Economic Censorship Games – Formula Playground

This page lets you experiment with some of the formulas from the paper "Economic Censorship Games in Fraud Proofs". Enter parameters and click the buttons to see which side can guarantee victory under different models.

G₁ Game (Single Proposer)

Theorem 1: Alice (attacker) has a winning strategy iff A ≥ ((T − N + 1) / N) · D, where:

T = total hours (1 round = 12s; 1 hour = 300 rounds)
N = rounds Daria (defender) must win (bisection steps)
A = Alice's budget ($)

T (total hours): = 49000 rounds

N (defender wins needed, rounds):

A (attacker budget, $):

G₁_k Game (Special Rounds – Bounds)

Theorem 3 gives bounds on Alice's threshold coefficient A(t, n, s) when there are special rounds with factor k:

Lower bound: A_lower = [t + s·(k − 1) − k·(n − 1)] / n
Upper bound: A_upper = [t + s·(k − 1) − (n − 1)] / n

t = remaining hours (1 round = 12s; 1 hour = 300 rounds)
n = remaining defender wins needed (rounds/bisection steps)
s = special rounds (% of total rounds)
k = factor in special rounds (attacker must bid ≥ k·b)
A = attacker budget ($)

t (hours): = 49000 rounds

n (defender wins needed, rounds):

s (special rounds, %): = 980 rounds

k (special factor):

A (attacker budget, $):

G_m Game (Multiple Proposers)

For the multi-proposer game, Theorems 4 and 5 give (roughly) scaled versions of the G₁ condition:

Theorem 4: if A ≥ ((T − N + 1)·m / N) · D, Alice can win with certainty (under the budget-balanced mechanism).
Theorem 5: if A < ((T − 4N + 1)·m / N) · D, Daria can win with high probability.

T (total hours): = 49000 rounds

N (defender wins needed, rounds):

m (number of proposers):

A (attacker budget, $):

Economic Censorship Games – Formula Playground

G₁ Game (Single Proposer)

G₁k Game (Special Rounds – Bounds)

Gm Game (Multiple Proposers)

G₁_k Game (Special Rounds – Bounds)

G_m Game (Multiple Proposers)