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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2309.08781 |
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| _version_ | 1866909228401164288 |
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| author | Eden, Alon Ma, Gary Qiurui Parkes, David C. |
| author_facet | Eden, Alon Ma, Gary Qiurui Parkes, David C. |
| contents | We introduce the theoretical study of a Platform Equilibrium in a market with unit-demand buyers and unit-supply sellers. Each seller can join a platform and transact with any buyer or remain off-platform and transact with a subset of buyers whom she knows. Given the constraints on trade, prices form a competitive equilibrium and clears the market. The platform charges a transaction fee to all on-platform sellers, in the form of a fraction of on-platform sellers' price. The platform chooses the fraction to maximize revenue. A Platform Equilibrium is a Nash equilibrium of the game where each seller decides whether or not to join the platform, balancing the effect of a larger pool of buyers to trade with, against the imposition of a transaction fee.
Our main insights are: (i) In homogeneous-goods markets, pure equilibria always exist and can be found by a polynomial-time algorithm; (ii) When the platform is unregulated, the resulting Platform Equilibrium guarantees a tight $Θ(log(min(m, n)))$-approximation of the optimal welfare in homogeneous-goods markets, where $n$ and $m$ are the number of buyers and sellers respectively; (iii) Even light regulation helps: when the platform's fee is capped at $α\in[0,1)$, the price of anarchy is 2-$α$/1-$α$ for general markets. For example, if the platform takes 30 percent of the seller's revenue, a rather high fee, our analysis implies the welfare in a Platform Equilibrium is still a 0.412-fraction of the optimal welfare. Our main results extend to markets with multiple platforms, beyond unit-demand buyers, as well as to sellers with production costs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08781 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Platform Equilibrium: Analayzing Social Welfare in Online Market Places Eden, Alon Ma, Gary Qiurui Parkes, David C. Computer Science and Game Theory We introduce the theoretical study of a Platform Equilibrium in a market with unit-demand buyers and unit-supply sellers. Each seller can join a platform and transact with any buyer or remain off-platform and transact with a subset of buyers whom she knows. Given the constraints on trade, prices form a competitive equilibrium and clears the market. The platform charges a transaction fee to all on-platform sellers, in the form of a fraction of on-platform sellers' price. The platform chooses the fraction to maximize revenue. A Platform Equilibrium is a Nash equilibrium of the game where each seller decides whether or not to join the platform, balancing the effect of a larger pool of buyers to trade with, against the imposition of a transaction fee. Our main insights are: (i) In homogeneous-goods markets, pure equilibria always exist and can be found by a polynomial-time algorithm; (ii) When the platform is unregulated, the resulting Platform Equilibrium guarantees a tight $Θ(log(min(m, n)))$-approximation of the optimal welfare in homogeneous-goods markets, where $n$ and $m$ are the number of buyers and sellers respectively; (iii) Even light regulation helps: when the platform's fee is capped at $α\in[0,1)$, the price of anarchy is 2-$α$/1-$α$ for general markets. For example, if the platform takes 30 percent of the seller's revenue, a rather high fee, our analysis implies the welfare in a Platform Equilibrium is still a 0.412-fraction of the optimal welfare. Our main results extend to markets with multiple platforms, beyond unit-demand buyers, as well as to sellers with production costs. |
| title | Platform Equilibrium: Analayzing Social Welfare in Online Market Places |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2309.08781 |