EvoLudoLab: Continuous Snowdrift Game - Branching (exp) - Revision history

Hauert at 07:06, 19 February 2026

2026-02-19T07:06:25Z

← Older revision		Revision as of 00:06, 19 February 2026
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	{{EvoLudoLab:CSD\|		{{EvoLudoLab:CSD\|
	options="--module cSD --run --delay 100 --view ~~Strategies_~~-_Distribution --timestep 50 --popsize 5000 --popupdate async --playerupdate imitate-better --geometry M --interactions r1 --references r1 --benefits 14 5,1 --costs 3 1,10 --traitrange 0,3 --init gaussian 2.8,0.02 --mutation 0.01 gaussian 0.02"\|		options="--module cSD --run --delay 100 --view Traits_-_Distribution --timestep 50 --popsize 5000 --popupdate async --playerupdate imitate-better --geometry M --interactions r1 --references r1 --benefits 14 5,1 --costs 3 1,10 --traitrange 0,3 --init gaussian 2.8,0.02 --mutation 0.01 gaussian 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

Hauert at 21:47, 12 August 2024

2024-08-12T21:47:34Z

← Older revision		Revision as of 14:47, 12 August 2024
Line 1:		Line 1:
	{{EvoLudoLab:CSD\|		{{EvoLudoLab:CSD\|
	options="--module cSD --run --delay 100 --view Strategies_-_Distribution --timestep 50 --popsize 5000 --popupdate async --playerupdate imitate-better --geometry M --interactions r1 --references r1 --benefits 14 5,1 --costs 3 1,10 --traitrange 0,3 --~~inittype~~ gaussian 2.8,0.02 --~~mutations~~ 0.01 gaussian 0.02"\|		options="--module cSD --run --delay 100 --view Strategies_-_Distribution --timestep 50 --popsize 5000 --popupdate async --playerupdate imitate-better --geometry M --interactions r1 --references r1 --benefits 14 5,1 --costs 3 1,10 --traitrange 0,3 --init gaussian 2.8,0.02 --mutation 0.01 gaussian 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

Hauert at 20:30, 4 August 2024

2024-08-04T20:30:28Z

← Older revision		Revision as of 13:30, 4 August 2024
Line 1:		Line 1:
	{{EvoLudoLab:CSD\|		{{EvoLudoLab:CSD\|
	options="--~~game~~ cSD --run --delay 100 --view Strategies_-_Distribution --~~reportfreq~~ 50 --popsize 5000 --popupdate async --playerupdate imitate --geometry M --~~intertype~~ r1 ~~--numinter 1~~ --references r1 --~~benefitfcn~~ 14 ~~--benefitparams~~ 5,1 --~~costfcn~~ 3 ~~--costparams~~ 1,10 --~~traitmax~~ 3 --~~init~~ 2.8,0.02 --~~inittype gaussian --mutation~~ 0.01 ~~--mutationtype g --mutationsdev~~ 0.02"\|		options="--module cSD --run --delay 100 --view Strategies_-_Distribution --timestep 50 --popsize 5000 --popupdate async --playerupdate imitate-better --geometry M --interactions r1 --references r1 --benefits 14 5,1 --costs 3 1,10 --traitrange 0,3 --inittype gaussian 2.8,0.02 --mutations 0.01 gaussian 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

Hauert at 22:16, 13 October 2023

2023-10-13T22:16:02Z

← Older revision		Revision as of 15:16, 13 October 2023
Line 1:		Line 1:
	{{EvoLudoLab:CSD\|		{{EvoLudoLab:CSD\|
	options="--game cSD --run --delay 100 --view Strategies_-_Distribution --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --geometry M --intertype a1 --numinter 1 --~~reprotype a1~~ --benefitfcn 14 --benefitparams 5:1 --costfcn 3 --costparams 1:10 --traitmax 3 --~~initmean~~ 2.8 ~~--initsdev~~ 0.02 --mutation 0.01 --mutationtype g --mutationsdev 0.02"\|		options="--game cSD --run --delay 100 --view Strategies_-_Distribution --reportfreq 50 --popsize 5000 --popupdate async --playerupdate imitate --geometry M --intertype r1 --numinter 1 --references r1 --benefitfcn 14 --benefitparams 5,1 --costfcn 3 --costparams 1,10 --traitmax 3 --init 2.8,0.02 --inittype gaussian --mutation 0.01 --mutationtype g --mutationsdev 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

Hauert at 00:22, 11 December 2020

2020-12-11T00:22:36Z

← Older revision		Revision as of 17:22, 10 December 2020
Line 1:		Line 1:
	{{EvoLudoLab:CSD\|		{{EvoLudoLab:CSD\|
	options="--game cSD --run --delay ~~200~~ --view Strategies_-_Distribution --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i ~~--updateprob 1.0~~ --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --~~benefitparam~~ 5:1 --costfcn 3 --~~costparam~~ 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"\|		options="--game cSD --run --delay 100 --view Strategies_-_Distribution --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparams 5:1 --costfcn 3 --costparams 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.02 --mutation 0.01 --mutationtype g --mutationsdev 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = ~~b_0~~[1-\exp(-~~b_1~~ x)]\) and \(C(x) =~~c_0~~ \ln(~~c_1~~ x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_1[1-\exp(-b_2 x)]\) and \(C(x) = c_1 \ln(c_2 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

	The parameters are set to \(~~b_0~~ = 5, ~~b_1~~ = 1, ~~c_0~~ = 1, ~~c_1~~ = 10\) with players imitating better strategies proportional to the payoff difference and an initial traits/investment of \(0.2 \pm 0.05\) in a population of \(5'000\) individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is \(0.01\).}}		The parameters are set to \(b_1 = 5, b_2 = 1, c_1 = 1, c_2 = 10\) with players imitating better strategies proportional to the payoff difference and an initial traits/investment of \(2.8 \pm 0.02\) in a population of \(5'000\) individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is \(0.02\).}}

	[[Category: Christoph Hauert]]		[[Category: Christoph Hauert]]

Hauert at 23:07, 23 August 2016

2016-08-23T23:07:40Z

← Older revision		Revision as of 16:07, 23 August 2016
Line 1:		Line 1:
	{{EvoLudoLab:CSD\|		{{EvoLudoLab:CSD\|
	options="--game cSD --run --delay 200 --view 2 -~~-no3D~~ --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparam 5:1 --costfcn 3 --costparam 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"\|		options="--game cSD --run --delay 200 --view Strategies_-_Distribution --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparam 5:1 --costfcn 3 --costparam 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_0[1-\exp(-b_1 x)]\) and \(C(x) =c_0 \ln(c_1 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_0[1-\exp(-b_1 x)]\) and \(C(x) =c_0 \ln(c_1 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

Wikiadmin at 19:36, 11 March 2016

2016-03-11T19:36:53Z

← Older revision		Revision as of 12:36, 11 March 2016
Line 1:		Line 1:
	{{EvoLudoLab:CSD\|		{{EvoLudoLab:CSD\|
	options="--run --delay 200 --view ~~Trait_-_Histogram~~ --no3D --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparam 5:1 --costfcn 3 --costparam 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"\|		options="--game cSD --run --delay 200 --view 2 --no3D --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparam 5:1 --costfcn 3 --costparam 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_0[1-\exp(-b_1 x)]\) and \(C(x) =c_0 \ln(c_1 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_0[1-\exp(-b_1 x)]\) and \(C(x) =c_0 \ln(c_1 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

Hauert at 01:51, 22 March 2012

2012-03-22T01:51:37Z

← Older revision		Revision as of 18:51, 21 March 2012
Line 1:		Line 1:
	{{~~VirtualLab~~:CSD\|		{{EvoLudoLab:CSD\|
	options="--run --delay 200 --view 3 --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1~~.0 --switchpref 0~~.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparam 5:1 --costfcn 3 --costparam 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"\|		options="--run --delay 200 --view Trait_-_Histogram --no3D --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparam 5:1 --costfcn 3 --costparam 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"\|
	title=Continuous Snowdrift game: Saturating investments\|		title=Continuous Snowdrift game: Saturating investments\|
	doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose ~~<math>~~B(x+y) = b_0[1-\exp(-b_1 x)]~~</math>~~ and ~~<math>~~C(x) =c_0 \ln(c_1 x+1)~~</math>~~. For the parameters below, we again observe a branching point near ~~<math>~~x^_1\approx 0.7~~</math>~~ accompanied by a repellor near ~~<math>~~x^_2\approx 0.2~~</math>~~. Starting with a population ~~<math>~~x_0 > 0.2~~</math>~~, selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around ~~<math>~~2.2~~</math>~~. Obviously, when starting with ~~<math>~~x_0 < 0.2~~</math>~~ branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near ~~<math>~~x^*_2\approx 0.2~~</math>~~ and therefore the lower branch evolves straight to minimal investments.		doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose \(B(x+y) = b_0[1-\exp(-b_1 x)]\) and \(C(x) =c_0 \ln(c_1 x+1)\). For the parameters below, we again observe a branching point near \(x^_1\approx 0.7\) accompanied by a repellor near \(x^_2\approx 0.2\). Starting with a population \(x_0 > 0.2\), selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around \(2.2\). Obviously, when starting with \(x_0 < 0.2\) branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near \(x^*_2\approx 0.2\) and therefore the lower branch evolves straight to minimal investments.

	The parameters are set to ~~<math>~~b_0 = 5, b_1 = 1, c_0 = 1, c_1 = 10~~</math>~~ with players imitating better strategies proportional to the payoff difference and an initial traits/investment of ~~<math>~~0.2 \pm 0.05~~</math>~~ in a population of 5'000 individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is ~~<math>~~0.01~~</math>~~.}}		The parameters are set to \(b_0 = 5, b_1 = 1, c_0 = 1, c_1 = 10\) with players imitating better strategies proportional to the payoff difference and an initial traits/investment of \(0.2 \pm 0.05\) in a population of \(5'000\) individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is \(0.01\).}}

	[[Category: Christoph Hauert]]		[[Category: Christoph Hauert]]

Wikiadmin: moved VirtualLab: Continuous Snowdrift Game - Branching (exp) to EvoLudoLab: Continuous Snowdrift Game - Branching (exp)

2010-01-26T22:31:35Z

moved VirtualLab: Continuous Snowdrift Game - Branching (exp) to EvoLudoLab: Continuous Snowdrift Game - Branching (exp)

← Older revision	Revision as of 15:31, 26 January 2010
(No difference)

Wikiadmin at 01:38, 20 January 2009

2009-01-20T01:38:22Z

New page

{{VirtualLab:CSD|
options="--run --delay 200 --view 3 --reportfreq 50 --popsize 5000 --popupdate r --playerupdate i --updateprob 1.0 --switchpref 0.0 --geometry M --intertype a1 --numinter 1 --reprotype a1 --benefitfcn 14 --benefitparam 5:1 --costfcn 3 --costparam 1:10 --traitmax 3 --initmean 2.8 --initsdev 0.05 --mutation 0.02 --mutationtype g --mutationsdev 0.02"|
title=Continuous Snowdrift game: Saturating investments|
doc=In all examples so far, if higher investments were advantageous (at least in one branch) then the investments would continue to increase until the upper boundary of the trait range is reached. This must not be the case. In this last example we choose <math>B(x+y) = b_0[1-\exp(-b_1 x)]</math> and <math>C(x) =c_0 \ln(c_1 x+1)</math>. For the parameters below, we again observe a branching point near <math>x^*_1\approx 0.7</math> accompanied by a repellor near <math>x^*_2\approx 0.2</math>. Starting with a population <math>x_0 > 0.2</math>, selection and mutations drive the population towards the branching point but now the emerging upper branch grows only to trait values of around <math>2.2</math>. Obviously, when starting with <math>x_0 < 0.2</math> branching can not occur and investment levels stay close to zero. Again note that the dimorphic population no longer has a repellor near <math>x^*_2\approx 0.2</math> and therefore the lower branch evolves straight to minimal investments.

The parameters are set to <math>b_0 = 5, b_1 = 1, c_0 = 1, c_1 = 10</math> with players imitating better strategies proportional to the payoff difference and an initial traits/investment of <math>0.2 \pm 0.05</math> in a population of 5'000 individuals. Mutations occur with a probability of 1% and the standard deviation of the Gaussian distributed mutations is <math>0.01</math>.}}

[[Category: Christoph Hauert]]