Concepts: claim / problem /solutionSCG is a multi-avatar game based on many two avatar games (round robin or Swiss-style), where the avatars compete for points by proposing and opposing claims to each other. Each avatar is produced by a small team of programmers, possibly only one. A claim is defined by a refutation protocol which decides which of the two avatars wins.
The avatars compete over a fixed number of rounds. During each round an avatar proposes challenging claims, and the opposing avatar has the option to oppose some of them by forcing the first avatar to contradict its own claim while following the refutation protocol.
The refutation protocol typically involves constructing problems and solutions. Problems conforming to the claim are exchanged to determine which avatar is correct. We focus on problem/solution refutation protocols.
The winner is determined at the end of the rounds as the one with the highest reputation. An avatar wins reputation by successfully refuting a claim of another avatar. An avatar also wins reputation by successfully defending his claims. In both cases, the refutation increase of the winner is proportional to the reputation of the loser.
General rules: Avatars must oppose at least o1 claims in each round. Avatars must propose at least p1 claims in each round. The ranking of the avatars is determined by their reputation. All avatars start with a reputation of 1.
We consider several restrictions of SCG. The SCG defined above could also be called SCG Intensional. In the general version of the game, avatars must have skills: ProposeClaim, OpposeClaim, SolveProblem, FindHardProblem. There are several levels of claims controled by the game designer.