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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.03476 |
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| _version_ | 1866914920085323776 |
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| author | Castiglioni, Matteo Chen, Junjie Li, Minming Xu, Haifeng Zuo, Song |
| author_facet | Castiglioni, Matteo Chen, Junjie Li, Minming Xu, Haifeng Zuo, Song |
| contents | The main result of this paper is an almost approximation-preserving polynomial-time reduction from the most general multi-parameter Bayesian contract design (BCD) to single-parameter BCD. That is, for any multi-parameter BCD instance $I^M$, we construct a single-parameter instance $I^S$ such that any $β$-approximate contract (resp. menu of contracts) of $I^S$ can in turn be converted to a $(β-ε)$-approximate contract (resp. menu of contracts) of $I^M$. The reduction is in time polynomial in the input size and $\log(\frac{1}ε)$; moreover, when $β= 1$ (i.e., the given single-parameter solution is exactly optimal), the dependence on $\frac{1}ε$ can be removed, leading to a polynomial-time exact reduction. This efficient reduction is somewhat surprising because in the closely related problem of Bayesian mechanism design, a polynomial-time reduction from multi-parameter to single-parameter setting is believed to not exist. Our result demonstrates the intrinsic difficulty of addressing moral hazard in Bayesian contract design, regardless of being single-parameter or multi-parameter.
As byproducts, our reduction answers two open questions in recent literature of algorithmic contract design: (a) it implies that optimal contract design in single-parameter BCD is not in APX unless P=NP even when the agent's type distribution is regular, answering the open question of [Alon et al. 2021] in the negative; (b) it implies that the principal's (order-wise) tight utility gap between using a menu of contracts and a single contract is $Θ(n)$ where $n$ is the number of actions, answering the major open question of [Guruganesh et al. 2021] for the single-parameter case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Reduction from Multi-Parameter to Single-Parameter Bayesian Contract Design Castiglioni, Matteo Chen, Junjie Li, Minming Xu, Haifeng Zuo, Song Computer Science and Game Theory The main result of this paper is an almost approximation-preserving polynomial-time reduction from the most general multi-parameter Bayesian contract design (BCD) to single-parameter BCD. That is, for any multi-parameter BCD instance $I^M$, we construct a single-parameter instance $I^S$ such that any $β$-approximate contract (resp. menu of contracts) of $I^S$ can in turn be converted to a $(β-ε)$-approximate contract (resp. menu of contracts) of $I^M$. The reduction is in time polynomial in the input size and $\log(\frac{1}ε)$; moreover, when $β= 1$ (i.e., the given single-parameter solution is exactly optimal), the dependence on $\frac{1}ε$ can be removed, leading to a polynomial-time exact reduction. This efficient reduction is somewhat surprising because in the closely related problem of Bayesian mechanism design, a polynomial-time reduction from multi-parameter to single-parameter setting is believed to not exist. Our result demonstrates the intrinsic difficulty of addressing moral hazard in Bayesian contract design, regardless of being single-parameter or multi-parameter. As byproducts, our reduction answers two open questions in recent literature of algorithmic contract design: (a) it implies that optimal contract design in single-parameter BCD is not in APX unless P=NP even when the agent's type distribution is regular, answering the open question of [Alon et al. 2021] in the negative; (b) it implies that the principal's (order-wise) tight utility gap between using a menu of contracts and a single contract is $Θ(n)$ where $n$ is the number of actions, answering the major open question of [Guruganesh et al. 2021] for the single-parameter case. |
| title | A Reduction from Multi-Parameter to Single-Parameter Bayesian Contract Design |
| topic | Computer Science and Game Theory |
| url | https://arxiv.org/abs/2404.03476 |