霊長類行動学7. ゲーム理論
霊長類行動学もくじ
- in order to pass genes
- eat
- survive
- reproduction
Evolutionary Stable Strategy (ESS)
進化的に安定な戦略(しんかてきにあんていなせんりゃく、ESS:evolutionarily stable strategy)は、進化生物学およびゲーム理論の重要な概念である。ジョン・メイナード=スミスとジョージ・プライスによって1973年に提唱された(詳細はMaynard Smith, 1982)。これは、生物の母集団のとる、「侵略されない戦略」の概念を基礎としている。仮に突然変異で対立遺伝子が発生し、別の戦略を取って他の生物に働きかけようとしても、母集団を侵略することはできず、逆に自然淘汰で排除されてしまうような戦略である。
(Wikipedia)
- Developed by J. Maynard Smith (1973)
- Strategy is a programmed behavioral policy
- e.g., Attack opponent. If he flees, chase him; if he turns around and fight back, run away.
- ESS is a strategy, adopted by most members of a population, that cannot be bettered by an alternative strategy
- Once it is fixed in a population, natural selection alone is sufficient to prevent alternative strategies from taking over.
- off course environment change, behavior has to be changed
Hawk and Dove Model
- they can interact as either:
- Hawk: Fight hard; retreat only when seriously injured
- Dove: threatens but retreat to avoid injury
- so, what happens when...
- Hawk fights dove
- Dove retreats, Hawk wins
- Hawk fight hawk
- one dies or is seriously injured, the other wins
- Dove fight dove
- threaten till one tires and retreats
- Hawk fights dove
- The caveat is that neither individual knows whether the other one is a hawk or dove. the only way to find out is to fight.
- Question is that which strategy is more stable (works best)?
- To answer this question we assign mathematical values which represent potential gains and loses
points | End result |
50 | win |
0 | loose |
-100 | seriously injured |
-10 | wasting time |
- wasting time for Dove is detrimental because engaging in fighting and gaining nothing, wasting time for foraging and reproduction opportunity
- e.g., bird has to catch food every 30s to feed children
Take 2 Doves
- How many points does the winner get?
- 50 - 10 = 40
- How many points does the loser get?
- 0 - 10 = -10
- Average pay-off of strategy
- On average an individual wins half the time and looses half the time
- Thus, the average spread off is the average of the payoff of the 2 strategies: +40 and -10 = 15.
- Let's throw in hawks and do the math for all scenarios
Hawk | Dove | |
Hawk | 50 / -100 | 50 / 0 |
Dove | 0 / 50 | -10 /40 |
Comparing the 2 strategies
- Dove = 15
- Hawk = -25
- Then, why have hawks at all?
- The ESS is having a stable ration of doves and hawks (5:7)
- Evolutionarily speaking limited war strategies benefit individual animals as well as the species.
Example of Doves strategy
- Lemur
- stink fight: scent competition by 手をこすりあわせてくさいにおいを出す。
The retaliator
- In this strategy, the individual plays like a dove at the beginning of every fight. If his opponent attacks he retaliates.
- He acts like a hawk when faced with a hawk, and like a dove when face with a dove.
- This is another strategy, in which the behavior of the individual is based on the behavior of his opponent. He is a "conditional strategist"
Other conditional strategists
- Bully - behaves like a hawk until someone hits back. Then the bully retreats.
- Prober-retaliator - like retaliator but occasionally tries an escalation and continuous if not retaliated.
Which is the best? stable?
- Dove
- not stable because can be invaded by other
- Hawk
- could be invaded by Dove and Bully
- Retaliator
- most stable
- Bully
- Prober-retaliator
- nearly stable
→retaliator
Prisoner's Dilemma
- Introduced by Hamilton (1964) to outline how behavioral strategies get fixed in populations.
- Two suspects of are arrested for robbery
- the police does not have enough circumstantial evidence to convict of the robbery, only evidence is for trespassing. Thus, they need a confession.
- They offer incentives for a confession
- This would require the suspect to rat out his partner. What to do?
- Punishment for trespassing: 1 year in jail
- Punishment for robbery: 10 years
- Consequences of confession: Silent partner gets 10 years in jail; rat gets off with no jail time
- If both confess: 5 years in jail for both
- What to do?
Cooperate | Defect | |
Cooperate | -1 / -1 | -10 / 0 |
Defect | 0 / -10 | -5 / -5 |
How often do we rat out?
- there are other variables that may influence a person's decision besides the consequences for him/herself.
- related to kin selection
TIT for TAT
- One the first move co-operate. One each succeeding move do what your opponent did the previous move. Thus, TIT FOR TAT was a strategy of co-operation based on reciprocity
- This is an ESS, that may explain the evolution of cooperation.
- 1. Never be the first to defect
- 2. Retaliate only after your partner has defected
- 3. Be prepared to forgive after carrying out just one act of retaliation
- 4. adopt this strategy only if the probability of meeting the same player again exceeds 2/3.
- Provided that the probability of future interaction between two individuals is sufficiently great, co-operation based on reciprocity can indeed get started in an a social world, can flourish and can defend itself once fully established
- examples: predator calls in vervet monkeys.
- have different calls for different predator
- Colobus monkey, Diana monkey(?), Chimp
- examples: predator calls in vervet monkeys.
Another successful strategy
- living in groups
- theory of mind
- if primate have it or not?
- if they don't have , they can predict behavior of others?
- or they just predict based on past experience
Cheaters in ESS
- Tragedy of the commons- if everyone cheats then everyone will loose
- Thus, in a ESS there is selection against cheating. Cheaters are not eliminated completely but kept to a minimum
- Examples: monkey fooling con-specifics to hog food for itself. Can you think of other ones?
- 5人ぐらし。それぞれが家事を。1人がやらなくてもそこまで問題じゃないが、みんながやらなければ・・・。
- テストで話し合いが可だった。勉強しない人も点数が取れる。みんな勉強しなければ・・・
- Examples: monkey fooling con-specifics to hog food for itself. Can you think of other ones?
review
- Game theory is important
- Dove Hoke example
- evolutionary stable behavioral strategy
- cost-benefit of behavior
- retaliator and punishes model - represent human and chimp
- retaliator - against action
- punisher - against opponent
- come back later
- moral
- thing have to be learned
- evidence: varies depending on places
- religion
- culture
- social contract
- evidence: varies depending on places
- thing have to be learned
- game theory
- used to model behavior
- not have to be actual reality
- purpose is to test ideas
- evaluate condition mathematically
- test if the behavior or strategy is stable or not