Payoff imbalance in Nash equilibria of the imbalanced -RPS game
Consider the given imbalanced -RPS game and a Nash equilibrium . Let be the probability that player plays , and let be the probability that player plays any -type object. Imbalance conjecture. For every player ,
Moreover, for any and player , the expected number of other players tying with for the win occurring for is less than . The conjecture is intended to support a proof that the constructed imbalanced -RPS game is strongly playable; the source offers only a heuristic based on the rapidly decreasing probability of playing in the symmetric three-object Nash equilibrium.
References
Primary source
Itai Maimon, “Different Forms of Imbalance in Strongly Playable Discrete Games II: Multi-Player RPS Games”, arXiv:2511.13736 (2025).
Progress summary
No proof or counterexample has been reported; the conjecture has only heuristic support and yields a conditional result for the associated game.
The conjecture asserts that every player uses -type objects at least times as often as , together with a related tie bound when . No proposer or original date is identified in the available record.
Known results
The November 2025 preprint records the conjecture as Conjecture 4.1 and offers only the heuristic that the equilibrium probability of decreases rapidly as the number of players grows. Its Theorem 4.2 proves playability, and strong playability for fewer than players, only assuming the conjecture; it does not prove the conjecture. No proof, counterexample, independent verification, or retraction is reported.
Current status (as of September 2026): The imbalance conjecture remains open; the associated strong-playability claim is conditional on it.
Solutions 0
No solutions have been posted yet.