(1) virtual scientists are encouraged to offer hypotheses that are strong. Otherwise they lose reputation. (2) virtual scientists must produce solutions to problems that are consistent with the prediction function. (3) virtual scientists must propose prediction functions and they must oppose the prediction function of their opponent. This takes two forms: They strengthen the prediction function of their opponent or they challenge it by delivering a problem where the other agent cannot satisfy the prediction function. (4) virtual scientists must solve the problems they get and they must deliver hard problems to their opponents. (5) to win the game, virtual scientists must maximize their reputation.

Shell sort with different gap sequences: (1) original by Shell: O(n^2) (2) Hibbard: O(n^(3/2)) (3) Sedgewick: O(n^(4/3)) (4) Pratt: O(n * log^2(n)) Merge sort: (5) John von Neumann already had an O(n*log(n)) algorithm in 1945.Let's assume that Alice uses the basic algorithm (1) and Bob uses innovation (2). For sufficiently large n, Alice will have an advantage in two ways. Within the time bound of the game, Alice will solve more problems than Bob. Alice will make better predictions than Bob about how many comparisons are needed to accomplish the sorting. So even if Alice succeeds with sorting, she will lose at level 2 because Bob is the better predictor in that his prediction is tighter. The game limits the input sequences to have a maximum size. If this size is big enough, asymptotically faster algorithms with reasonable constants will have an advantage. A similar argument can be made for innovations (2) and (3), (3) and (4), (4) and (5). In summary, this sorting example shows how algorithmic innovations help to win in the SCG game.

Reputation is also gained by being a better predictor, i.e., by making tighter predictions. We use the following notation: pqXY describes the predicted quality achieved on X's problem by Y. Based on predicted quality: Alice is right if she achieves >= what she predicted: qBA >= pqBA and qAA >= pqAA. Bob is right if he achieves >= what he predicted. qBB >= pqBB and qAB >= pqAB. Both Alice and Bob may be right. Alice wins if she is right and Bob is wrong. Alice also wins if both Alice and Bob are right and Alice predicted more than Bob. pqAA > pqAB and pqBA > pqBB.

We assume here that predicting more is challenging. In other situations, predicting less is challenging. The reputation that Alice wins is all the reputation that Bob has at this point in the game against Alice times an at-risk-factor which is a constant defined for the entire game. Assume an at-risk-factor of 20%.

Should reputation be accumulated from competition to competition? How does his influence innovation?