Template:Clobenefitfunc: Difference between revisions

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Created page with "; <tt>--benefitfcn <f1[,f2[...]]></tt> : benefit function for each trait: :; <tt>0:</tt> \(B(x,y)=b_0\ y\) :: benefits linear in opponents investment \(y\). :; <tt>1:</tt> \(B(x,y)=b_0\ y+b_1\ y^2\) :: benefits quadratic in opponents investment \(y\). :; <tt>2:</tt> \(B(x,y)=b_0 \sqrt{y}\) :: \(\sqrt{\ }\)-saturating benefits for opponents investment \(y\) :; <tt>3:</tt> \(B(x,y)=b_0 \ln(b_1\ y+1)\) :: \(\ln\)-saturating benefits for opponents investment \(y\) :; <tt>4:<..."
 
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:; <tt>32:</tt> \(B(x,y)=b_0 x+b_1\ x^2+b_2\ x^3\)
:; <tt>32:</tt> \(B(x,y)=b_0 x+b_1\ x^2+b_2\ x^3\)
:: benefits cubic in own investments \(x\).
:: benefits cubic in own investments \(x\).
; <tt>--benefitparams <b0>[,<b1>[...[;<b'0>[,<b'1>[...]]]]]
; <tt>--benefitparams <b0>[,<b1>[...[;<b'0>[,<b'1>[...]]]]]</tt>
: parameters \(b_i\) for benefit function of each trait.
: parameters \(b_i\) for benefit function of each trait.

Latest revision as of 11:26, 13 October 2023

--benefitfcn <f1[,f2[...]]>
benefit function for each trait:
0: \(B(x,y)=b_0\ y\)
benefits linear in opponents investment \(y\).
1: \(B(x,y)=b_0\ y+b_1\ y^2\)
benefits quadratic in opponents investment \(y\).
2: \(B(x,y)=b_0 \sqrt{y}\)
\(\sqrt{\ }\)-saturating benefits for opponents investment \(y\)
3: \(B(x,y)=b_0 \ln(b_1\ y+1)\)
\(\ln\)-saturating benefits for opponents investment \(y\)
4: \(B(x,y)=b_0 (1-\exp(-b_1\ y))\)
\(\exp\)-saturating benefits for opponents investment \(y\)
10: \(B(x,y)=b_0 (x+y)\)
benefits linear in joint investments \(x+y\).
11: \(B(x,y)=b_0 (x+y)+b_1\ (x+y)^2\)
benefits quadratic in joint investments \(x+y\) (default).
12: \(B(x,y)=b_0 \sqrt{x+y}\)
\(\sqrt{\ }\)-saturating benefits for joint investments \(x+y\)
13: \(B(x,y)=b_0 \ln(b_1\ (x+y)+1)\)
\(\ln\)-saturating benefits for joint investments \(x+y\)
14: \(B(x,y)=b_0 (1-\exp(-b_1\ (x+y)))\)
\(\exp\)-saturating benefits for joint investments \(x+y\)
20: \(B(x,y)=b_0 x+b_1\ y+b_2\ x\ y\)
benefits linear in investments \(x\) and \(y\) as well as cross term \(x\,y\).
30: \(B(x,y)=b_0 x\)
benefits linear in own investments \(x\).
31: \(B(x,y)=b_0 x+b_1\ x^2\)
benefits quadratic in own investments \(x\).
32: \(B(x,y)=b_0 x+b_1\ x^2+b_2\ x^3\)
benefits cubic in own investments \(x\).
--benefitparams <b0>[,<b1>[...[;<b'0>[,<b'1>[...]]]]]
parameters \(b_i\) for benefit function of each trait.