUTIONARY GAMES

Слайд 2

Описание 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)

Слайд 3

Описание 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

Слайд 4

Описание 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.

Слайд 5

Описание 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.

Слайд 6

Описание слайда:

Price competition Two firms compete on prices. The NE is to set low prices to gain market shares.

Слайд 7

Описание 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.

Слайд 8

Описание 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.

Слайд 9

Описание слайда:

Defectors are successful Expected payoff of cooperators: π(C)=324x+216(1-x) = 216+108x Expected payoff of defectors: π (D)=360x+288(1-x) = 288+72x π (D)-π (C)=72-36x  π (D)>π (C)  defectors have a higher payoff

Слайд 10

Описание 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.

Слайд 11

Описание слайда:

ESS The likely outcome is (D,D) Why do firms defect? Not because they choose to defect, but because those that don’t defect have a lower rate of survival

Слайд 12

Описание слайда:

ESS

Слайд 13

Описание 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.

Слайд 14

Описание слайда:

Repetition: payoffs A vs. A: 288+288+288 T vs. T: 324+324+324 A vs. T: 360+288+288 T vs. A: 216+288+288

Слайд 15

Описание 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.

Слайд 16

Описание 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

Слайд 17

Описание слайда:

Repetition: performance

Слайд 18

Описание 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

Слайд 19

Описание 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.

Слайд 20

Описание слайда:

Repetition: ESS

Слайд 21

Описание слайда:

n-repetitions π(T)> π(A) if 324nx+(216+288(n-1))(1-x)>(360+288(n-1))x+288n(1-x) i.e. if x>2/n

Слайд 22

Описание 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.

Слайд 23

Описание слайда:

ESS vs. Nash equilibrium Two PSNE: They Correspond to ESS. An ESS must be a NE of the game played by rational players

Слайд 24

Описание 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.

Слайд 25

Описание слайда:

ESS vs. Nash equilibrium One mixed strategy NE in which T is played with probability 2/3, and A 1/3: Does not correspond to ESS. The mixed strategy NE is “unstable”. Although all ESS are NE, not all NE are ESS. Number of NE ≥ number of ESS.

Слайд 26

Описание слайда:

Chicken game Quantity game: x is the proportion of H type. π(L)=0(1-x)-1x=-x π(H)=1(1-x)-2x=1-3x

Слайд 27

Описание слайда:

Chicken game π(H)> π(L) if x

Слайд 28

Описание слайда:

Chicken game If x>1/2, L are more successful and x declines If x

Слайд 29

Описание слайда:

Chicken game

Слайд 30

Описание 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.

Слайд 31

Описание слайда:

Summary Criticism of classic game theory: rationality; multiple equilibria; EGT does not assume rationality, and helps select between multiple NE. EGT provides a backdoor justification for the NE. All ESS are NE, not all NE are ESS.