Specific cycles, trust minimization, and the kula ring

While responding to Ian Grigg's comment to my previous blog entry on kula, I came up with what is the most rigorous explanation for the two-collectible cycle that I've seen. The explanation neatly incorporates two patterns I've talked about in the past, namely (1) the literal circulation of collectibles in specific cycles to minimize non-coincidence transaction costs in a bilateral monopoly economy, and (2) trust minimization in institution design.