math 180 - game theorychhays/lecture24.pdf · i an introduction to game theory (osborne) (contains...
TRANSCRIPT
![Page 1: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/1.jpg)
Administration
There are three more books on reserve:
I Strategies and Games: Theory and Practice (Dutta)(also available online)
I An Introduction to Game Theory (Osborne)(contains evolutationarily strategic strategies)
I Thinking Strategically (Dixit and Nalebuff)
![Page 2: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/2.jpg)
Administration
Find a real world application of the quantitative reasoning thatwe’ve covered in class
By Friday, November 8. turn in:
I topic
I one paragraph summary
I at least one reference
![Page 3: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/3.jpg)
Administration
Find a real world application of the quantitative reasoning thatwe’ve covered in classBy Friday, November 8. turn in:
I topic
I one paragraph summary
I at least one reference
![Page 4: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/4.jpg)
Evolutionarily Stable Strategies
I Idea: some small percentage of a population develops amutation
I This creates a competing ‘strategy’, compared to animalswithout the mutation
I A strategy is a genetic dispositionI The payoff corresponds to the likelihood of offspring
![Page 5: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/5.jpg)
Evolutionarily Stable Strategies
I Idea: some small percentage of a population develops amutation
I This creates a competing ‘strategy’, compared to animalswithout the mutation
I A strategy is a genetic dispositionI The payoff corresponds to the likelihood of offspring
![Page 6: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/6.jpg)
Evolutionarily Stable Strategies
I Idea: some small percentage of a population develops amutation
I This creates a competing ‘strategy’, compared to animalswithout the mutation
I A strategy is a genetic disposition
I The payoff corresponds to the likelihood of offspring
![Page 7: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/7.jpg)
Evolutionarily Stable Strategies
I Idea: some small percentage of a population develops amutation
I This creates a competing ‘strategy’, compared to animalswithout the mutation
I A strategy is a genetic dispositionI The payoff corresponds to the likelihood of offspring
![Page 8: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/8.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while hunting
I A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 9: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/9.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defect
I This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 10: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/10.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 11: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/11.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 12: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/12.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 13: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/13.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 14: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/14.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2ε
I u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 15: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/15.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2ε
I Defectors will thriveI Cooperation is not evolutionarily stable
![Page 16: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/16.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thrive
I Cooperation is not evolutionarily stable
![Page 17: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/17.jpg)
Evolutionarily Stable StrategiesI An example: a species cooperates while huntingI A mutation causes some to defectI This creates a game such as:
C D
2, 2
3, 0 1, 1
0, 3C
D
I Question: is cooperation evolutionarily stable?(will the defecting mutation die out?)
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (1 − ε, ε)(ε is the proportion with the mutation)
I u(C , (1 − ε, ε)) = 2 − 2εI u(D, (1 − ε, ε)) = 3 − 2εI Defectors will thriveI Cooperation is not evolutionarily stable
![Page 18: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/18.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defect
I Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)I u(C , (ε, 1 − ε)) = 2εI u(D, (ε, 1 − ε)) = 1 + 2εI Cooperators will not thriveI Defection is evolutionarily stable
![Page 19: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/19.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defectI Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)I u(C , (ε, 1 − ε)) = 2εI u(D, (ε, 1 − ε)) = 1 + 2εI Cooperators will not thriveI Defection is evolutionarily stable
![Page 20: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/20.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defectI Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)I u(C , (ε, 1 − ε)) = 2εI u(D, (ε, 1 − ε)) = 1 + 2εI Cooperators will not thriveI Defection is evolutionarily stable
![Page 21: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/21.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defectI Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)
I u(C , (ε, 1 − ε)) = 2εI u(D, (ε, 1 − ε)) = 1 + 2εI Cooperators will not thriveI Defection is evolutionarily stable
![Page 22: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/22.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defectI Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)I u(C , (ε, 1 − ε)) = 2ε
I u(D, (ε, 1 − ε)) = 1 + 2εI Cooperators will not thriveI Defection is evolutionarily stable
![Page 23: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/23.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defectI Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)I u(C , (ε, 1 − ε)) = 2εI u(D, (ε, 1 − ε)) = 1 + 2ε
I Cooperators will not thriveI Defection is evolutionarily stable
![Page 24: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/24.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defectI Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)I u(C , (ε, 1 − ε)) = 2εI u(D, (ε, 1 − ε)) = 1 + 2εI Cooperators will not thrive
I Defection is evolutionarily stable
![Page 25: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/25.jpg)
Evolutionarily Stable Strategies
C D
2, 2
3, 0 1, 1
0, 3C
D
I Now suppose that the default behavior was to defectI Is defection evolutionarily stable?
I Need to compare payoffs of cooperation and defection againstrandom animal in population
I Look at payoffs of C and D against (ε, 1 − ε)I u(C , (ε, 1 − ε)) = 2εI u(D, (ε, 1 − ε)) = 1 + 2εI Cooperators will not thriveI Defection is evolutionarily stable
![Page 26: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/26.jpg)
Definition
In a 2-player symmetric game, a strategy s is evolutionarily stableif for sufficiently small numbers ε > 0, and any other strategy s∗,
(1 − ε) u(s, s) + ε u(s, s∗) > (1 − ε) u(s∗, s) + ε u(s∗, s∗)
This is saying that the utility of s in a mixed population (1 − ε, ε)is better than the utility of s∗ is the mixed population
![Page 27: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/27.jpg)
Definition
In a 2-player symmetric game, a strategy s is evolutionarily stableif for sufficiently small numbers ε > 0, and any other strategy s∗,
(1 − ε) u(s, s) + ε u(s, s∗) > (1 − ε) u(s∗, s) + ε u(s∗, s∗)
This is saying that the utility of s in a mixed population (1 − ε, ε)is better than the utility of s∗ is the mixed population
![Page 28: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/28.jpg)
Evolutionarily Stable Strategies
I See Handout #7
I Morals:
I evolutionarily stable strategies give Nash equilibriaI (symmetric) Nash equilibria are not necessarily evolutionarily
stableI evolutionarily stable strategies are not strictly dominated by
other strategiesI evolutionarily stable strategies do not necessarily strongly
dominate other strategies
![Page 29: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/29.jpg)
Evolutionarily Stable Strategies
I See Handout #7I Morals:
I evolutionarily stable strategies give Nash equilibriaI (symmetric) Nash equilibria are not necessarily evolutionarily
stableI evolutionarily stable strategies are not strictly dominated by
other strategiesI evolutionarily stable strategies do not necessarily strongly
dominate other strategies
![Page 30: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/30.jpg)
Evolutionarily Stable Strategies
I See Handout #7I Morals:
I evolutionarily stable strategies give Nash equilibria
I (symmetric) Nash equilibria are not necessarily evolutionarilystable
I evolutionarily stable strategies are not strictly dominated byother strategies
I evolutionarily stable strategies do not necessarily stronglydominate other strategies
![Page 31: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/31.jpg)
Evolutionarily Stable Strategies
I See Handout #7I Morals:
I evolutionarily stable strategies give Nash equilibriaI (symmetric) Nash equilibria are not necessarily evolutionarily
stable
I evolutionarily stable strategies are not strictly dominated byother strategies
I evolutionarily stable strategies do not necessarily stronglydominate other strategies
![Page 32: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/32.jpg)
Evolutionarily Stable Strategies
I See Handout #7I Morals:
I evolutionarily stable strategies give Nash equilibriaI (symmetric) Nash equilibria are not necessarily evolutionarily
stableI evolutionarily stable strategies are not strictly dominated by
other strategies
I evolutionarily stable strategies do not necessarily stronglydominate other strategies
![Page 33: Math 180 - Game Theorychhays/lecture24.pdf · I An Introduction to Game Theory (Osborne) (contains evolutationarily strategic strategies) I Thinking Strategically (Dixit and Nalebu](https://reader035.vdocuments.us/reader035/viewer/2022063013/5fcc155226cb6439155f59b3/html5/thumbnails/33.jpg)
Evolutionarily Stable Strategies
I See Handout #7I Morals:
I evolutionarily stable strategies give Nash equilibriaI (symmetric) Nash equilibria are not necessarily evolutionarily
stableI evolutionarily stable strategies are not strictly dominated by
other strategiesI evolutionarily stable strategies do not necessarily strongly
dominate other strategies