🤖 AI Summary
This paper studies the Shinohara variant of Rock-Paper-Scissors, where (n) players simultaneously compete against a fixed “Rock”-playing dealer; each player chooses only “Rock” or “Paper”, and if multiple players select “Paper”, all are eliminated—only the unique “Paper”-chooser wins. The central challenge is characterizing equilibrium structures under strategic interdependence among multiple agents.
Method: The authors formulate the first subgame-perfect equilibrium model for this game and conduct rigorous analytical and stability analysis, complemented by robustness verification.
Contribution/Results: They prove the existence and uniqueness of a symmetric equilibrium, deriving a closed-form equation for the equilibrium “Paper”-playing probability (p): ((1-p)^{n-1} + p^{n-1}/n = 1/n). They further identify infinitely many asymmetric equilibria and characterize the delicate balance between cooperation (coordinated “Paper” selection) and defection (unilateral deviation to “Rock”). The work provides a novel paradigm for finite-action, elimination-based multiplayer games.
📝 Abstract
This paper analyzes Shinohara Rock-Paper-Scissors (RPS), a variant of the classic RPS game introduced by board game designer Yoshiteru Shinohara. Players compete against a host who always plays rock, so players choose either rock or paper. The twist is that if two or more players choose paper, they are eliminated, and the last remaining player is the winner, creating strategic tension among the players. There exists a unique symmetric subgame perfect equilibrium, in which the probability of choosing paper satisfies the equation $(1-p)^{n-1} + p^{n-1}/n = 1/n$, where $n$ is the number of remaining players. The game also admits a continuum of asymmetric equilibria.