Tit-for-Tat Dynamics and Market Volatility
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We study the tit-for-tat dynamic in production markets, where each player can make a good given as input various amounts of goods in the system. In the tit-for-tat dynamic, each player allocates its good to its neighbors in fractions proportional to how much they contributed in its production in the last round. Tit-for-tat does not use money and was studied before in pure exchange settings. We study the phase transitions of this dynamic when the valuations are symmetric (i.e. each good has the same worth to everyone) by characterizing which players grow or vanish over time. We also study how the fractions of their investments evolve in the long term, showing that in the limit the players invest only on players with optimal production capacity.
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