Athena: utility maximum value instead of argmax location

Read the equation

For U(x,y)=−y²+2xy, the maximizing location is y=x. The function returns x², which is the maximum utility value U(x,x), rather than the argmax location. The distinction is substantive: at x=2 the location is two and the returned value is four.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

	for n := 1; n <= 10; n++ {
		an := 1.0 / float64(n) // Harmonic coefficients
		sum += an * math.Sin(float64(n)*math.Pi*x)
	}
	return sum
}

// FAthena: F_Athena(x) = argmax_y U(x,y) (Strategy - utility maximization)
func FAthena(x float64) float64 {
	// Simplified: find max of utility function U(x,y) = -y² + 2xy
	// argmax_y: dU/dy = -2y + 2x = 0 => y* = x
	// U(x, x) = -x² + 2x² = x²
	return x * x
}

// FApollo: F_Apollo(x) = φ^x + φ^{-x} (Mathematics - golden ratio)
func FApollo(x float64) float64 {
	return math.Pow(PHI, x) + math.Pow(PHI, -x)

FAthena: F_Athena(x) = argmax_y U(x,y) (Strategy - utility maximization)

Related builds