Slopey quantizers are locally optimal for Witsenhausen's counterexample
We study the perfect Bayesian equilibria of a leader-follower game of incomplete information. The follower makes a noisy observation of the leader's action (who moves first) and chooses an action minimizing her expected deviation from the leader's action. Knowing this, leader who observes...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2017
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| Online Access: | http://hdl.handle.net/1721.1/111985 https://orcid.org/0000-0003-3553-4638 |
| _version_ | 1826205818136035328 |
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| author | Ajorlou, Amir Jadbabaie-Moghadam, Ali |
| author2 | Massachusetts Institute of Technology. Institute for Data, Systems, and Society |
| author_facet | Massachusetts Institute of Technology. Institute for Data, Systems, and Society Ajorlou, Amir Jadbabaie-Moghadam, Ali |
| author_sort | Ajorlou, Amir |
| collection | MIT |
| description | We study the perfect Bayesian equilibria of a leader-follower game of incomplete information. The follower makes a noisy observation of the leader's action (who moves first) and chooses an action minimizing her expected deviation from the leader's action. Knowing this, leader who observes the realization of the state, chooses an action that minimizes her distance to the state of the world and the ex-ante expected deviation from the follower's action. We show the existence of what we call “near piecewise-linear equilibria” when there is strong complementarity between the leader and the follower and the precision of the prior is poor. As a major consequence of this result, we prove local optimality of a class of slopey quantization strategies which had been suspected of being the optimal solution in the past, based on numerical evidence for Witsenhausen's counterexample. |
| first_indexed | 2024-09-23T13:19:34Z |
| format | Article |
| id | mit-1721.1/111985 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:19:34Z |
| publishDate | 2017 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1119852022-09-28T13:26:16Z Slopey quantizers are locally optimal for Witsenhausen's counterexample Ajorlou, Amir Jadbabaie-Moghadam, Ali Massachusetts Institute of Technology. Institute for Data, Systems, and Society Jadbabaie, Ali Ajorlou, Amir Jadbabaie-Moghadam, Ali We study the perfect Bayesian equilibria of a leader-follower game of incomplete information. The follower makes a noisy observation of the leader's action (who moves first) and chooses an action minimizing her expected deviation from the leader's action. Knowing this, leader who observes the realization of the state, chooses an action that minimizes her distance to the state of the world and the ex-ante expected deviation from the follower's action. We show the existence of what we call “near piecewise-linear equilibria” when there is strong complementarity between the leader and the follower and the precision of the prior is poor. As a major consequence of this result, we prove local optimality of a class of slopey quantization strategies which had been suspected of being the optimal solution in the past, based on numerical evidence for Witsenhausen's counterexample. 2017-10-27T15:07:29Z 2017-10-27T15:07:29Z 2016-12 2016-12 Article http://purl.org/eprint/type/ConferencePaper 978-1-5090-1837-6 http://hdl.handle.net/1721.1/111985 Ajorlou, Amir, and Jadbabaie, Ali. “Slopey Quantizers Are Locally Optimal for Witsenhausen’s Counterexample.” 2016 IEEE 55th Conference on Decision and Control (CDC), December 12-14 2016, Las Vegas, Nevada, USA, Institute of Electrical and Electronics Engineers (IEEE), December 2016 © 2016 Institute of Electrical and Electronics Engineers (IEEE) https://orcid.org/0000-0003-3553-4638 en_US http://dx.doi.org/10.1109/CDC.2016.7798805 2016 IEEE 55th Conference on Decision and Control (CDC) Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) Prof. Jadbabaie via Anne Graham |
| spellingShingle | Ajorlou, Amir Jadbabaie-Moghadam, Ali Slopey quantizers are locally optimal for Witsenhausen's counterexample |
| title | Slopey quantizers are locally optimal for Witsenhausen's counterexample |
| title_full | Slopey quantizers are locally optimal for Witsenhausen's counterexample |
| title_fullStr | Slopey quantizers are locally optimal for Witsenhausen's counterexample |
| title_full_unstemmed | Slopey quantizers are locally optimal for Witsenhausen's counterexample |
| title_short | Slopey quantizers are locally optimal for Witsenhausen's counterexample |
| title_sort | slopey quantizers are locally optimal for witsenhausen s counterexample |
| url | http://hdl.handle.net/1721.1/111985 https://orcid.org/0000-0003-3553-4638 |
| work_keys_str_mv | AT ajorlouamir slopeyquantizersarelocallyoptimalforwitsenhausenscounterexample AT jadbabaiemoghadamali slopeyquantizersarelocallyoptimalforwitsenhausenscounterexample |