“If I destroy you, what business is it of yours?” ― Liu Cixin, The Dark Forest

Inspire by Dark Forest zKSNARK Space Warefare

Ruleset

1. Every player starts the game with three planets hidden from all other players.
2. Planets build up energy over time (equation 1).
3. At anypoint in the game a player can choose to reveal one or more of their planets for rest of the game.
4. A player can send energy from a planet they own to their other planets or to any other player's revealed planets (equation 2).
5. A planet is also revealed for rest of the game when it sends energy to a planet that is not yours.
6. At the end of the game the player with the most energy summed across their 3 planets wins (equation 3).

Equation 1)

E = ln(t + 1)

• E is the current energy of the planet.
• t is the number of epochs since game start.
• ln is the natural log.

Plot

An astute read might notice this looks similiar to the bitcoin supply over time

Equation 2)

a)

R = (1 / j) * integral_0_to_j(ln(t + 1))

• R is the threshhold variable of the below sigmoid function.

b)

E_1' = E_1 * σ (E_1 − R)

• E_1' is the new energy of the planet after sending energy.
• E_1 is the current energy of the planet sending energy.
• σ is the sigmoid function.
• R is the the threshold equation.

c)

E_2' = E_2 * σ (E_2 − R)

• E_2' is the new energy of the planet receiving the energy.
• E_2 is the current energy of the planet receiving energy.
• σ is the sigmoid function.
• R is the the threshold equation.

Equation 3)

P = E1 + E2 + E3

• P is the number of points and E1 is the energy from planet 1 and so on.

"In the cosmos, no matter how fast you are, someone will be faster; no matter how slow you are, someone will be slower."

• Liu Cixin, Death's End