Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality
Mechanism design enables a social planner to obtain a desired outcome by leveraging the players’ rationality and their beliefs. It is thus a fundamental, but yet unproven, intuition that the higher the level of rationality of the players, the better the set of obtainable outcomes. In this paper, we...
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| Format: | Article |
| Language: | en_US |
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The Econometric Society
2016
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| Online Access: | http://hdl.handle.net/1721.1/100963 https://orcid.org/0000-0002-0816-4064 |
| _version_ | 1826215654962757632 |
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| author | Chen, Jing Micali, Silvio Pass, Rafael |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Chen, Jing Micali, Silvio Pass, Rafael |
| author_sort | Chen, Jing |
| collection | MIT |
| description | Mechanism design enables a social planner to obtain a desired outcome by leveraging the players’ rationality and their beliefs. It is thus a fundamental, but yet unproven, intuition that the higher the level of rationality of the players, the better the set of obtainable outcomes. In this paper, we prove this fundamental intuition for players with possibilistic beliefs, a model long considered in epistemic game theory. Specifically,
• We define a sequence of monotonically increasing revenue benchmarks for single-good auctions, G[superscript 0≤]G[superscript 1≤]G[superscript 2≤]···,where each G[superscript i] is defined over the players’ beliefs and G[superscript 0] is the second-highest valuation (i.e., the revenue benchmark achieved by the second-price mechanism).
• We (1) construct a single, interim individually rational, auction mechanism that, without any clue about the rationality level of the players, guarantees revenue G[superscript k] if all players have rationality levels ≥ k + 1, and (2) prove that no such mechanism can guarantee revenue even close to G[superscript k] when at least two players are at most level- k rational. |
| first_indexed | 2024-09-23T16:37:21Z |
| format | Article |
| id | mit-1721.1/100963 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:37:21Z |
| publishDate | 2016 |
| publisher | The Econometric Society |
| record_format | dspace |
| spelling | mit-1721.1/1009632022-10-02T08:32:02Z Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality Chen, Jing Micali, Silvio Pass, Rafael Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Micali, Silvio Mechanism design enables a social planner to obtain a desired outcome by leveraging the players’ rationality and their beliefs. It is thus a fundamental, but yet unproven, intuition that the higher the level of rationality of the players, the better the set of obtainable outcomes. In this paper, we prove this fundamental intuition for players with possibilistic beliefs, a model long considered in epistemic game theory. Specifically, • We define a sequence of monotonically increasing revenue benchmarks for single-good auctions, G[superscript 0≤]G[superscript 1≤]G[superscript 2≤]···,where each G[superscript i] is defined over the players’ beliefs and G[superscript 0] is the second-highest valuation (i.e., the revenue benchmark achieved by the second-price mechanism). • We (1) construct a single, interim individually rational, auction mechanism that, without any clue about the rationality level of the players, guarantees revenue G[superscript k] if all players have rationality levels ≥ k + 1, and (2) prove that no such mechanism can guarantee revenue even close to G[superscript k] when at least two players are at most level- k rational. United States. Office of Naval Research (Grant N00014-09-1-0597) 2016-01-21T00:56:21Z 2016-01-21T00:56:21Z 2015-07 Article http://purl.org/eprint/type/JournalArticle 0012-9682 1468-0262 http://hdl.handle.net/1721.1/100963 Chen, Jing, Silvio Micali, and Rafael Pass. “Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality.” Econometrica 83, no. 4 (2015): 1619–1639. https://orcid.org/0000-0002-0816-4064 en_US http://dx.doi.org/10.3982/ECTA12563 Econometrica Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf The Econometric Society Other univ. web domain |
| spellingShingle | Chen, Jing Micali, Silvio Pass, Rafael Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality |
| title | Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality |
| title_full | Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality |
| title_fullStr | Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality |
| title_full_unstemmed | Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality |
| title_short | Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality |
| title_sort | tight revenue bounds with possibilistic beliefs and level k rationality |
| url | http://hdl.handle.net/1721.1/100963 https://orcid.org/0000-0002-0816-4064 |
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