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T12. 攻擊與賽局理論 ( Aggression and Game theory) 鄭先祐 (Ayo) 教授 國立台南大學 環境與生態學院 生態科學與技術學系 環境生態研究所 + 生態旅遊研究所 動物行為學 ( 通識 ) 國立臺南大學 通識課程 2011 年春 Ayo NUTN Web: http://myweb.nutn.edu.tw/~hycheng/ http://myweb.nutn.edu.tw/~hycheng/

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攻擊與賽局理論 Ayo 2011 Ethology ( 通識 ) 2 Fight or flight? ( 攻擊或逃走？ ) Game theory ( 賽局理論 ) The Hawk-Dove Game ( 鷹鴿賽局 ) Winner, loser, bystander, and audience effects

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Ayo 2011 Ethology ( 通識 ) 3 Intruder aggression When a wasp (left) approaches a nest, guards at the nest determine whether it ’ s a hive mate or an intruder. Intruders are aggressively repelled. Conflict → fight or flight?

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Fight or flight? ( 攻擊或逃走？ ) Ayo 2011 Ethology ( 通識 ) 4 If fighting is costly, then once it is clear that an animal is losing a fight, it will often be beneficial for it to signal subordination, and hence reduce future costs. It may inhibit its aggressive behaviors. Color change may be particularly good communication vehicle in aggressive contests, where color may be linked to “badges of status”, and hence color change can quickly indicate an individual’s relative rank in a hierarchy and whether it will engage in aggressive behaviors. (Atlantic salmon)

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Ayo 2011 Ethology ( 通識 ) 5 color as a signal

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Serotonin ( 血清素 ) and aggression Ayo 2011 Ethology ( 通識 ) 6 In crustaceans, increased serotonergic function leads to enhanced aggression and high social status. 案例： when lobsters are paired up in fights, they generally escalate their aggressive behaviors through a series of ritualized combats. Once an individual loses a fight, however, it avoids aggressive interactions for days. But losers can be made more aggressive if they are given injections of serotonin.

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Ayo 2011 Ethology ( 通識 ) 7 When serotonin was continuously infused into subordinates (red bar), their aggressive levels surged. (A)the intensity of the aggression over time, and (B)the duration of the aggression.

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Game theory ( 賽局理論 ) Ayo 2011 Ethology ( 通識 ) 8 All game theory models must have some sort of variable that represents the value of the resource being contested. Deciding to fight (A) one of the many resources animals will fight over is food, as shown here by these vultures that are fighting over a carcass. (B) males also fight over females, here, male elephant seals are fighting over access to reproductively active females.

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Ayo 2011 Ethology ( 通識 ) 9 Game theory ( 賽局理論 ) Deciding to fight (A) one of the many resources animals will fight over is food, as shown here by these vultures that are fighting over a carcass. (B) males also fight over females, here, male elephant seals are fighting over access to reproductively active females.

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Value of a resource ( 某項資源的價值 ) Ayo 2011 Ethology ( 通識 ) 10 Two individuals contesting a resource may not assign the same value to that resource. For example, imaging that two animals – one of whom is starving, and the other of whom is hungry, but not starving – are contesting a ten-pounds of meat. To a starving animal, ten-pounds of food might make the difference between life and death, while to a less hungry animal the value of the ten pounds of meat might be much lower.

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Ayo 2011 Ethology ( 通識 ) 11 value estimation

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Territory ( 領域 ) Ayo 2011 Ethology ( 通識 ) 12 Consider the value of territory to a potential intruder and to a territory holder The territory holder will value a contested area (its territory) more because it has already invested time and energy in learning where the resources in such a territory are located

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The hawk-dove game( 鷹與鴿賽局 ) Ayo 2011 Ethology ( 通識 ) 13 Imagine that individuals can adopt one of two behavioral strategies when contesting some resource: (1) hawk( 鷹 )- wherein a player will escalate ( 增加 占有 ) and continue to escalate until either it is injured or its opponent cedes( 讓出 ) the resource, (2) dove( 鴿 ) – wherein a player displays as if it will escalate, but retreats and cedes ( 讓出 ) the resource if its opponent escalate.

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Ayo 2011 Ethology ( 通識 ) 14 V = the value of the contested resource C = the cost of fighting

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Ayo 2011 Ethology ( 通識 ) 15 Game theory ( 賽局理論 ) Why don’t animals always fight with maximum effort? Natural selection favors the individual that passes on more of its genes Game theory can help to understand the evolution of conflict Game theory: predicts an animal’s optimal behavior While taking into account the behavior of other animals

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Ayo 2011 Ethology ( 通識 ) 16 hawk-dove Game ( 鷹鴿賽局 ) The simplest game-theory model of aggression Two players fight over a resource Each opponent can play one of two strategies: hawk and dove Hawk strategy: immediately attack its opponent Dove strategy: flee immediately if confronted by a hawk Display if confronted by another dove If a hawk meets a hawk or a dove meets a dove Each opponent has a 50% chance of winning

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Ayo 2011 Ethology ( 通識 ) 17 The payoff matrix for the hawk-dove game Three variables measure a currency that relates to fitness: V = the value( 價值 ) of the resource being contested W = the cost of being wounded( 受傷 ) in a fight D = the cost of displaying( 展示 ) to an opponent Add some numbers: V = 30 W = 60 D = 5

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Ayo 2011 Ethology ( 通識 ) 18 Payoff for hawk – hawk interaction If an animal playing the hawk strategy meets another hawk Both attack immediately One hawk wins the resource: its payoff is V The other hawk will be wounded: its payoff is –W The average payoff for a hawk vs. hawk interaction Payoff for the winning hawk + the payoff for the losing hawk Divide by 2 to get the average V – W 2

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Ayo 2011 Ethology ( 通識 ) 19 Payoffs for other interactions Hawk against dove The hawk immediately attacks The dove flees Hawk wins the resource, so its payoff is V Dove against hawk The dove immediately flees The dove does not get injured Nor does it win anything - its payoff is 0

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Ayo 2011 Ethology ( 通識 ) 20 The payoff for dove vs. dove One wins the resource The other walks away Both pay the cost of display The payoff for the winning dove is V-D The payoff for the losing dove it is just –D Sum these and divide by 2 V ─ D ─ D V ─ 2D V = = ─ D 2 2 2

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Ayo 2011 Ethology ( 通識 ) 21

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Ayo 2011 Ethology ( 通識 ) 22

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How many hawks and doves? Ayo 2011 Ethology ( 通識 ) 23 Neither hawk nor dove is an evolutionarily stable strategy. Rather, the stable equilibrium composition of the population is some combination of hawks and doves in a mixed ESS. The stable proportion of hawks and doves occurs when the average payoff for the hawk strategy equals the average payoff for the dove strategy. Assume: p = the proportion of hawks in a population 1- p = the proportion of doves

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How many hawks and doves? Ayo 2011 Ethology ( 通識 ) 24 Payoff for hawk strategy = p (V-W)/2 + (1-p) V Payoff for dove strategy = p (0) + (1 – p) (V/2 – D) At equilibrium…. -15p + (1-p)30 = 0 + (1-p) 10 -15p + 30 -30p = 10 – 10p 30 – 45p = 10 – 10p 20 = 35 p p = 0.57

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Ayo 2011 Ethology ( 通識 ) 25 Understanding the game The currency = units of fitness These strategies are heritable Successful doves have offspring That also play the dove strategy Hawks give rise to hawks Game-theory models predict whether strategies in a population Increase in frequency Remain stable Or disappear

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Ayo 2011 Ethology ( 通識 ) 26 An evolutionarily stable strategy (ESS) A strategy that, when played by all members of the population Cannot be invaded by another strategy If the dove strategy is an ESS All members of the population play the dove strategy If an animal playing hawk entered All of its opponents would be doves The hawk strategy will do well The hawk’s genes increase The hawk strategy increases in frequency

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Ayo 2011 Ethology ( 通識 ) 27 Is the hawk strategy an ESS? Will the population eventually become all hawks? If the population is comprised of all hawks The average payoff drastically decreases If a dove enters the population It won’t win But it won’t be wounded during half its battles The frequency of the dove strategy would increase Neither a “pure hawk” strategy nor a “pure dove” strategy is an ESS

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Ayo 2011 Ethology ( 通識 ) 28 A mixed ESS is stable A mixed ESS: some combination of hawk and dove strategies that is stable The stable proportion of hawks and doves occurs When the average payoff for the hawk strategy equals the average payoff for the dove strategy A certain proportion of animals always plays hawk And another proportion always plays dove Or all animals play both hawk and dove

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Bourgeois （中產者） butterflies Ayo 2011 Ethology ( 通識 ) 29 In the Speckled wood butterfly, territories are not set in space. That is, rather than having territory with a set place in three dimensions, a male has a territory that is an open patch defined by well-lit areas that emerge when the sun breaks through the clouds. When a male comes upon an empty well-lit patch, he immediately occupies it and secures a mating advantage, compared to males not in sunlit territories. Resident wins rule （居住者贏）

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Ayo 2011 Ethology ( 通識 ) 30 Resident wins rule （居住者贏）

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Ayo 2011 Ethology ( 通識 ) 31 Antibourgeois Mexican spiders These spiders establish their territories under rocks, and when an intruder approaches a territory, the territory holder flees rather than fighting. The former territory holder then searches for a new territory. reverse bourgeois strategy

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Ayo NUTN website: http://myweb.nutn.edu.tw/~hycheng/ 問題與討論 動物行為學 ( 通識 ) 國立臺南大學 通識課程 2011 年春

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Chap.15 Play 鄭先祐 (Ayo) 教授 國立台南大學 環境與生態學院 生態科學與技術學系 環境生態研究所 + 生態旅遊研究所.

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