Epistemic Implementation and The Arbitrary-Belief Auction
In settings of incomplete information we put forward an epistemic framework for designing mechanisms that successfully leverage the players' arbitrary higher-order beliefs, even when such beliefs are totally wrong, and even when the players are rational in a very weak sense. Following Aumann (1...
| Main Authors: | , , |
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| Language: | en-US |
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2012
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| Online Access: | http://hdl.handle.net/1721.1/71232 |
| _version_ | 1811076099320315904 |
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| author | Chen, Jing Micali, Silvio Pass, Rafael |
| author2 | Silvio Micali |
| author_facet | Silvio Micali Chen, Jing Micali, Silvio Pass, Rafael |
| author_sort | Chen, Jing |
| collection | MIT |
| description | In settings of incomplete information we put forward an epistemic framework for designing mechanisms that successfully leverage the players' arbitrary higher-order beliefs, even when such beliefs are totally wrong, and even when the players are rational in a very weak sense. Following Aumann (1995), we consider a player i rational if he uses a pure strategy s_i such that no alternative pure strategy s_i' performs better than s_i in every world i considers possible, and consider him order-k rational if he is rational and believes that all other players are order-(k-1) rational. We then introduce an iterative deletion procedure of dominated strategies and use it to precisely characterize the strategies consistent with the players being order-k rational. We exemplify the power of our framework in single-good auctions by introducing and achieving a new class of revenue benchmarks, defined over the players' arbitrary beliefs, that can be much higher than classical ones, and are unattainable by traditional mechanisms. Namely, we exhibit a mechanism that, for every k greater than or equal to 0 and epsilon>0 and whenever the players are order-(k+1) rational, guarantees revenue greater than or equal to G^k-epsilon, where G^k is the second highest belief about belief about ... (k times) about the highest valuation of some player, even when such a player's identity is not precisely known. Importantly, our mechanism is possibilistic interim individually rational. Essentially this means that, based on his beliefs, a player's utility is non-negative not in expectation, but in each world he believes possible. We finally show that our benchmark G^k is so demanding that it separates the revenue achievable with order-k rational players from that achievable with order-(k+1) rational ones. That is, no possibilistic interim individually rational mechanism can guarantee revenue greater than or equal to G^k-c, for any constant c>0, when the players are only order-k rational. |
| first_indexed | 2024-09-23T10:16:06Z |
| id | mit-1721.1/71232 |
| institution | Massachusetts Institute of Technology |
| language | en-US |
| last_indexed | 2024-09-23T10:16:06Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | mit-1721.1/712322019-04-12T15:41:00Z Epistemic Implementation and The Arbitrary-Belief Auction Chen, Jing Micali, Silvio Pass, Rafael Silvio Micali Theory of Computation higher-order beliefs higher-order rationality revenue In settings of incomplete information we put forward an epistemic framework for designing mechanisms that successfully leverage the players' arbitrary higher-order beliefs, even when such beliefs are totally wrong, and even when the players are rational in a very weak sense. Following Aumann (1995), we consider a player i rational if he uses a pure strategy s_i such that no alternative pure strategy s_i' performs better than s_i in every world i considers possible, and consider him order-k rational if he is rational and believes that all other players are order-(k-1) rational. We then introduce an iterative deletion procedure of dominated strategies and use it to precisely characterize the strategies consistent with the players being order-k rational. We exemplify the power of our framework in single-good auctions by introducing and achieving a new class of revenue benchmarks, defined over the players' arbitrary beliefs, that can be much higher than classical ones, and are unattainable by traditional mechanisms. Namely, we exhibit a mechanism that, for every k greater than or equal to 0 and epsilon>0 and whenever the players are order-(k+1) rational, guarantees revenue greater than or equal to G^k-epsilon, where G^k is the second highest belief about belief about ... (k times) about the highest valuation of some player, even when such a player's identity is not precisely known. Importantly, our mechanism is possibilistic interim individually rational. Essentially this means that, based on his beliefs, a player's utility is non-negative not in expectation, but in each world he believes possible. We finally show that our benchmark G^k is so demanding that it separates the revenue achievable with order-k rational players from that achievable with order-(k+1) rational ones. That is, no possibilistic interim individually rational mechanism can guarantee revenue greater than or equal to G^k-c, for any constant c>0, when the players are only order-k rational. 2012-06-27T20:15:03Z 2012-06-27T20:15:03Z 2012-06-22 http://hdl.handle.net/1721.1/71232 en-US MIT-CSAIL-TR-2012-017 31 p. application/pdf |
| spellingShingle | higher-order beliefs higher-order rationality revenue Chen, Jing Micali, Silvio Pass, Rafael Epistemic Implementation and The Arbitrary-Belief Auction |
| title | Epistemic Implementation and The Arbitrary-Belief Auction |
| title_full | Epistemic Implementation and The Arbitrary-Belief Auction |
| title_fullStr | Epistemic Implementation and The Arbitrary-Belief Auction |
| title_full_unstemmed | Epistemic Implementation and The Arbitrary-Belief Auction |
| title_short | Epistemic Implementation and The Arbitrary-Belief Auction |
| title_sort | epistemic implementation and the arbitrary belief auction |
| topic | higher-order beliefs higher-order rationality revenue |
| url | http://hdl.handle.net/1721.1/71232 |
| work_keys_str_mv | AT chenjing epistemicimplementationandthearbitrarybeliefauction AT micalisilvio epistemicimplementationandthearbitrarybeliefauction AT passrafael epistemicimplementationandthearbitrarybeliefauction |