Tit-for-Tat Dynamics and Market Volatility
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866910295509696512 |
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| author | Brânzei, Simina |
| author_facet | Brânzei, Simina |
| contents | We consider tit-for-tat dynamics in production markets, where there is a set of $n$ players connected via a weighted graph. Each player $i$ can produce an eponymous good using its linear production function, given as input various amounts 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 they helped player $i$'s production in the last round.
Our contribution is to characterize the asymptotic behavior of the dynamic as a function of the graph structure, finding that the fortune of a player grows in the long term if and only if the player has a good self loop (i.e. the player works well alone) or works well with at least one other player. We also consider a generalized damped update, where the players may update their strategies with different speeds, and obtain a lower bound on their rate of growth by identifying a function that gives insight into the behavior of the dynamical system.
The model can capture circular economies, where players use each other's products, and organizational partnerships, where fostering long-term growth of an organization hinges on creating relationships in which reciprocal exchanges between the agents in the organization are paramount. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_03629 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Tit-for-Tat Dynamics and Market Volatility Brânzei, Simina Computer Science and Game Theory Theoretical Economics We consider tit-for-tat dynamics in production markets, where there is a set of $n$ players connected via a weighted graph. Each player $i$ can produce an eponymous good using its linear production function, given as input various amounts 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 they helped player $i$'s production in the last round. Our contribution is to characterize the asymptotic behavior of the dynamic as a function of the graph structure, finding that the fortune of a player grows in the long term if and only if the player has a good self loop (i.e. the player works well alone) or works well with at least one other player. We also consider a generalized damped update, where the players may update their strategies with different speeds, and obtain a lower bound on their rate of growth by identifying a function that gives insight into the behavior of the dynamical system. The model can capture circular economies, where players use each other's products, and organizational partnerships, where fostering long-term growth of an organization hinges on creating relationships in which reciprocal exchanges between the agents in the organization are paramount. |
| title | Tit-for-Tat Dynamics and Market Volatility |
| topic | Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/1911.03629 |