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The article formulates a dynamic mathematical model where arbitrarily many players produce, consume, exchange, loan, and deposit arbitrarily many goods over time to maximize utility. Consuming goods constitutes a benefit, and producing, exporting, and loaning away goods constitute a cost. Utilities are benefits minus costs, which depend on the exchange ratios and bargaining functions. Three-way exchange occurs when one player acquires, through exchange, one good from another player with the sole purpose of using this good to exchange against the desired good from a third player. Such a triple handshake is not merely a set of double handshakes since the player assigns no interest to the first good in his benefit function. Cognitive and organization costs increase dramatically for higher order exchanges. An exchange theory accounting for media of exchange follows from simple generalization of two-way exchange. The examples of r-way exchange are the triangle trade between Africa, the USA, and England in the 17th and 18th centuries, the hypothetical hypercycle involving RNAs as players and enzymes as goods, and reaction–diffusion processes. The emergence of exchange, and the role of trading agents are discussed. We simulate an example where two-way exchange gives zero production and zero utility, while three-way exchange causes considerable production and positive utility. Maximum utility for each player is reached when exchanges of the same order as the number of players in society are allowed. The article merges micro theory and macro theory within the social, natural, and physical sciences.

Systems concepts are applied to solve the problem of how early life could have emerged from an initially abiotic organic environment. Proteinoid or lipid microspheres are proposed to have polymerized from a primordial organic soup and to contain various amino acids and several different nucleobases. A self-replicating "basic set" hypercycle consisting of 10 XNA gene strands and 10 enzymes is proposed that utilizes inorganic phosphates as an energy source. The genes would utilize triplet combinations of adenosine and uracil to code for a replicase enzyme, a polymerase enzyme and eight-code translator (synthetase) enzymes. It is shown that there is a high probability that the basic set genes would emerge. Fissioning of the basic set microspheres into a population of microspheres all containing the basic set, could eliminate the problem of a single gene monopolizing use of the replicator enzyme at the expense of the others and greatly enhance the survivability of the replicating population as a whole. A thermodynamic analysis of such a self-replicating system is also presented. It is shown that genetic mutations will, in the long run allow the basic set to evolve to increased diversity, higher rates of enzyme synthesis and greater rates of entropy production. Long-term evolution could have resulted in organisms similar to contemporary bacteria that utilize RNA genes with a four nucleobase codon system.

We discuss how recursive production of a proto-cell consisting of a mutually catalytic reaction network is possible. It is shown that a minority molecule species plays an essential role in carrying heredity, in the sense that the molecule is preserved well and controls replication of the cell. The cell state controlled by such a minority molecule is shown to have evolvability. Successive switches over quasi-recursive states are found, caused by extinction of minority molecules. Experimental demonstration of the theory is also discussed.

The behavior of hypercycle spirals in a two-dimensional cellular automaton model is analyzed. Each spiral can be approximated by an Archimedean spiral with center, width, and phase change according to Brownian motion. A barrier exists between two spirals if the phase synchronization hypothesis is taken into account, and the occurrence rate of pair decay (simultaneous disappearance of two spirals) can be explained through a random walk simulation with the barrier. Simulation experiments show that adjacent species violation is necessary to create new spirals. A hypercycle system can live for a long time if spirals in the system are somewhat unstable, since new spirals cannot emerge when existing spirals are too stable.