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We consider tit-for-tat dynamics in production markets, where there is a setof $n$ players connected via a weighted graph. Each player $i$ can produce aneponymous good using its linear production function, given as input variousamounts of goods in the system. In the tit-for-tat dynamic, each player $i$shares its good with its neighbors in fractions proportional to how much theyhelped player $i$'s production in the last round.  Our contribution is to characterize the asymptotic behavior of the dynamic asa function of the graph structure, finding that the fortune of a player growsin the long term if and only if the player has a good self loop (i.e. theplayer works well alone) or works well with at least one other player. We alsoconsider a generalized damped update, where the players may update theirstrategies with different speeds, and obtain a lower bound on their rate ofgrowth by identifying a function that gives insight into the behavior of thedynamical system.  The model can capture circular economies, where players use each other'sproducts, and organizational partnerships, where fostering long-term growth ofan organization hinges on creating relationships in which reciprocal exchangesbetween the agents in the organization are paramount.

Tit-for-Tat Dynamics and Market Volatility