## Information uncertainty in auction theory

van Welbergen N (2016)

Bielefeld: Universität Bielefeld.

**Bielefelder E-Dissertation**|

**Englisch**

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Autor*in

**van Welbergen, Nikoleta**

Gutachter*in / Betreuer*in

Einrichtung

Abstract / Bemerkung

For a long time in the literature, the usual way of modeling an auction participant's beliefs has been exogenous - the distribution of private value is simply given, fixed, commonly known and out of any doubt for the involved participants. Growing awareness on information uncertainty and its strong influence on decision choices and social outcomes is the reason why we focus on introducing information uncertainty in auction theory. In particular, we allow involved subjects to question underlying information structure. We propose three different ways to design the endogenous belief formation process and explore its influence on state of the art in auction theory. This research approach results in three different setups, each examined in depth in a separate chapter.

Chapter 2 shows the importance of our modeling approach. The genericity of an optimal auction format - in the literature known as the Crémer-McLean auction - is challenged and its robustness against a change of information structure is examined. We show that participation constraints in the auction format fail to hold once the seller and bidders have slightly different beliefs over the joint distribution of private values. We propose the definition of a belief neighborhood in order to capture this slight discrepancy between seller's and bidders' beliefs. Moreover, we also give a quantitative assessment of how often the failure occurs in the case of a common prior assumption as well as once the common prior assumption among bidders is relaxed. In particular, participation constraints fail in at least one half of any plausible belief's neighborhood. Once the common prior assumption among bidders is relaxed, the failure occurs everywhere except in 1/(2^(2m)) of a belief's neighborhood, where m is the number of possible private values for each bidder.

The origin of private values in auction models is examined in Chapter 3. In contrast with the standard literature, we let participants question the information structure involved in auctions. We focus on the most prevalent forms of sealed-bid auctions on the market: the first-price and second-price auctions. Instead of being exogenously given, we permit the observed distribution of private value to take the form of mixture probability distribution, which in turn allows participants to speculate on the true distribution of the values. The speculations are done in accordance with Bayes' rule - the bidders use their private value to infer the distribution, whereas the seller bases his belief on an observed mixture form of the values' distribution. We explore the consequences of allowing this particular belief formation on bidders' and seller's behavior. First of all, despite the independently and identically distributed values, we show that the belief formation leads to the revenue equivalence failure in such a way that the seller prefers the second-price auction. Moreover, in our setup, truthfully bidding one's own private value continues to be optimal in the second-price auction. However, the bidding behavior in the first-price auction is influenced by the belief formation in the following way. Comparison of bidding strategies in the standard framework and our model leads to the statement that these two strategies cross at most once. In other words, we discover that there is either dominance ordering or a single-crossing property between the compared strategies.

The final chapter presents a model with a new kind of information uncertainty - the uncertainty about seller's type. Motivated by recent security and fraud issues in auctions, we develop a model where a manipulative seller has an opportunity to send an agent to bid secretly on the seller's behalf. Out of the possible auction formats, we choose the second-price auction and the all-pay auction. We look at the all-pay auction because of its design: everyone pays her own bid, irrespective of whether she wins the auction. Consequently, it seems that the manipulative seller can make the best use of his manipulation in the all-pay auction. In the all-pay auction, the seller may keep the object and collect all bids, which is not the case with either a second-price or first-price auction. In this way we change the standard information structure of an auction by proposing that the seller also holds private information, whether or not he is a manipulative (with an agent) or an honest seller (without an agent). Even though a priori there is a common prior over the possibility of facing a cheating seller, bidders in our model perceive the choice of auction format as a signal about the seller's intentions. Thus, our setup extends the standard auction framework to a form of signaling game. To this end, we explore the pure weak perfect Bayesian Nash equilibria of this game. We show that the only robust weak Bayesian Nash equilibrium is pooling on the second-price: that is, it is beneficial for both type of sellers to choose the second-price auction. In addition, there is a special non-generic equilibrium scenario in which the honest seller chooses the all-pay auction and the cheating seller chooses the second-price auction. However, this equilibrium is very unstable and not robust against the smallest change of bidders' belief on seller's honesty. Thus, it turns out that the signaling effect is stronger than the effect of manipulation. Unlike the discussion in related literature on the disadvantage of the application of the second-price auction in a setup with independently and identically distributed private values and a similar seller's manipulation (with different timing), our model favors the second-price auction.

Chapter 2 shows the importance of our modeling approach. The genericity of an optimal auction format - in the literature known as the Crémer-McLean auction - is challenged and its robustness against a change of information structure is examined. We show that participation constraints in the auction format fail to hold once the seller and bidders have slightly different beliefs over the joint distribution of private values. We propose the definition of a belief neighborhood in order to capture this slight discrepancy between seller's and bidders' beliefs. Moreover, we also give a quantitative assessment of how often the failure occurs in the case of a common prior assumption as well as once the common prior assumption among bidders is relaxed. In particular, participation constraints fail in at least one half of any plausible belief's neighborhood. Once the common prior assumption among bidders is relaxed, the failure occurs everywhere except in 1/(2^(2m)) of a belief's neighborhood, where m is the number of possible private values for each bidder.

The origin of private values in auction models is examined in Chapter 3. In contrast with the standard literature, we let participants question the information structure involved in auctions. We focus on the most prevalent forms of sealed-bid auctions on the market: the first-price and second-price auctions. Instead of being exogenously given, we permit the observed distribution of private value to take the form of mixture probability distribution, which in turn allows participants to speculate on the true distribution of the values. The speculations are done in accordance with Bayes' rule - the bidders use their private value to infer the distribution, whereas the seller bases his belief on an observed mixture form of the values' distribution. We explore the consequences of allowing this particular belief formation on bidders' and seller's behavior. First of all, despite the independently and identically distributed values, we show that the belief formation leads to the revenue equivalence failure in such a way that the seller prefers the second-price auction. Moreover, in our setup, truthfully bidding one's own private value continues to be optimal in the second-price auction. However, the bidding behavior in the first-price auction is influenced by the belief formation in the following way. Comparison of bidding strategies in the standard framework and our model leads to the statement that these two strategies cross at most once. In other words, we discover that there is either dominance ordering or a single-crossing property between the compared strategies.

The final chapter presents a model with a new kind of information uncertainty - the uncertainty about seller's type. Motivated by recent security and fraud issues in auctions, we develop a model where a manipulative seller has an opportunity to send an agent to bid secretly on the seller's behalf. Out of the possible auction formats, we choose the second-price auction and the all-pay auction. We look at the all-pay auction because of its design: everyone pays her own bid, irrespective of whether she wins the auction. Consequently, it seems that the manipulative seller can make the best use of his manipulation in the all-pay auction. In the all-pay auction, the seller may keep the object and collect all bids, which is not the case with either a second-price or first-price auction. In this way we change the standard information structure of an auction by proposing that the seller also holds private information, whether or not he is a manipulative (with an agent) or an honest seller (without an agent). Even though a priori there is a common prior over the possibility of facing a cheating seller, bidders in our model perceive the choice of auction format as a signal about the seller's intentions. Thus, our setup extends the standard auction framework to a form of signaling game. To this end, we explore the pure weak perfect Bayesian Nash equilibria of this game. We show that the only robust weak Bayesian Nash equilibrium is pooling on the second-price: that is, it is beneficial for both type of sellers to choose the second-price auction. In addition, there is a special non-generic equilibrium scenario in which the honest seller chooses the all-pay auction and the cheating seller chooses the second-price auction. However, this equilibrium is very unstable and not robust against the smallest change of bidders' belief on seller's honesty. Thus, it turns out that the signaling effect is stronger than the effect of manipulation. Unlike the discussion in related literature on the disadvantage of the application of the second-price auction in a setup with independently and identically distributed private values and a similar seller's manipulation (with different timing), our model favors the second-price auction.

Jahr

2016

Page URI

https://pub.uni-bielefeld.de/record/2907314

## Zitieren

van Welbergen N.

*Information uncertainty in auction theory*. Bielefeld: Universität Bielefeld; 2016.van Welbergen, N. (2016).

*Information uncertainty in auction theory*. Bielefeld: Universität Bielefeld.van Welbergen, Nikoleta. 2016.

*Information uncertainty in auction theory*. Bielefeld: Universität Bielefeld.van Welbergen, N. (2016). Information uncertainty in auction theory. Bielefeld: Universität Bielefeld.

van Welbergen, N., 2016.

*Information uncertainty in auction theory*, Bielefeld: Universität Bielefeld. N. van Welbergen,

*Information uncertainty in auction theory*, Bielefeld: Universität Bielefeld, 2016. van Welbergen, N.: Information uncertainty in auction theory. Universität Bielefeld, Bielefeld (2016).

van Welbergen, Nikoleta.

*Information uncertainty in auction theory*. Bielefeld: Universität Bielefeld, 2016.**Alle Dateien verfügbar unter der/den folgenden Lizenz(en):**

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**Dieses Objekt ist durch das Urheberrecht und/oder verwandte Schutzrechte geschützt.**[...]

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2019-09-06T09:18:41Z

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