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2011-10-13

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
  • 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
pointsEnd result
50win
0loose
-100seriously injured
-10wasting 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

HawkDove
Hawk50 / -10050 / 0
Dove0 / 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?

CooperateDefect
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.
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

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・・・

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

  • 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


霊長類行動学もくじ

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