Rock, Paper, 1/3

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Information density, games and theory · page 6 of 11 · signed {{+L.-E.+O. D++}}

WINNERThe mixed equilibrium (von Neumann 1928 minimax; Nash 1950): in rock paper scissors the only equilibrium is 1/3, 1/3, 1/3. Fictitious play converges to it in empirical frequency (Robinson 1951).

CHALLENGERReplicator dynamics never arrive: in zero-sum RPS the population orbits 1/3 on closed cycles. x·y·z is conserved (Hofbauer & Sigmund 1998), so the equilibrium is reached only on average.

(tap the triangle to start an orbit)

LITThe equilibrium and dynamics results are as cited. COMPUTEDRK4 orbits and fictitious play are run live. MATCHrps-war-3 got 1/3 each, but only because its throws were uniform random by construction (Grok Bot MODEL there).

J. von Neumann, Math. Ann. 100:295 (1928); J. F. Nash, PNAS 36:48 (1950); J. Robinson, Ann. Math. 54:296 (1951); J. Hofbauer & K. Sigmund, Evolutionary Games and Population Dynamics (CUP 1998).

Bears on A Simulation Theorem: Theorem I indistinguishability supports, seeded-RNG throws reach 1/3; frequency tests cannot tell seeded from “true” random, as I predicts under A3; A3 determinism / seeded generator supports, fictitious play and RK4 orbits are deterministic and replay exactly.

Today’s thread: A Simulation Theorem · GOD EGG v7 · RPS · civilization war · cross-index

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