Concepts: claim / problem /solutionSCG is a multi-player game based on many two player games (round robin or Swiss-style), where the players compete for points by proposing and opposing claims to each other.
The players compete over a fixed number of rounds. During each round a player proposes challenging claims, and the opposing player has the option to oppose some of them through one of two means:
1.) (refuting) by forcing the first player to contradict its own claim by constructing problems and solutions, or 2.) (strengthening) by refining the claim to make it stronger but not refutable.Concrete problems conforming to the claim are exchanged to determine which player is correct.
The winner is determined at the end of the rounds as the player who has proposed the largest fraction of unopposed claims compared to all claims. If there is a tie, we count how many claims each player successfully opposed.
We consider several restrictions of SCG. The SCG defined above could also be called SCG Intensional. In the general version of the game, scholars must have skills: ProposeClaim, OpposeClaim, SolveProblem, FindHardProblem. Several levels of claims controled by game designer.