Suppose we have two identical agents, labeled A and B. Agent A will act to maximize their lifetime utility: U (c1,A, c2,A) = max {c1,A,c2,A } log c1,A + log c2,A such that aA = y1,A c1,A c2,A = y2,A + (1 + r) aA And agent B does the same, subject to their own constraints