scholarly journals Equilibrium Bids in Sponsored Search Auctions: Theory and Evidence

2013 ◽  
Vol 5 (4) ◽  
pp. 163-187 ◽  
Author(s):  
Tilman Börgers ◽  
Ingemar Cox ◽  
Martin Pesendorfer ◽  
Vaclav Petricek
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Sponsored Search ◽  
Theoretic Analysis ◽  
Game Theoretic Analysis ◽  
Sponsored Search Auctions ◽  
Price Auction ◽  
Game Theoretic ◽  
Second Price Auction ◽  
Generalized Second Price Auction

This paper presents a game theoretic analysis of the generalized second-price auction that the company Overture operated in 2004 to sell sponsored search listings on search engines. We construct a model that embodies few prior assumptions about parameters, and we present results that indicate that this model has under quite general assumptions a multiplicity of Nash equilibria. We then analyze bid data assuming that advertisers choose Nash equilibrium bids. We offer preliminary conclusions about advertisers' true willingness to bid for sponsored search listings. We find that advertisers' true willingness to bid is multi-dimensional and decreasing in listing position. (JEL D44, L86, M31, M37)

scholarly journals Bounding Regret in Empirical Games

2020 ◽  
Vol 34 (04) ◽  
pp. 4280-4287
Author(s):  
Steven Jecmen ◽  
Arunesh Sinha ◽  
Zun Li ◽  
Long Tran-Thanh
Keyword(s):  
Large Scale ◽  
Nash Equilibria ◽  
Sample Complexity ◽  
Bandit Problem ◽  
Theoretic Analysis ◽  
Present Sample ◽  
Game Theoretic Analysis ◽  
Approximate Nash Equilibria ◽  
Game Theoretic

Empirical game-theoretic analysis refers to a set of models and techniques for solving large-scale games. However, there is a lack of a quantitative guarantee about the quality of output approximate Nash equilibria (NE). A natural quantitative guarantee for such an approximate NE is the regret in the game (i.e. the best deviation gain). We formulate this deviation gain computation as a multi-armed bandit problem, with a new optimization goal unlike those studied in prior work. We propose an efficient algorithm Super-Arm UCB (SAUCB) for the problem and a number of variants. We present sample complexity results as well as extensive experiments that show the better performance of SAUCB compared to several baselines.

scholarly journals Evolutionary stability in the generalized second-price auction

2019 ◽  
Author(s):  
Thomas W. L. Norman
Keyword(s):  
Nash Equilibrium ◽  
Stable Equilibrium ◽  
Evolutionary Stability ◽  
Internet Advertising ◽  
Price Auction ◽  
Second Price Auction ◽  
Generalized Second Price Auction ◽  
Evolutionarily Stable

AbstractThe “generalized second-price auction” is widely employed to sell internet advertising positions and has many equilibria. Analysis of this auction has assumed that myopic players commonly know each others’ position values, and that the resulting equilibrium play is “locally envy-free”. Here, I argue that the appropriate refinement of Nash equilibrium for this setting is evolutionary stability, and show that it implies that an equilibrium is locally envy-free if the whole population of players bids in each auction and the set of possible bids is not too coarse. However, not all locally envy-free equilibria are evolutionarily stable in this case, as I show by example for the popular Vickrey–Clarke–Groves outcome. The existence of evolutionarily stable equilibrium is established when one position is auctioned, as well as for two positions and a large number of bidders.

scholarly journals A game theoretic approach reveals that discretizing clinical information can reduce antibiotic misuse

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Maya Diamant ◽  
Shoham Baruch ◽  
Eias Kassem ◽  
Khitam Muhsen ◽  
Dov Samet ◽  
...  
Keyword(s):  
Antibiotic Prescription ◽  
Clinical Information ◽  
Social Optimum ◽  
Theoretic Approach ◽  
Theoretic Analysis ◽  
Game Theoretic Analysis ◽  
Optimal Output ◽  
The Social ◽  
Game Theoretic ◽  
Game Theoretic Approach

AbstractThe overuse of antibiotics is exacerbating the antibiotic resistance crisis. Since this problem is a classic common-goods dilemma, it naturally lends itself to a game-theoretic analysis. Hence, we designed a model wherein physicians weigh whether antibiotics should be prescribed, given that antibiotic usage depletes its future effectiveness. The physicians’ decisions rely on the probability of a bacterial infection before definitive laboratory results are available. We show that the physicians’ equilibrium decision rule of antibiotic prescription is not socially optimal. However, we prove that discretizing the information provided to physicians can mitigate the gap between their equilibrium decisions and the social optimum of antibiotic prescription. Despite this problem’s complexity, the effectiveness of the discretization solely depends on the type of information available to the physician to determine the nature of infection. This is demonstrated on theoretic distributions and a clinical dataset. Our results provide a game-theory based guide for optimal output of current and future decision support systems of antibiotic prescription.

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