The Scientific Community Game (SCG)

Karl Lieberherr

Short High-Level Definition

```Concepts: claim / problem /solution
```
SCG 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.

SCG Extensional

For some applications of SCG, it is better to formulate a heterogeneous market of claims from which the players must take the claims they propose. Instead of defining the allowed claims intensionally through a predicate, they are defined extensionally by enumerating them. Scholars must have skills: ChooseClaim, OpposeClaim, SolveProblem, FindHardProblem.

SCG Problem Solving

In another instance of SCG, players are forced to propose a specific claim to test their skills to support the claim. Scholars must have skills: SolveProblem, FindHardProblem. The evaluation function needs to be adjusted. If the claim is true, the scholar should defend the claim.