Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

Chen, Jing; Micali, Silvio; Pass, Rafael

doi:10.3982/ecta12563

Cited by 17 publications

(19 citation statements)

References 60 publications

(70 reference statements)

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“…As mentioned in the introduction of the paper, since the common prior assumption implies that every player has correct and exact (that is, no more, no less) knowledge about all the distributions, in the main body of this paper we do not consider scenarios where the players have "insider" knowledge. Incorrect insider knowledge has been studied in [7,2,19,20,8] and is not the focus of this paper. However, sometimes each player may have correct insider knowledge about the other players' value distributions 11 : that is, his knowledge is a refinement of the prior.…”

Section: E Aggregating the Players' Refined Insider Knowledgementioning

confidence: 99%

“…Different players' knowledge, although all correct, may refine the prior in different ways. For example, when the prior distribution of a player i's value for an item j is uniform over [0, 100], after v ij is drawn, another player i ′ may observe whether v ij ≥ 50 or not, and a third player i ′′ may observe whether v ij ∈ [20,80]. Thus, player i ′ knows whether v ij is uniform over [0, 50] or (50, 100], depending on his signal; and player i ′′ knows whether v ij is uniform over [20,80] or [0, 20)∪(80, 100], depending on the signal i ′′ observes.…”

Section: E Aggregating the Players' Refined Insider Knowledgementioning

confidence: 99%

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Information Elicitation for Bayesian Auctions

Chen

2018

Algorithmic Game Theory

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In this paper we design information elicitation mechanisms for Bayesian auctions. While in Bayesian mechanism design the distributions of the players' private types are often assumed to be common knowledge, information elicitation considers the situation where the players know the distributions better than the decision maker. To weaken the information assumption in Bayesian auctions, we consider an information structure where the knowledge about the distributions is arbitrarily scattered among the players. In such an unstructured information setting, we design mechanisms for unit-demand auctions and additive auctions that aggregate the players' knowledge, generating revenue that are constant approximations to the optimal Bayesian mechanisms with a common prior. Our mechanisms are 2-step dominant-strategy truthful and the revenue increases gracefully with the amount of knowledge the players collectively have.Extensions of our results. In our main results, the seller asks the players to report the distributions in their entirety, without being concerned with the communication complexity for doing so. This is common in information elicitation and allows us to focus on the main difficulties in aggregating the players' knowledge. In Appendix D, we show how to modify our mechanisms so that the players only report a small amount of information about the distributions.Furthermore, in the main body of this paper we consider auction settings where a player i's knowledge about another player i ′ for an item j is exactly the prior distribution D i ′ j . This simplifies the description of the knowledge graphs. In Appendix E, we consider settings where a player may observe private signals about other players and can further refine the prior.Future directions. As Bayesian auctions require the seller (and the players under common-prior assumption) has correct knowledge about all distributions, in our main results we do not consider scenarios where players have "insider" knowledge. If the insider knowledge is correct (i.e., is a refinement of the prior), then our mechanisms' revenue increases; see Appendix E. Still, how to aggregate even the incorrect information that the players may have about each other is a very interesting question for future studies.Another important direction is to elicit players' information for BIC mechanisms. For example, the BIC mechanisms in [23,10] are optimal in their own settings, and it is unclear how to convert them to information elicitation mechanisms. Related WorkInformation elicitation. Following [35], information elicitation has become an important research area in the past decade [38,44,33]. A mechanism asks each player to report his private signal and his private knowledge about the prior distribution. The decision maker wants the mechanism to be BIC, and a player is rewarded based on his reported distribution and the other players' reported signals. Different from auctions, there are no allocations or prices, and a player's utility equals his reward. Proper scoring rules [9,22] are widely ...

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Section: E Aggregating the Players' Refined Insider Knowledgementioning

confidence: 99%

Section: E Aggregating the Players' Refined Insider Knowledgementioning

confidence: 99%

Information Elicitation for Bayesian Auctions

Chen

2018

Algorithmic Game Theory

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“…Our prior work on robust mechanism design (Bergemann and Morris (2012)) did so under a full support assumption on payo¤ types. Chen, Micali, and Pass (2015) report elegant robust revenue maximization results using belief-free rationalizability under private values (they also work with …nite level version of the solution concept).…”

Section: Applications Of Belief-free Rationalizabilitymentioning

confidence: 99%

“…There are private values if u i ((a i ; a i ) ; ( i ; i )) is independent of i . Under the private values assumption, the solution concept of belief-free rationalizability is studied by Chen, Micali, and Pass (2015) and used to develop novel results about robust revenue maximization.…”

Section: Payo¤ Type Spacesmentioning

confidence: 99%

“…A leading example of a payo¤ type environment is a private values environment (where a player's payo¤ depends only on his own payo¤ type), and Chen, Micali, and Pass (2015) have proposed what we are calling belief-free rationalizability in this context and used it for novel results on robust revenue maximization. Payo¤ type environments without private values were the focus of earlier work of ours on robust mechanism design collected in Bergemann and Morris (2012).…”

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Informational Robustness and Solution Concepts

Bergemann¹,

Morris

2014

SSRN Journal

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Consider the following "informational robustness" question: what can we say about the set of outcomes that may arise in equilibrium of a Bayesian game if players may observe some additional information? This set of outcomes will correspond to a solution concept that is weaker than equilibrium, with the solution concept depending on what restrictions are imposed on the additional information.We describe a uni…ed approach encompassing prior informational robustness results, as well as identifying the solution concept that corresponds to no restrictions on the additional information; this version of rationalizability depends only on the support of players'beliefs and implies novel predictions in classic economic environments of coordination and trading games.Our results generalize from complete to incomplete information the classical results in Aumann (1974Aumann ( , 1987 and Brandenburger and Dekel (1987) which can be (and were) given informational robustness interpretations. We discuss the relation between informational robustness and "epistemic" foundations of solution concepts.Jel Classification: C72, C79, D82, D83.Keywords: Incomplete Information, Informational Robustness, Bayes Correlated Equilibrium, Interim Corrrelated Rationalizability, Belief Free RationalizabilityWe acknowledge …nancial support from NSF ICES 1215808. We are grateful for discussions about an earlier version of this paper with

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Epistemic Reasoning About Rationality and Bids in Auctions

Mittelmann

Herzig

Perrussel

2021

Logics in Artificial Intelligence

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In this paper, we investigate strategic reasoning in the context of auctions. More precisely, we establish an explicit link between bidding actions and bounded rationality. To do so, we extend the Auction Description Language with an epistemic operator and an action choice operator and use it to represent a classical auction where agents have imperfect information about other agents' valuations. We formalize bounded rationality concepts in iterative protocols and show how to use them to reason about the players' actions. Finally, we provide a model checking algorithm.

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Tight Revenue Bounds With Possibilistic Beliefs and Level-k Rationality

Cited by 17 publications

References 60 publications

Information Elicitation for Bayesian Auctions

Information Elicitation for Bayesian Auctions

Informational Robustness and Solution Concepts

Epistemic Reasoning About Rationality and Bids in Auctions

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