The credibility of an agent summarizes the quality of an agent = account balance

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The confidence of an agent in a belief depends on
how much time it had to "think" about the belief.

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if Alice has high credibility and Bob discounts Alice' belief, Bob should get brownie points.

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b1 = Belief classic ([(2,0) (1,0)] 0.65). Exists S
in niche so that for all J: fsat(S,J) < 0.65 and S can be found in polynomial
time.
I am super confident: It is a theorem
challenge(b1, 1)

b2 = Belief classic complement ([(2,0) (1,0)] 0.60). For all S
in niche there exists J: fsat(S,J) >= 0.60
and J can be found in polynomial time.
I am super confident: It is a theorem
challenge(b2, confidence 1)

Belief secret ([(2,0) (1,0)] 0.6). For niche Exists polynomial algorithm 
that approximates the secret solution within 0.6.
fsat(S,J) >= 0.6 * SQ.
I am super confident.

Challenge = Belief Confidence.

if Belief discounted, pay 3*confidence.
if Belief supported,  pay 0

Lower confidence, when reoffering???