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pslct026

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<title>Modelling nature's non-linearity: evolutionary game theory </title></titleStmt>

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<idno>pslct026</idno>

<availability><p>The British Academic Spoken English (BASE) corpus was developed at the

Universities of Warwick and Reading, under the directorship of Hilary Nesi

(Centre for English Language Teacher Education, Warwick) and Paul Thompson

(Department of Applied Linguistics, Reading), with funding from BALEAP,

EURALEX, the British Academy and the Arts and Humanities Research Board. The

original recordings are held at the Universities of Warwick and Reading, and

at the Oxford Text Archive and may be consulted by bona fide researchers

upon written application to any of the holding bodies.

The BASE corpus is freely available to researchers who agree to the

following conditions:</p>

<p>1. The recordings and transcriptions should not be modified in any

way</p>

<p>2. The recordings and transcriptions should be used for research purposes

only; they should not be reproduced in teaching materials</p>

<p>3. The recordings and transcriptions should not be reproduced in full for

a wider audience/readership, although researchers are free to quote short

passages of text (up to 200 running words from any given speech event)</p>

<p>4. The corpus developers should be informed of all presentations or

publications arising from analysis of the corpus</p><p>

Researchers should acknowledge their use of the corpus using the following

form of words:

The recordings and transcriptions used in this study come from the British

Academic Spoken English (BASE) corpus, which was developed at the

Universities of Warwick and Reading under the directorship of Hilary Nesi

(Warwick) and Paul Thompson (Reading). Corpus development was assisted by

funding from the Universities of Warwick and Reading, BALEAP, EURALEX, the

British Academy and the Arts and Humanities Research Board. </p></availability>

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<date>19/10/1998</date><equipment><p>video</p></equipment>

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<u who="nm0867"> <vocal desc="clears throat" iterated="n"/> <pause dur="0.5"/> okay <pause dur="0.4"/> can i have your attention please <pause dur="2.1"/> we shall do the test in the last <pause dur="0.5"/> # <pause dur="0.3"/> fifteen twenty minutes of the <pause dur="0.6"/> lecture <pause dur="1.2"/> and now i will briefly remind you what we were doing last week <pause dur="1.6"/> first <pause dur="0.3"/> well <pause dur="0.2"/> and the week before that first we can see that <pause dur="1.2"/> # <pause dur="0.5"/> in a game <pause dur="0.5"/> of hawks <pause dur="0.3"/> and doves <pause dur="1.4"/> we <pause dur="0.2"/> found <pause dur="0.4"/> an equilibrium <pause dur="1.2"/> in this game <pause dur="2.5"/> then we introduced <pause dur="0.5"/> another strategy of the game <pause dur="0.6"/> bullies <pause dur="2.5"/> and we can see that the three subgames of the game of three <pause dur="0.5"/> strategies <pause dur="1.3"/> and that's what we found <pause dur="0.5"/> don't # <pause dur="0.8"/> # draw this picture in your notebooks <pause dur="0.2"/> # we'll <pause dur="0.4"/> # draw something like that a little later <pause dur="0.6"/> just remind you what they have <pause dur="0.9"/> three strategies <pause dur="0.5"/> if we <pause dur="0.6"/> omit <pause dur="0.6"/> a third one <pause dur="0.4"/> then <pause dur="0.2"/> in the remaining two <pause dur="0.3"/> that's what we call the subgame <pause dur="0.6"/> hawk <pause dur="0.2"/> doves <pause dur="0.8"/> and <sic corr="equilibria">equilibriums</sic> <pause dur="0.8"/> one-third <pause dur="0.5"/> from hawks <pause dur="1.5"/> # in the subgame <pause dur="0.3"/> consisting of hawks and bullies <pause dur="0.8"/> we <pause dur="0.7"/> again had an equilibrium <pause dur="0.5"/> somewhere between <pause dur="0.5"/> those two strategies <pause dur="0.6"/> and if we considered <pause dur="0.7"/> and when we considered <pause dur="0.2"/> that such game consisting of <pause dur="0.2"/> doves <pause dur="0.4"/> and bullies <pause dur="0.6"/> we didn't find any equilibrium <pause dur="0.6"/> and the

system was evolving <pause dur="0.3"/> towards <pause dur="0.2"/> bullies <pause dur="0.7"/> # <pause dur="0.2"/> doves <pause dur="0.2"/> did not survive <pause dur="2.1"/> # <pause dur="1.5"/> interaction with bullies <pause dur="0.9"/> now the question okay <pause dur="0.4"/> these <pause dur="1.1"/> # <pause dur="0.4"/> well <pause dur="2.4"/><kinesic desc="indicates point on board" iterated="n"/> this <pause dur="0.3"/><kinesic desc="indicates point on board" iterated="n"/> this <pause dur="0.2"/> and <kinesic desc="indicates point on board" iterated="n"/> this <pause dur="1.2"/> are <pause dur="0.6"/> some <pause dur="0.2"/> # <pause dur="0.4"/> evolutionist table <pause dur="0.8"/> populations for the subgames <pause dur="0.4"/> what happens if we introduce <pause dur="1.9"/> the third strategy <pause dur="1.2"/> that's where we start the lecture <pause dur="13.1"/><event desc="turns on overhead projector" iterated="n"/><kinesic desc="puts on transparency" iterated="n"/> in other words <pause dur="10.8"/> we found <pause dur="0.4"/> three <pause dur="0.4"/> evolutionary stable <pause dur="0.3"/> populations <pause dur="0.5"/> for the subgames <pause dur="0.5"/><kinesic desc="indicates point on board" iterated="n"/> this one <pause dur="0.5"/><kinesic desc="indicates point on board" iterated="n"/> this one <pause dur="0.6"/> and <kinesic desc="indicates point on board" iterated="n"/> this one <pause dur="1.1"/> the question is <pause dur="0.7"/> are these <pause dur="2.1"/> E-S-Ps <pause dur="0.2"/> stable with respect <pause dur="0.2"/> to introduction <pause dur="0.6"/> of the <pause dur="0.3"/> third strategy <pause dur="0.7"/> and that's how we're going to approach it <pause dur="1.9"/> can see that for example <pause dur="7.6"/> can see that for example <pause dur="1.4"/><kinesic desc="indicates point on board" iterated="n"/> this point <pause dur="2.4"/> # <pause dur="3.2"/><kinesic desc="writes on board" iterated="y" dur="8"/> this point is described <pause dur="0.5"/> by <pause dur="0.3"/> the vector <pause dur="1.5"/> of <pause dur="0.2"/> i think it's two-thirds <pause dur="6.8"/><kinesic desc="writes on board" iterated="y" dur="5"/> two-thirds <pause dur="0.9"/> one-third <pause dur="0.7"/> zero <pause dur="4.7"/> so this is <pause dur="0.9"/><kinesic desc="writes on board" iterated="y" dur="1"/> X <pause dur="1.7"/> if we multiply that by the pay-off <pause dur="0.2"/> matrix <pause dur="1.1"/><kinesic desc="writes on board" iterated="y" dur="2"/> we get <pause dur="1.1"/> the fitnesses <pause dur="6.9"/><kinesic desc="writes on board" iterated="y" dur="14"/> and for this case it is <pause dur="0.3"/> four-thirds <pause dur="2.3"/> four-thirds <pause dur="1.6"/> and eight-thirds <pause dur="2.5"/> so the <pause dur="0.2"/> hawks <pause dur="0.3"/> and the doves <pause dur="1.2"/> they're doing on par <pause dur="0.2"/> which is expected after all <pause dur="0.4"/> it is <pause dur="0.4"/> the equilibrium <pause dur="0.2"/> of the subgame <pause dur="0.8"/> but interestingly <pause dur="0.6"/><kinesic desc="writes on board" iterated="y" dur="1"/><kinesic desc="indicates point on board" iterated="n"/> the bullies <pause dur="1.0"/> are doing

better than the other two <pause dur="0.8"/> what it means it means that if we introduce a very small proportion <pause dur="0.3"/> of bullies <pause dur="1.1"/> to this <pause dur="0.7"/> system <pause dur="1.3"/> it'll drive away <pause dur="1.3"/> from the E-S-P <pause dur="1.3"/> because <trunc>bu</trunc> bullies are doing better <pause dur="0.3"/> than both <pause dur="0.2"/> hawks <pause dur="0.5"/> and doves <pause dur="27.7"/><kinesic desc="reveals covered part of transparency" iterated="n"/> now it's clear what we should do in the general case <pause dur="0.7"/> oh <pause dur="0.2"/> for <pause dur="0.4"/> the other two <pause dur="0.2"/> E-S-Ps <pause dur="0.9"/> the same thing <pause dur="1.7"/> describe for example <kinesic desc="indicates point on board" iterated="n"/> this point or <kinesic desc="indicates point on board" iterated="n"/> this point by <pause dur="1.7"/> a similar vector <pause dur="1.8"/> multiply it by the pay-off matrix <pause dur="6.3"/> and obtain the fitness <pause dur="1.2"/> vector <pause dur="1.7"/> and then <pause dur="12.9"/><event desc="presses light switches" iterated="y" dur="1"/> i'm not really sure what's going on with the lights <vocal desc="laughter" iterated="y" n="sl" dur="1"/><pause dur="4.3"/> and # <pause dur="0.3"/> just check <pause dur="0.5"/> which of the strategies <pause dur="0.6"/> is <pause dur="0.3"/> bigger <pause dur="6.4"/><kinesic desc="reveals covered part of transparency" iterated="n"/> i skipped <pause dur="1.1"/> the calculations <pause dur="1.3"/> in fact i have included them <pause dur="1.0"/> in the <pause dur="1.0"/> problem sheet <pause dur="0.2"/> in the next problem sheet <pause dur="6.0"/> just the conclusions <pause dur="1.7"/> so <kinesic desc="writes on board" iterated="y" dur="1"/><kinesic desc="indicates point on board" iterated="n"/> this point is <pause dur="1.9"/> unstable <pause dur="1.1"/> as we found out in the first place <pause dur="1.4"/> # <kinesic desc="writes on board" iterated="y" dur="1"/><kinesic desc="indicates point on board" iterated="n"/> this point is stable <pause dur="1.3"/> and <kinesic desc="writes on board" iterated="y" dur="1"/><kinesic desc="indicates point on board" iterated="n"/> this point is <pause dur="0.9"/> unstable <pause dur="3.0"/> so that's what we've got <pause dur="8.8"/><kinesic desc="reveals covered part of transparency" iterated="n"/> now we're going to introduce the notion of a flow chart <pause dur="4.2"/> and this is more or less <pause dur="0.3"/> the same kind of picture <pause dur="1.0"/> as we've got here <pause dur="31.9"/><kinesic desc="writes on board" iterated="y" dur="7"/> three strategies <pause dur="0.7"/> three coordinates <pause dur="1.5"/> X hawks <pause dur="1.4"/><kinesic desc="writes on board" iterated="y" dur="8"/> X <pause dur="0.2"/> doves <pause dur="1.0"/>

and X <pause dur="0.6"/> # <pause dur="0.7"/> X <pause dur="1.3"/> bullies <pause dur="5.9"/> but not <pause dur="0.2"/> any point <pause dur="0.8"/> is allowable <pause dur="0.5"/> in this space clearly <pause dur="0.5"/> we <pause dur="0.3"/> # <pause dur="0.8"/> should satisfy the condition <pause dur="1.0"/><kinesic desc="writes on board" iterated="y" dur="1"/> that <pause dur="0.2"/> the proportions of the strategies <pause dur="0.2"/> add up <pause dur="0.2"/> to one <pause dur="0.2"/><kinesic desc="writes on board" iterated="y" dur="6"/> so it's <pause dur="0.4"/> X-H-plus-<pause dur="0.5"/>X-dove-<pause dur="0.4"/>plus-<pause dur="0.2"/>X-<pause dur="0.5"/>bullies <pause dur="0.8"/> add up to unity <pause dur="1.2"/> which cuts <pause dur="3.4"/><kinesic desc="writes on board" iterated="y" dur="2"/> and of course <pause dur="1.2"/> the the three <pause dur="0.8"/> corners should be positive <pause dur="1.0"/> so this cuts <pause dur="2.3"/><kinesic desc="indicates points on board" iterated="n"/> a triangle <pause dur="0.6"/> in between <pause dur="1.0"/> the axes <pause dur="1.4"/><kinesic desc="reveals covered part of transparency" iterated="n"/> and figure one <pause dur="1.6"/> is this one <pause dur="1.3"/> one <pause dur="0.4"/> one <pause dur="0.7"/> and one <pause dur="8.1"/> so what is <pause dur="0.4"/> the flow chart <pause dur="1.3"/> we want <pause dur="0.2"/> to show the trajectories <pause dur="0.2"/> of our system <pause dur="0.3"/> on this <pause dur="0.7"/><kinesic desc="indicates point on board" iterated="n"/> triangle <pause dur="0.8"/> so what <pause dur="0.2"/> what do we need to do <pause dur="1.8"/> we know we need <pause dur="0.3"/> to <pause dur="1.5"/> write down <pause dur="0.3"/> the <pause dur="0.2"/> dynamics equations <pause dur="3.9"/> solve them <pause dur="3.8"/><kinesic desc="writes on transparency" iterated="y" dur="1"/> and <pause dur="0.2"/> draw <pause dur="1.1"/> the solutions <pause dur="16.2"/><kinesic desc="puts on transparency" iterated="n"/> on the triangle <pause dur="11.8"/> the second and the third items <pause dur="2.2"/> on this list <pause dur="1.1"/> on this list <pause dur="0.2"/> # they are effectively <pause dur="1.2"/> # <pause dur="0.4"/> equivalent to <pause dur="0.6"/> solving <pause dur="0.2"/> the dynamics equations <pause dur="6.0"/><kinesic desc="reveals covered part of transparency" iterated="n"/> but <pause dur="0.2"/> we don't really need to be very precise <pause dur="1.0"/> about drawing the trajectories <pause dur="2.7"/> we want to # <pause dur="0.5"/> understand <pause dur="0.2"/> just qualitatively <pause dur="1.2"/> how the trajectories go <pause dur="1.1"/> and for that we don't really need to solve equations or follow <pause dur="0.4"/> these three <pause dur="2.9"/> items <pause dur="1.3"/>

what we really need to know <pause dur="1.9"/> is <pause dur="5.5"/> is this <pause dur="8.0"/><kinesic desc="indicates point on board" iterated="n"/> the equilibrium positions <pause dur="0.2"/> and evolutionarist table <pause dur="0.5"/> populations <pause dur="0.5"/> of the subgames <pause dur="0.4"/> and of the game <pause dur="0.3"/> itself <pause dur="0.6"/><kinesic desc="indicates point on board" iterated="n"/> this particular game <pause dur="0.2"/> doesn't have any <pause dur="0.9"/> E-P <pause dur="0.2"/> any equilibrium positions <pause dur="1.6"/> # <pause dur="0.4"/> in the middle of this triangle only <pause dur="0.6"/> subgames have <pause dur="1.0"/> equilibrium <pause dur="5.7"/> positions <pause dur="3.8"/> so then there is two <pause dur="13.5"/><kinesic desc="writes on board" iterated="y" dur="4"/> two possibilities <pause dur="2.1"/> # <pause dur="0.3"/> at this stage you <pause dur="0.6"/> probably need to stop <pause dur="1.0"/> writing and just watch <pause dur="1.7"/> what i'm <pause dur="0.7"/> going to draw here <pause dur="1.2"/><kinesic desc="indicates point on board" iterated="n"/> how <pause dur="1.0"/> what <pause dur="0.3"/> i know <pause dur="0.2"/> how trajectories <pause dur="0.4"/> behave <pause dur="0.6"/> on the sides <pause dur="0.2"/> of the triangle <pause dur="0.5"/> if <pause dur="0.3"/> i'm <kinesic desc="indicates point on board" iterated="n"/> here <pause dur="0.5"/> then <pause dur="0.2"/> the system evolves <pause dur="0.4"/> towards <pause dur="0.2"/> bullies <pause dur="0.6"/> if i'm <kinesic desc="indicates point on board" iterated="n"/> here <pause dur="0.6"/> the system evolves <pause dur="0.3"/> towards the equilibrium position <pause dur="0.8"/> on <kinesic desc="indicates point on board" iterated="n"/> this side <pause dur="0.4"/> the same <trunc>thi</trunc> thing <kinesic desc="indicates point on board" iterated="n"/> here <pause dur="0.3"/> and <kinesic desc="indicates point on board" iterated="n"/> here <pause dur="0.5"/> so how what happens <pause dur="0.3"/> if i am <pause dur="1.4"/> somewhere <kinesic desc="indicates point on board" iterated="n"/> here <pause dur="1.1"/> clearly if i'm closer to <kinesic desc="indicates point on board" iterated="n"/> this side <pause dur="0.6"/> i'll go <pause dur="2.3"/><kinesic desc="writes on board" iterated="y" dur="1"/> some way along <pause dur="0.5"/><kinesic desc="indicates point on board" iterated="n"/> this side if i'm closer <pause dur="0.2"/> to <kinesic desc="indicates point on board" iterated="n"/> this side <pause dur="0.5"/><kinesic desc="writes on board" iterated="y" dur="1"/> then i'll go <pause dur="0.2"/><kinesic desc="indicates point on board" iterated="n"/> this way <pause dur="2.7"/><kinesic desc="writes on board" iterated="y" dur="1"/> then i go go this way <pause dur="0.4"/> what can happen here clearly i can't <pause dur="0.5"/> hit <pause dur="0.5"/> the <trunc>vor</trunc> # the vertex <pause dur="1.0"/> # because if i am <kinesic desc="indicates point on board" iterated="n"/> here i will go <kinesic desc="indicates point on board" iterated="n"/> this way <pause dur="0.3"/> so <pause dur="0.7"/> clearly the trajectory has to <pause dur="0.3"/><kinesic desc="writes on board" iterated="y" dur="1"/>

turn at some stage <pause dur="0.8"/> and go <pause dur="0.2"/><kinesic desc="indicates point on board" iterated="n"/><kinesic desc="writes on board" iterated="y" dur="1"/> this way <pause dur="2.8"/> and <pause dur="0.7"/><kinesic desc="indicates point on board" iterated="n"/><kinesic desc="writes on board" iterated="y" dur="2"/> here <pause dur="2.7"/> it may go for example <pause dur="0.2"/><kinesic desc="writes on board" iterated="y" dur="1"/> toward <kinesic desc="indicates point on board" iterated="n"/> this equilibrium <pause dur="1.4"/> and <kinesic desc="indicates point on board" iterated="n"/> here <pause dur="1.3"/><kinesic desc="writes on board" iterated="y" dur="1"/> this equilibrium <pause dur="5.1"/> two possibilities <pause dur="0.2"/> # like i said <pause dur="0.4"/><kinesic desc="writes on board" iterated="y" dur="1"/> one of them <pause dur="0.2"/> is <kinesic desc="indicates point on board" iterated="n"/> this one <pause dur="2.7"/> in this case <pause dur="0.2"/><kinesic desc="writes on board" iterated="y" dur="1"/> it can't go this way <pause dur="0.4"/><kinesic desc="writes on board" iterated="y" dur="3"/> then it goes <pause dur="0.3"/> this way <pause dur="3.5"/> and <kinesic desc="indicates point on board" iterated="n"/> this case this one can't go this way <pause dur="0.4"/><kinesic desc="writes on board" iterated="y" dur="1"/> goes <pause dur="0.4"/> this way <pause dur="1.5"/> the other possibility <pause dur="3.9"/><kinesic desc="writes on board" iterated="y" dur="28"/> this bit <pause dur="0.2"/> is exactly the same <pause dur="4.4"/> hawks <pause dur="0.3"/> doves <pause dur="0.9"/> bullies <pause dur="0.9"/> equilibrium equilibrium <pause dur="1.0"/> but the difference between <kinesic desc="indicates point on board" iterated="n"/> this would be <pause dur="0.9"/> for this way <pause dur="1.1"/> and in this case <pause dur="5.5"/> which one is correct <pause dur="4.0"/> which which of the two scenarios is correct </u><pause dur="0.5"/> <u who="sm0868" trans="pause"> the first </u><pause dur="0.6"/> <u who="nm0867" trans="pause"> the first why </u><pause dur="0.5"/> <u who="sm0868" trans="pause"> because <pause dur="0.2"/> the other two the other two points are unstable </u><pause dur="0.5"/> <u who="nm0867" trans="pause"> that's correct <pause dur="0.7"/><kinesic desc="indicates point on board" iterated="n"/> this implies that <kinesic desc="indicates point on board" iterated="n"/> this is unstable and <kinesic desc="indicates point on board" iterated="n"/> this is stable <pause dur="1.2"/> # <kinesic desc="indicates point on board" iterated="n"/> this one is <pause dur="0.2"/> the other way around <pause dur="0.4"/> and we just now we just checked <pause dur="0.6"/><kinesic desc="writes on board" iterated="y" dur="15"/> before that <pause dur="0.5"/> this is unstable <pause dur="1.5"/> and this <pause dur="0.2"/> is stable so that's <pause dur="0.8"/> the way to go <pause dur="1.1"/> correct <pause dur="4.5"/> wrong <pause dur="3.6"/> and that's how we <pause dur="1.1"/> will approach <pause dur="0.9"/> similar problems in the future <pause dur="1.2"/> we won't solve <pause dur="0.4"/> differential equations <pause dur="1.6"/> we shall examine <pause dur="2.0"/> # <pause dur="0.2"/> equilibria <pause dur="1.4"/>

we <trunc>sh</trunc> well we shall find <pause dur="0.4"/> the equilibria of the system <pause dur="0.9"/> we shall examine the stability <pause dur="0.7"/> of those equilibria <pause dur="1.1"/> and then we just draw <pause dur="0.9"/> a flow chart <pause dur="0.2"/> and if we know <pause dur="0.2"/> the <pause dur="0.2"/> the flow chart then <pause dur="0.2"/> we'll <trunc>ba</trunc> we'll basically know everything about <pause dur="0.5"/> our system <pause dur="10.5"/><kinesic desc="changes transparency" iterated="y" dur="15"/> i know that you haven't done differential <pause dur="0.3"/> equations <pause dur="0.8"/> at this stage you are going to do that next term i suppose <pause dur="1.7"/> # <pause dur="4.1"/> but <pause dur="0.2"/> i will <pause dur="0.7"/> just introduce bits and pieces from <pause dur="0.3"/> the theory of differential equations </u><pause dur="1.4"/> <u who="sm0869" trans="pause"> excuse me <pause dur="0.2"/> just one question </u><pause dur="0.5"/> <u who="nm0867" trans="pause"> yeah sure </u><u who="sm0869" trans="latching"> # <pause dur="0.4"/> you're saying <pause dur="0.2"/> that it's an unstable point for the equilibrium at the bottom <pause dur="0.8"/> but is it 'cause it's a subgame of hawks and doves yeah </u><pause dur="0.4"/> <u who="nm0867" trans="pause"> that's correct </u><u who="sm0869" trans="latching"> is this a subgame of hawks and doves will it be a stable one </u><pause dur="0.9"/> <u who="nm0867" trans="pause"> in the subgame yes </u><u who="sm0869" trans="overlap"> subgame but when you </u><u who="nm0867" trans="overlap"> so </u><u who="sm0869" trans="latching"> introduce the bullies it becomes unstable </u><u who="nm0867" trans="overlap"> yeah that's correct if we're exactly on <pause dur="0.3"/><kinesic desc="indicates point on board" iterated="n"/> this side of the triangle <pause dur="0.2"/> we do go <pause dur="0.4"/><kinesic desc="indicates point on board" iterated="n"/> this way <pause dur="0.4"/> but <pause dur="0.2"/> any trajectory which is <pause dur="0.6"/> infinitesimally <pause dur="0.3"/> above <pause dur="0.7"/> the set <pause dur="0.3"/> will go away <pause dur="1.3"/> it will never enter <pause dur="0.7"/> the point <pause dur="3.2"/> so the # separatrix <pause dur="1.2"/> so

forget this <kinesic desc="indicates point on board" iterated="n"/> that's an arrow <kinesic desc="indicates point on board" iterated="n"/> that's what is really going on <pause dur="0.5"/> and the <pause dur="0.3"/> separatrix <pause dur="0.9"/> is <pause dur="0.9"/><kinesic desc="indicates point on board" iterated="n"/> this bit <pause dur="3.7"/> so <pause dur="0.9"/> to the right from the separatrix <pause dur="0.3"/> the trajectories <pause dur="0.2"/> originate <pause dur="0.4"/> basically from <pause dur="1.5"/> # <pause dur="0.2"/><kinesic desc="indicates point on board" iterated="n"/> this point <pause dur="1.4"/> and <pause dur="0.5"/> to the left <pause dur="0.2"/> from the separatrix <pause dur="0.5"/> all the trajectories originate <pause dur="0.4"/><kinesic desc="indicates point on board" iterated="n"/> from this point <pause dur="2.8"/> and <pause dur="0.7"/> well basically <pause dur="0.3"/><kinesic desc="indicates point on board" iterated="n"/> at this point <pause dur="0.2"/> you you should <pause dur="0.2"/> consider it <pause dur="0.6"/> not as an origin of <kinesic desc="indicates point on board" iterated="n"/> this trajectory <pause dur="0.4"/> but rather a midpoint <pause dur="0.5"/> of this <pause dur="0.9"/><kinesic desc="indicates point on board" iterated="n"/> trajectory <pause dur="5.5"/> # <pause dur="6.3"/><kinesic desc="reveals covered part of transparency" iterated="n"/> so that is # very unfortunate <pause dur="0.3"/> for the doves <pause dur="0.5"/> conclusion </u><pause dur="8.0"/> <u who="nm0867" trans="pause"> when i was lecturing this course <pause dur="0.5"/> last year <pause dur="2.2"/> # <pause dur="2.8"/> i was curious <pause dur="0.2"/> if it is <pause dur="0.2"/> possible at all <pause dur="0.9"/> to modify the rules of the game <pause dur="0.5"/> so <pause dur="0.9"/> the doves will survive <pause dur="1.4"/> and it turned out that it is very difficult <pause dur="1.1"/> they can't survive in direction of the hawks <pause dur="0.4"/> but if you've got hawks and bullies <pause dur="0.4"/> which act slightly differently <pause dur="0.6"/> with respect to doves <pause dur="1.3"/> # doves have very slim chances of surviving <pause dur="0.4"/> still i was experimenting and eventually i did find <pause dur="0.4"/> a couple of <pause dur="1.0"/> ways to <pause dur="1.0"/> let # the doves survive <pause dur="0.9"/><kinesic desc="reveals covered part of transparency" iterated="n"/> so the next <pause dur="1.3"/> section is <pause dur="0.5"/> new

species <pause dur="0.5"/> of <pause dur="0.5"/> <unclear>oh well</unclear> <pause dur="0.4"/> mathematically speaking more <pause dur="1.0"/> strategies <pause dur="6.9"/> first <pause dur="1.0"/> retaliators <pause dur="3.7"/><kinesic desc="reveals covered part of transparency" iterated="n"/> ah sorry <vocal desc="laugh" iterated="n"/></u><pause dur="1.0"/> <u who="sm0870" trans="pause"> could you put it back down a little <gap reason="inaudible" extent="1 sec"/> </u><u who="nm0867" trans="overlap"> yeah sure </u><gap reason="break in recording" extent="uncertain"/> <u who="nm0867" trans="pause"> first i tried to make bullies <pause dur="0.2"/> sillier <pause dur="2.7"/> # <pause dur="0.3"/> remember when <pause dur="0.2"/> two <pause dur="0.3"/> bullies <pause dur="0.5"/> meet <pause dur="0.4"/> and fight over a piece of resources <pause dur="0.7"/> they share their win <pause dur="0.4"/> without <pause dur="0.4"/> wasting time <pause dur="0.4"/> which <pause dur="0.2"/> gave them <pause dur="0.2"/> three <pause dur="0.2"/> and <pause dur="0.3"/> three <pause dur="4.1"/> and <pause dur="0.4"/> and that's what <pause dur="0.3"/> made them very difficult to compete with <pause dur="0.7"/> with respect to <pause dur="0.2"/> doves <pause dur="1.0"/> 'cause # doves do <pause dur="0.3"/> waste <pause dur="0.6"/> time <pause dur="0.8"/> so i tried to make <pause dur="0.3"/> bullies <pause dur="2.4"/> waste time <pause dur="3.0"/> and i checked <pause dur="0.7"/> the game <pause dur="0.2"/> consisting of <pause dur="1.1"/> hawks <pause dur="0.2"/> doves and silly bullies <pause dur="1.9"/> and it turned <pause dur="0.7"/> out that <pause dur="0.2"/> doves <pause dur="0.3"/> don't survive <pause dur="3.2"/> even with # <pause dur="1.0"/> with this modification <pause dur="20.3"/><kinesic desc="reveals covered part of transparency" iterated="n"/><kinesic desc="writes on transparency" iterated="y" dur="1"/> next i'll try i tried to make <pause dur="0.5"/> doves <pause dur="0.9"/> more clever <pause dur="9.4"/><kinesic desc="puts on transparency" iterated="n"/> so the difference <pause dur="0.2"/> here is <pause dur="3.5"/><kinesic desc="writes on transparency" iterated="y" dur="2"/> those numbers <pause dur="1.4"/> now <pause dur="2.9"/> doves do not <pause dur="0.4"/> waste time <pause dur="10.8"/> i don't really <pause dur="0.2"/><vocal desc="laugh" iterated="n"/> remember if this worked but apparently it didn't <pause dur="2.4"/> # because i tried <pause dur="0.5"/> then to introduce <pause dur="0.4"/> a species <pause dur="0.4"/> which would protect <pause dur="1.1"/> doves <pause dur="0.7"/> from <pause dur="1.2"/> hawks <pause dur="3.0"/> that is it would compete with hawks stronger <pause dur="0.5"/> than it would compete with doves <pause dur="0.6"/> and that's <pause dur="0.4"/> what <pause dur="0.3"/> the so-called

retaliators do <pause dur="13.0"/><kinesic desc="reveals covered part of transparency" iterated="n"/> basically # the <pause dur="1.1"/> notion of retaliators <pause dur="1.3"/> they <trunc>beha</trunc> with hawks <pause dur="0.3"/> they behave <pause dur="0.3"/> like hawks <pause dur="2.0"/> and with doves <pause dur="0.4"/> they behave <pause dur="0.3"/> like <pause dur="0.5"/> like doves <pause dur="23.9"/> so that is <pause dur="0.6"/><kinesic desc="indicates point on screen" iterated="n"/> you see <pause dur="0.6"/> the difference here <pause dur="1.0"/> # <pause dur="0.5"/> retaliators <pause dur="0.4"/> don't <pause dur="0.3"/> waste time <pause dur="1.0"/> doves <pause dur="2.0"/> do waste time <pause dur="0.3"/> and in fact this didn't work either <pause dur="0.6"/> # <pause dur="0.2"/> in a game <pause dur="1.3"/><gap reason="inaudible" extent="1 sec"/> which includes <pause dur="0.3"/> hawks <pause dur="0.6"/> retaliators and doves <pause dur="0.7"/> # <pause dur="1.2"/> # <pause dur="0.5"/> doves do not survive <pause dur="0.3"/> and when <pause dur="0.4"/> # they disappear from the system then <pause dur="0.2"/> retaliators don't <pause dur="0.3"/> # differ from hawks <pause dur="1.5"/> and in fact it's fairly interesting <pause dur="0.4"/> situation here <pause dur="0.8"/> # if you draw <pause dur="0.4"/> a flow chart for this <pause dur="0.2"/> game <pause dur="1.9"/><kinesic desc="writes on board" iterated="y" dur="42"/> like <pause dur="0.3"/> hawks <pause dur="0.5"/> # don't write this down just <pause dur="0.4"/> aside <pause dur="0.5"/> hawks <pause dur="0.5"/> <trunc>do</trunc> # <pause dur="0.2"/> doves <pause dur="0.5"/> and retaliators <pause dur="0.8"/> we still have this <kinesic desc="indicates point on board" iterated="n"/><pause dur="1.1"/> # <pause dur="1.5"/> unstable <pause dur="0.4"/> equilibrium <pause dur="1.7"/> # <pause dur="0.2"/> but in fact <pause dur="0.2"/> any point <pause dur="0.5"/> of this <pause dur="0.5"/> any point of <kinesic desc="indicates point on board" iterated="n"/> this side <pause dur="0.2"/> is a stable equilibrium <pause dur="1.1"/> if a trajectory from here for example <pause dur="0.3"/> hits <pause dur="1.9"/> # <pause dur="0.3"/> a point <pause dur="0.3"/> and the set <pause dur="0.2"/> is going to be stable <pause dur="0.3"/> i don't <trunc>re</trunc> actually remember how the flow chart goes but <pause dur="0.6"/> # <pause dur="1.7"/> i vaguely remember that it is like this <pause dur="0.3"/> and every trajectory <pause dur="0.4"/> # ends <pause dur="0.3"/><kinesic desc="indicates point on board" iterated="n"/> at this side and <pause dur="0.2"/> the system doesn't

evolve <pause dur="0.3"/> after that <pause dur="5.5"/><kinesic desc="puts on transparency" iterated="n"/> then i <pause dur="1.8"/> can see that <pause dur="3.6"/> well <pause dur="0.3"/> obviously <pause dur="9.1"/> silly retaliators <pause dur="2.3"/> again the difference is that <pause dur="1.8"/> silly <pause dur="0.6"/> retaliators waste time <pause dur="0.7"/> unlike their cleverer <pause dur="2.1"/> brothers <pause dur="1.4"/> just <pause dur="0.8"/> wait a second <pause dur="8.5"/><kinesic desc="writes on transparency" iterated="y" dur="1"/> and eventually the pinnacle <pause dur="0.2"/> of my creativity <pause dur="0.7"/> swingers <pause dur="5.4"/><kinesic desc="reveals covered part of transparency" iterated="n"/><vocal desc="laughter" iterated="y" n="ss" dur="4"/> # <vocal desc="laugh" iterated="n"/> these guys they don't <pause dur="0.3"/> # follow <unclear>just like</unclear> strategies <pause dur="0.6"/> they follow <pause dur="0.8"/> they behave like hawks <pause dur="0.3"/> or doves <pause dur="0.3"/> with fifty per cent probability depending on random things <pause dur="0.4"/> like # <pause dur="0.3"/> what they had <pause dur="0.8"/> eaten <pause dur="0.6"/> the day before yesterday or <pause dur="1.0"/> to the the mood they <pause dur="0.2"/> and in fact # i'd <vocal desc="laugh" iterated="n"/> to tell the truth i haven't <pause dur="0.7"/> # examined this situation but <pause dur="1.0"/> # <pause dur="0.3"/> what <trunc>at</trunc> attracts me in this particular thing is that <pause dur="0.4"/> i've met a lot of people like that </u><pause dur="10.8"/><vocal desc="laughter" iterated="y" n="ss" dur="2"/> <u who="sm0871" trans="pause"> sorry can you move it down a bit </u><pause dur="0.6"/> <u who="sm0872" trans="pause"> <gap reason="inaudible" extent="5 secs"/></u><pause dur="0.4"/> <u who="nm0867" trans="pause"> <trunc>s</trunc> sorry say it again </u><pause dur="0.4"/> <u who="sm0872" trans="pause"> i mean the <pause dur="0.4"/> there are four <pause dur="0.6"/> species now <pause dur="0.2"/> i mean <pause dur="0.2"/> shouldn't you have <gap reason="inaudible" extent="1 sec"/> </u><u who="nm0867" trans="overlap"> no no what i was thinking <pause dur="0.5"/> of is <pause dur="0.4"/> hawks and doves they stay in the system in all cases <pause dur="0.6"/> and then i was trying to replace bullies with something else <pause dur="0.6"/> which would <pause dur="0.8"/> # </u><pause dur="0.7"/> <u who="sm0873" trans="pause"> no i <trunc>th</trunc> i think he means on that table <gap reason="inaudible" extent="1 sec"/></u><u who="sm0872" trans="overlap"> yeah

i mean <gap reason="inaudible" extent="1 sec"/> </u><pause dur="1.0"/> <u who="sm0874" trans="pause"> yeah it's S </u><pause dur="0.3"/> <u who="sm0875" trans="pause"> should be S </u><u who="nm0867" trans="latching"> ah yeah that should be S so sorry S-R <pause dur="0.8"/> yeah three strategies <pause dur="0.3"/> when you can see the four strategies there <pause dur="0.4"/> # <pause dur="0.3"/> # the system <trunc>me</trunc> # becomes fairly difficult to examine <trunc>m</trunc> mathematically <pause dur="0.5"/> it's <trunc>n</trunc> just just cumbersome not difficult <pause dur="15.8"/><kinesic desc="reveals covered part of transparency" iterated="n"/> unfortunately # like i said the numbers here become <pause dur="0.6"/> # fractional # <pause dur="1.2"/> i just don't have the patience to <pause dur="0.5"/> examine if <pause dur="0.2"/> how <pause dur="0.5"/> # <pause dur="0.2"/> how this species behaves <pause dur="0.9"/> in a in # <pause dur="2.3"/> in a game with <pause dur="0.9"/> other species <pause dur="30.0"/> and <pause dur="0.7"/> i take you understand <pause dur="0.6"/> the meaning <pause dur="0.2"/> of <kinesic desc="indicates point on screen" iterated="n"/> those numbers <pause dur="0.2"/> here </u><u who="sf0876" trans="latching"> <gap reason="inaudible" extent="1 sec"/></u><pause dur="0.9"/> <u who="nm0867" trans="pause"> minus-two means both swingers fight choose to fight <pause dur="1.1"/><kinesic desc="indicates point on screen" iterated="n"/> this <pause dur="0.2"/> means that <pause dur="0.2"/> the first <pause dur="0.2"/> well <pause dur="0.2"/> any <pause dur="0.6"/> well the first <pause dur="0.8"/> # <pause dur="0.2"/> swinger runs away <pause dur="0.5"/> # the second gets the prize <pause dur="0.6"/><kinesic desc="indicates point on screen" iterated="n"/> this <pause dur="0.9"/> is the reverse situation <pause dur="0.2"/> the first takes the prize the second one <pause dur="0.2"/> runs away <pause dur="0.2"/> and <kinesic desc="indicates point on screen" iterated="n"/> that's they share <pause dur="0.7"/> without waste wasting time <pause dur="0.8"/> # <shift feature="voice" new="laugh"/>again <shift feature="voice" new="normal"/>you can consider <pause dur="0.2"/> silly swingers but swingers are <pause dur="1.1"/> again my <pause dur="0.8"/> # <pause dur="0.9"/> the people i know they <pause dur="0.2"/> never waste time <pause dur="0.3"/><vocal desc="laughter" iterated="y" n="ss" dur="1"/> they just do what # <pause dur="0.9"/> # <pause dur="0.4"/> what they want on the spur of the moment <pause dur="2.9"/> it would be uncharacteristic of the swinger to <pause dur="0.9"/> but <pause dur="1.6"/> # <pause dur="0.9"/> and i'm afraid that's # <pause dur="0.6"/> where we have to proceed with the test

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