scholarly journals Bayes-Nash Equilibrium of the Generalized First-Price Auction

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaohu Han ◽  
Shulin Liu
Keyword(s):  
Nash Equilibrium ◽  
Incomplete Information ◽  
Explicit Expression ◽  
Search Engine ◽  
Reserve Price ◽  
Price Auction ◽  
Expected Revenue ◽  
The Difference ◽  
Optimal Reserve

We analyze the generalized first-price auction under incomplete information setting. Without setting a reserve price, the efficient symmetrical Bayes-Nash equilibrium is characterized and found to be increasing as the number of bidders is sufficiently large. Then, the explicit expression for the expected revenue of the search engine is found and the effect of the click rates of all the positions on the expected revenue is obtained. Finally, with setting of the reserve price, we have found the optimal reserve price and examine how the difference of the search engine’s revenues with setting reserve price and without setting reserve price varies with the reserve price.

Why the Reserve Price Should Not Be Kept Secret

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Karine Brisset ◽  
Florence Naegelen
Keyword(s):  
Price Policy ◽  
Risk Averse ◽  
Relative Risk Aversion ◽  
Reserve Price ◽  
Bayesian Equilibrium ◽  
Ascending Auctions ◽  
Price Auction ◽  
Second Price Auction ◽  
Optimal Reserve ◽  
Secret Reserve Price

This paper considers the optimality of setting a secret reserve price in ascending auctions. Contrary to intuition, an ascending auction is no longer equivalent to a second price auction when the reserve price is secret. We determine the seller's optimal reserve price policy when the bidders' values are private and independently distributed and when the bidders are risk averse. We show that an optimal secret reserve price policy can dominate an optimal public reserve price policy when the bidders' degree of constant relative risk aversion is sufficiently high and when the seller can commit to a reserve price policy before learning her type. In contrast, a secret reserve price policy can never be part of a Bayesian equilibrium when the seller is informed.

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

2021 ◽  
Author(s):  
Muhammad Ejaz ◽  
Stephen Joe ◽  
Chaitanya Joshi
Keyword(s):  
Nash Equilibrium ◽  
Risk Analysis ◽  
Equilibrium Solution ◽  
Risk Averse ◽  
Prior Work ◽  
Reserve Price ◽  
Solution Concepts ◽  
Risk Seeking ◽  
Sealed Bid ◽  
Sealed Bid Auctions

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

scholarly journals Projection of Private Values in Auctions

2021 ◽  
Vol 111 (10) ◽  
pp. 3256-3298
Author(s):  
Tristan Gagnon-Bartsch ◽  
Marco Pagnozzi ◽  
Antonio Rosato
Keyword(s):  
Allocative Efficiency ◽  
Reserve Price ◽  
English Auctions ◽  
Common Value ◽  
Private Values ◽  
Optimal Reserve ◽  
Intensity Of Competition

We explore how taste projection—the tendency to overestimate how similar others’ tastes are to one’s own—affects bidding in auctions. In first-price auctions with private values, taste projection leads bidders to exaggerate the intensity of competition and, consequently, to overbid—irrespective of whether values are independent, affiliated, or (a)symmetric. Moreover, the optimal reserve price is lower than the rational benchmark, and decreasing in the extent of projection and the number of bidders. With an uncertain common-value component, projecting bidders draw distorted inferences about others’ information. This misinference is stronger in second-price and English auctions, reducing their allocative efficiency compared to first-price auctions. (JEL D11, D44, D82, D83)

scholarly journals Distance Metrics of D Numbers

2020 ◽  
Author(s):  
Liguo Fei ◽  
Yuqiang Feng
Keyword(s):  
Number Theory ◽  
Incomplete Information ◽  
Distance Function ◽  
Distance Measure ◽  
Complete Information ◽  
Belief Function ◽  
Distance Metrics ◽  
Modeling Methods ◽  
The Difference ◽  
D Numbers

Belief function has always played an indispensable role in modeling cognitive uncertainty. As an inherited version, the theory of D numbers has been proposed and developed in a more efficient and robust way. Within the framework of D number theory, two more generalized properties are extended: (1) the elements in the frame of discernment (FOD) of D numbers do not required to be mutually exclusive strictly; (2) the completeness constraint is released. The investigation shows that the distance function is very significant in measuring the difference between two D numbers, especially in information fusion and decision. Modeling methods of uncertainty that incorporate D numbers have become increasingly popular, however, very few approaches have tackled the challenges of distance metrics. In this study, the distance measure of two D numbers is presented in cases, including complete information, incomplete information, and non-exclusive elements

scholarly journals Revenue-Capped Efficient Auctions

2019 ◽  
Vol 18 (3) ◽  
pp. 1284-1320 ◽  
Author(s):  
Nozomu Muto ◽  
Yasuhiro Shirata ◽  
Takuro Yamashita
Keyword(s):  
Upper Bound ◽  
Private Information ◽  
Weighted Sum ◽  
Reserve Price ◽  
Total Surplus ◽  
Good For ◽  
Expected Revenue ◽  
Social Surplus

Abstract We study an auction that maximizes the expected social surplus under an upper-bound constraint on the seller’s expected revenue, which we call a revenue cap. Such a constrained-efficient auction may arise, for example, when (i) the auction designer is “pro-buyer”, that is, he maximizes the weighted sum of the buyers’ and seller’s auction payoffs, where the weight for the buyers is greater than that for the seller; (ii) the auction designer maximizes the (unweighted) total surplus in a multiunit auction in which the number of units the seller owns is private information; or (iii) multiple sellers compete to attract buyers before the auction. We characterize the mechanisms for constrained-efficient auctions and identify their important properties. First, the seller sets no reserve price and sells the good for sure. Second, with a nontrivial revenue cap, “bunching” is necessary. Finally, with a sufficiently severe revenue cap, the constrained-efficient auction has a bid cap, so that bunching occurs at least “at the top,” that is, “no distortion at the top” fails.

scholarly journals Learning to Set the Reserve Price Optimally in Laboratory First Price Auctions

Games ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 79
Author(s):  
Priyodorshi Banerjee ◽  
Shashwat Khare ◽  
P. Srikant
Keyword(s):  
Choice Behavior ◽  
Reserve Price ◽  
Price Auction ◽  
Equilibrium Bidding ◽  
Fixed Period

We analyze choices of sellers, each setting a reserve price in a laboratory first price auction with automated equilibrium bidding. Subjects are allowed to gain experience for a fixed period of time prior to making a single payoff-relevant choice. Behavior of more experienced sellers was consistent with benchmark theory: average reserve price for these sellers was independent of the number of bidders and equaled the predicted level. Less experienced sellers however deviated from the theoretical benchmark: on average, they tended to shade reserve price below the predicted level and positively relate it to the number of bidders.

scholarly journals Stochastic Brownian Game of Absolute Dominance

2014 ◽  
Vol 51 (2) ◽  
pp. 436-452
Author(s):  
Shangzhen Luo
Keyword(s):  
Nash Equilibrium ◽  
Value Function ◽  
The Other ◽  
Equilibrium Strategy ◽  
Minimax Criterion ◽  
Nash Equilibrium Strategy ◽  
Suitable Parameter ◽  
The Difference ◽  
The Value Function ◽  
Absolute Dominance

In this paper we study a reinsurance game between two insurers whose surplus processes are modeled by arithmetic Brownian motions. We assume a minimax criterion in the game. One insurer tries to maximize the probability of absolute dominance while the other tries to minimize it through reinsurance control. Here absolute dominance is defined as the event that liminf of the difference of the surplus levels tends to -∞. Under suitable parameter conditions, the game is solved with the value function and the Nash equilibrium strategy given in explicit form.

Stochastic Brownian Game of Absolute Dominance

2014 ◽  
Vol 51 (02) ◽  
pp. 436-452 ◽  
Author(s):  
Shangzhen Luo
Keyword(s):  
Nash Equilibrium ◽  
Value Function ◽  
The Other ◽  
Equilibrium Strategy ◽  
Minimax Criterion ◽  
Nash Equilibrium Strategy ◽  
Suitable Parameter ◽  
The Difference ◽  
The Value Function ◽  
Absolute Dominance

In this paper we study a reinsurance game between two insurers whose surplus processes are modeled by arithmetic Brownian motions. We assume a minimax criterion in the game. One insurer tries to maximize the probability of absolute dominance while the other tries to minimize it through reinsurance control. Here absolute dominance is defined as the event that liminf of the difference of the surplus levels tends to -∞. Under suitable parameter conditions, the game is solved with the value function and the Nash equilibrium strategy given in explicit form.

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