Equilibrium Bidding Strategies under the English and the Second-Price Auctions

2002 ◽  
pp. 197-205 ◽  
Author(s):  
Soo Hong Chew ◽  
Naoko Nishimura
Keyword(s):  
Bidding Strategies ◽  
Equilibrium Bidding ◽  
Second Price Auctions

scholarly journals Reserve price of risk-averse search engine in keyword auctions with advertisers’endogenous investment

2019 ◽  
Author(s):  
Qin Yang ◽  
Xianpei Hong ◽  
Zongjun Wang ◽  
Huaige Zhang
Keyword(s):  
Risk Aversion ◽  
Social Welfare ◽  
Search Engine ◽  
Optimal Investment ◽  
Total Efficiency ◽  
Risk Averse ◽  
Reserve Price ◽  
Bidding Strategies ◽  
Keyword Auctions ◽  
Equilibrium Bidding

Motivated by vigorous development of keyword auctions, this paper analyzes the reserve price policies in keyword auction with advertisers’ endogenous investment and risk-averse search engine. We explore advertisers’ optimal investment and equilibrium bidding strategies , and derive the determination functions where utility-maximizing reserve price and efficient reserve price which maximizes the social welfare satisfy respectively. The results show that advertisers’ equilibrium bidding is monotonously increasing in bidders’ valuations, the number of advertisers, as well as the reserve price. Meanwhile, advertisers’ optimal investment is negatively correlated with reserve price and the number of advertisers. By numerical examples, the utility-maximizing reserve price decreases with the risk aversion parameter and the number of advertisers. Search engine’s expected utility increases with risk aversion parameter and decreases with the number of advertisers. Moreover, we declare that search engine can use reserve price as a regulatory tool to increase the utility. But there is an upper bound on search engine’s utility. It is interesting to find the efficient reserve price equals to zero. Hence there is a trade-off between total efficiency and search engine’s utility by search engine that has incentive to withhold reserve price that would benefit social welfare.

Nash equilibrium bidding strategies in a bilateral electricity market

2002 ◽  
Vol 17 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Haili Song ◽  
Chen-Ching Liu ◽  
J. Lawarree
Keyword(s):  
Nash Equilibrium ◽  
Electricity Market ◽  
Bidding Strategies ◽  
Equilibrium Bidding

scholarly journals Sequential auctions and price anomalies

2014 ◽  
Vol 59 (200) ◽  
pp. 7-42 ◽  
Author(s):  
Dejan Trifunovic
Keyword(s):  
Empirical Research ◽  
Theoretical Models ◽  
Sequential Auctions ◽  
English Auctions ◽  
Bidding Strategies ◽  
Empirical Results ◽  
Heterogeneous Objects ◽  
Increasing Trend ◽  
Private Values ◽  
Equilibrium Bidding

In sequential auctions objects are sold one by one in separate auctions. These sequential auctions might be organized as sequential first-price, second-price, or English auctions. We will derive equilibrium bidding strategies for these auctions. Theoretical models suggest that prices in sequential auctions with private values or with randomly assigned heterogeneous objects should have no trend. However, empirical research contradicts this result and prices exhibit a declining or increasing trend, which is called declining and increasing price anomaly. We will present a review of these empirical results, as well as different theoretical explanations for these anomalies.

Reference-Dependent Preferences and Overbidding in Private and Common Value Auctions

2020 ◽  
Vol 9 (2) ◽  
pp. 20-37
Author(s):  
Mariano Gabriel Runco
Keyword(s):  
Information Criterion ◽  
Experimental Auctions ◽  
Bidding Strategies ◽  
Common Value ◽  
Common Value Auctions ◽  
Equilibrium Bidding ◽  
Private Value ◽  
Standard Risk ◽  
Better Than ◽  
Reference Dependent Preferences

This paper proposes a model of reference dependent preferences to explain overbidding in private and common value auctions. It is assumed that the reference point is proportional to the value of the object and that losses are weighed more heavily than gains in the utility function. Equilibrium bidding strategies are derived for first- and second-price private and common value auctions. I find that this model fits the data of all experiments analyzed, both private and common value, better in terms of the Bayesian Information Criterion than a standard risk neutral model; moreover, it explains overbidding in all private value and some common value auctions better than other alternative models. These results suggest that reference dependence, among other factors, might play a role in the widespread tendency of subjects to overbid in most experimental auctions.

Auctioning Emission Permits with Market Power

2016 ◽  
Vol 16 (4) ◽  
Author(s):  
Francisco Alvarez ◽  
Francisco J. André
Keyword(s):  
Market Power ◽  
Cost Effective ◽  
Secondary Market ◽  
Interior Solution ◽  
Specific Design ◽  
Dominant Firm ◽  
Bidding Strategies ◽  
Ex Post ◽  
Equilibrium Bidding ◽  
The Cost

Abstract We analyze emission permit auctions in a framework in which a dominant firm enjoys market power both in the auction and in the secondary market while its competitor behaves in a competitive way. We obtain linear equilibrium bidding strategies for both firms and a unique equilibrium of the auction, which is optimal ex-post for the dominant firm. Under specific distributional assumptions we conclude that the auction always awards less permits to the dominant firm than the cost-effective amount. Our results serve as a warning about the properties of auctioning under market power. Under interior solution the auction allocation is dominated by grandfathering in terms of aggregated cost with probability one. As a policy implication, the specific design of the auction turns out to be crucial for cost-effectiveness. The chances of the auction to outperform grandfathering require that the former is capable of diluting the market power that is present in the secondary market.

scholarly journals Contract Enforcement and Productive Efficiency: Evidence From the Bidding and Renegotiation of Power Contracts in India

Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 383-424 ◽  
Author(s):  
Nicholas Ryan
Keyword(s):  
Structural Model ◽  
Productive Efficiency ◽  
Production Costs ◽  
Procurement Auctions ◽  
Contract Enforcement ◽  
Bidding Strategies ◽  
Ex Post ◽  
Study Heterogeneity ◽  
Equilibrium Bidding ◽  
The Government

Weak contract enforcement may reduce the efficiency of production in developing countries. I study how contract enforcement affects efficiency in procurement auctions for the largest power projects in India. I gather data on bidding and ex post contract renegotiation and find that the renegotiation of contracts in response to cost shocks is widespread, despite that bidders are allowed to index their bids to future costs like the price of coal. To study heterogeneity in bidding strategies, I construct a new measure of firm connectedness, based on whether a firm has been awarded coal concessions by the Government. Connected firms choose to index less of the value of their bids to coal prices and, through this strategy, expose themselves to cost shocks to induce renegotiation. I use a structural model of bidding in a scoring auction to characterize equilibrium bidding when bidders are heterogeneous both in cost and in the payments they expect after renegotiation. The model estimates show that bidders offer power below cost due to the expected value of later renegotiation. The model is used to simulate bidding and efficiency with strict contract enforcement. Contract enforcement is found to be pro‐competitive. With no renegotiation, equilibrium bids would rise to cover cost, but markups relative to total contract value fall sharply. Production costs decline, due to projects being allocated to lower‐cost bidders over those who expect larger payments in renegotiation.

Learning in Repeated Auctions with Budgets: Regret Minimization and Equilibrium

2019 ◽  
Vol 65 (9) ◽  
pp. 3952-3968 ◽  
Author(s):  
Santiago R. Balseiro ◽  
Yonatan Gur
Keyword(s):  
Stochastic Models ◽  
Online Advertising ◽  
Asymptotic Optimality ◽  
Sample Path ◽  
Complete Information ◽  
Regret Minimization ◽  
Bidding Strategies ◽  
Approximate Nash Equilibrium ◽  
Pacing Strategies ◽  
Equilibrium Bidding

In online advertising markets, advertisers often purchase ad placements through bidding in repeated auctions based on realized viewer information. We study how budget-constrained advertisers may compete in such sequential auctions in the presence of uncertainty about future bidding opportunities and competition. We formulate this problem as a sequential game of incomplete information, in which bidders know neither their own valuation distribution nor the budgets and valuation distributions of their competitors. We introduce a family of practical bidding strategies we refer to as adaptive pacing strategies, in which advertisers adjust their bids according to the sample path of expenditures they exhibit, and analyze the performance of these strategies in different competitive settings. We establish the asymptotic optimality of these strategies when competitors’ bids are independent and identically distributed over auctions, but also when competing bids are arbitrary. When all the bidders adopt these strategies, we establish the convergence of the induced dynamics and characterize a regime (well motivated in the context of online advertising markets) under which these strategies constitute an approximate Nash equilibrium in dynamic strategies: the benefit from unilaterally deviating to other strategies, including ones with access to complete information, becomes negligible as the number of auctions and competitors grows large. This establishes a connection between regret minimization and market stability, by which advertisers can essentially follow approximate equilibrium bidding strategies that also ensure the best performance that can be guaranteed off equilibrium. This paper was accepted by Noah Gans, stochastic models and simulation.

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