scispace - formally typeset
Search or ask a question

Showing papers on "Bidding published in 2008"


Proceedings ArticleDOI
14 Sep 2008
TL;DR: Analytically, it is shown that VERITAS is truthful, efficient, and has a polynomial complexity of O(n3k) when n bidders compete for k spectrum bands, which makes an important contribution of maintaining truthfulness while maximizing spectrum utilization.
Abstract: Market-driven dynamic spectrum auctions can drastically improve the spectrum availability for wireless networks struggling to obtain additional spectrum. However, they face significant challenges due to the fear of market manipulation. A truthful or strategy-proof spectrum auction eliminates the fear by enforcing players to bid their true valuations of the spectrum. Hence bidders can avoid the expensive overhead of strategizing over others and the auctioneer can maximize its revenue by assigning spectrum to bidders who value it the most. Conventional truthful designs, however, either fail or become computationally intractable when applied to spectrum auctions. In this paper, we propose VERITAS, a truthful and computationally-efficient spectrum auction to support an eBay-like dynamic spectrum market. VERITAS makes an important contribution of maintaining truthfulness while maximizing spectrum utilization. We show analytically that VERITAS is truthful, efficient, and has a polynomial complexity of O(n3k) when n bidders compete for k spectrum bands. Simulation results show that VERITAS outperforms the extensions of conventional truthful designs by up to 200% in spectrum utilization. Finally, VERITAS supports diverse bidding formats and enables the auctioneer to reconfigure allocations for multiple market objectives.

465 citations


Journal ArticleDOI
TL;DR: In this article, the authors examine the bidding behavior of firms in the Texas electricity spot market, where bidders submit hourly supply schedules to sell power, and characterize an equilibrium model of bidding and use detailed firm-level data on bids and marginal costs to compare actual bidding behavior to theoretical benchmarks.
Abstract: We examine the bidding behavior of firms in the Texas electricity spot market, where bidders submit hourly supply schedules to sell power. We characterize an equilibrium model of bidding and use detailed firm-level data on bids and marginal costs to compare actual bidding behavior to theoretical benchmarks. Firms with large stakes in the market performed close to the theoretical benchmark of static profit maximization. However, smaller firms utilized excessively steep bid schedules significantly deviating from this benchmark. Further analysis suggests that payoff scale has an important effect on firms' willingness and ability to participate in complex, strategic market environments.

418 citations


Journal ArticleDOI
TL;DR: In this paper, the authors reviewed and analyzed U.S. agri-environmental programs using literature review and program data, focusing on several key questions: has benefit-cost targeting increased the environmental benefit obtained from program budgets? Has competitive bidding reduced program costs? To what extent have these program designs resulted in additional gain (that would not have otherwise been obtained)?

374 citations


Journal ArticleDOI
TL;DR: In this paper, an adaptive wavelet neural network (AWNN) was proposed for short-term price forecasting in the electricity markets, where a commonly used Mexican hat wavelet has been chosen as the activation function for hidden-layer neurons of feed-forward neural network.
Abstract: In a competitive electricity market, an accurate forecasting of energy prices is an important activity for all the market participants either for developing bidding strategies or for making investment decisions. An adaptive wavelet neural network (AWNN) is proposed in this paper for short-term price forecasting (STPF) in the electricity markets. A commonly used Mexican hat wavelet has been chosen as the activation function for hidden-layer neurons of feed-forward neural network (FFNN). To demonstrate the effectiveness of the proposed approach, day-ahead prediction of market clearing price (MCP) of Spain market, which is a duopoly market with a dominant player, and locational marginal price (LMP) forecasting in PJM electricity market, are considered. The forecasted results clearly show that AWNN has good prediction properties compared to other forecasting techniques, such as wavelet-ARIMA, multi-layer perceptron (MLP) and radial basis function (RBF) neural networks as well as recently proposed fuzzy neural network (FNN).

305 citations


Posted Content
B. Espen Eckbo1
TL;DR: In this article, the authors review recent empirical research documenting offer premiums and bidding strategies in corporate takeovers, ranging from optimal auction bidding to the choice of deal payment form and premium effects of poison pills.
Abstract: I review recent empirical research documenting offer premiums and bidding strategies in corporate takeovers. The discussion ranges from optimal auction bidding to the choice of deal payment form and premium effects of poison pills. The evidence describes the takeover process at a detailed level, from initial premiums to bid jumps, entry of rival bidders, and toehold strategies. Cross-sectional tests illuminate whether bidders properly adjust for winner's curse, whether target stock price runups force offer price markups, and whether auctions of bankrupt firms result in reflect fire-sale discounts. The evidence is suggestive of rational strategic bidding behavior in specific contexts.

246 citations


Proceedings ArticleDOI
01 Dec 2008
TL;DR: This algorithm is an extension to the parallel auction algorithm proposed by Bertsekas et al to the case where only local information is available and it is shown to always converge to an assignment that maximizes the total assignment benefit within a linear approximation of the optimal one.
Abstract: The assignment problem constitutes one of the fundamental problems in the context of linear programming. Besides its theoretical significance, its frequent appearance in the areas of distributed control and facility allocation, where the problems? size and the cost for global computation and information can be highly prohibitive, gives rise to the need for local solutions that dynamically assign distinct agents to distinct tasks, while maximizing the total assignment benefit. In this paper, we consider the linear assignment problem in the context of networked systems, where the main challenge is dealing with the lack of global information due to the limited communication capabilities of the agents. We address this challenge by means of a distributed auction algorithm, where the agents are able to bid for the task to which they wish to be assigned. The desired assignment relies on an appropriate selection of bids that determine the prices of the tasks and render them more or less attractive for the agents to bid for. Up to date pricing information, necessary for accurate bidding, can be obtained in a multi-hop fashion by means of local communication between adjacent agents. Our algorithm is an extension to the parallel auction algorithm proposed by Bertsekas et al to the case where only local information is available and it is shown to always converge to an assignment that maximizes the total assignment benefit within a linear approximation of the optimal one.

210 citations


Proceedings ArticleDOI
21 Apr 2008
TL;DR: With sniping and parameter tuning enabled, the budget-constrained bidding optimization problem for sponsored search auctions is considered, and the bidding algorithms can achieve a performance ratio above 90% against the optimum by the omniscient bidder.
Abstract: We consider the budget-constrained bidding optimization problem for sponsored search auctions, and model it as an online (multiple-choice) knapsack problem. We design both deterministic and randomized algorithms for the online (multiple-choice) knapsack problems achieving a provably optimal competitive ratio. This translates back to fully automatic bidding strategies maximizing either profit or revenue for the budget-constrained advertiser. Our bidding strategy for revenue maximization is oblivious (i.e., without knowledge) of other bidders' prices and/or click-through-rates for those positions. We evaluate our bidding algorithms using both synthetic data and real bidding data gathered manually, and also discuss a sniping heuristic that strictly improves bidding performance. With sniping and parameter tuning enabled, our bidding algorithms can achieve a performance ratio above 90% against the optimum by the omniscient bidder.

207 citations


Journal ArticleDOI
TL;DR: In this article, a data mining-based approach is proposed to forecast the value of the electricity price series, which is widely accepted as a nonlinear time series, and to accurately estimate the prediction interval of the electric price series.
Abstract: Electricity price forecasting is a difficult yet essential task for market participants in a deregulated electricity market. Rather than forecasting the value, market participants are sometimes more interested in forecasting the prediction interval of the electricity price. Forecasting the prediction interval is essential for estimating the uncertainty involved in the price and thus is highly useful for making generation bidding strategies and investment decisions. In this paper, a novel data mining-based approach is proposed to achieve two major objectives: 1) to accurately forecast the value of the electricity price series, which is widely accepted as a nonlinear time series; 2) to accurately estimate the prediction interval of the electricity price series. In the proposed approach, support vector machine (SVM) is employed to forecast the value of the price. To forecast the prediction interval, we construct a statistical model by introducing a heteroscedastic variance equation for the SVM. Maximum likelihood estimation (MLE) is used to estimate model parameters. Results from the case studies on real-world price data prove that the proposed method is highly effective compared with existing methods such as GARCH models.

182 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examine the consequences of vote buying, assuming this practice were allowed and free of stigma, and analyze the role of the parties' and voters' preferences in determining the winner and the payments to voters.
Abstract: We examine the consequences of vote buying, assuming this practice were allowed and free of stigma. Two parties compete in a binary election and may purchase votes in a sequential bidding game via up‐front binding payments and/or campaign promises (platforms) that are contingent on the outcome of the election. We analyze the role of the parties’ and voters’ preferences in determining the winner and the payments to voters.

174 citations


Journal ArticleDOI
TL;DR: This work investigates the effect of regret-related feedback information on bidding behavior in sealed-bid first-price auctions and finds strong support for both predictions.
Abstract: We investigate the effect of regret-related feedback information on bidding behavior in sealed-bid first-price auctions. Two types of regret are possible in this auction format. A winner of the auction may regret paying too much relative to the second highest bid, and a loser may regret missing an opportunity to win at a favorable price. In theory, under very general conditions, being sensitive to winning and paying too much should result in lower average bids, and being sensitive to missing opportunities to win at a favorable price should result in higher bids. For example, the U.S. Government's policy of revealing losing bids may cause regret-sensitive bidders to anticipate regret and bid conservatively, decreasing the government's revenue. We test these predictions in the laboratory and find strong support for both.

170 citations


Journal ArticleDOI
TL;DR: A novel bidding strategy that autonomous trading agents can use to participate in Continuous Double Auctions (CDAs) that is based on both short and long-term learning that allows such agents to adapt their bidding behaviour to be efficient in a wide variety of environments.

Journal ArticleDOI
David S. Evans1
TL;DR: In this paper, the authors describe the online advertising industry as populated by a number of multi-sided platforms that facilitate connecting advertisers to viewers, including search-based advertising platforms, which have interesting economic features that result from the combination of keyword bidding by advertisers and single-homing.
Abstract: Internet-based technologies are revolutionizing the stodgy $625 billion global advertising industry. There are a number of public policy issues to consider. Will a single ad platform emerge or will several remain viable? What are the consequences of alternative market structures for a web economy that is increasingly based on selling eyeballs to advertisers? This article describes the online advertising industry. The industry is populated by a number of multi-sided platforms that facilitate connecting advertisers to viewers. Search-based advertising platforms, the most developed of these, have interesting economic features that result from the combination of keyword bidding by advertisers and single-homing.

Book ChapterDOI
17 Dec 2008
TL;DR: A Markovian user model is studied that retains the core bidding dynamics of the GSP auction that make it useful for advertisers, and shows that the optimal assignment can be found efficiently (even in near-linear time).
Abstract: Sponsored search involves running an auction among advertisers who bid in order to have their ad shown next to search results for specific keywords. The most popular auction for sponsored search is the "Generalized Second Price" (GSP) auction where advertisers are assigned to slots in the decreasing order of their score , which is defined as the product of their bid and click-through rate. One of the main advantages of this simple ranking is that bidding strategy is intuitive: to move up to a more prominent slot on the results page, bid more. This makes it simple for advertisers to strategize. However this ranking only maximizes efficiency under the assumption that the probability of a user clicking on an ad is independent of the other ads shown on the page. We study a Markovian user model that does not make this assumption. Under this model, the most efficient assignment is no longer a simple ranking function as in GSP. We show that the optimal assignment can be found efficiently (even in near-linear time). As a result of the more sophisticated structure of the optimal assignment, bidding dynamics become more complex: indeed it is no longer clear that bidding more moves one higher on the page. Our main technical result is that despite the added complexity of the bidding dynamics, the optimal assignment has the property that ad position is still monotone in bid. Thus even in this richer user model, our mechanism retains the core bidding dynamics of the GSP auction that make it useful for advertisers.

Journal ArticleDOI
TL;DR: An analytical model for the effect of shared information on individual bidding behavior in a secret reserve price auction with a single buyer facing a single seller similar to eBay's Best Offer and some variants of NYOP is developed.
Abstract: The interactive nature of the Internet promotes collaborative business models (e.g., auctions) and facilitates information-sharing via social networks. In Internet auctions, an important design option for sellers is the setting of a secret reserve price that has to be met by a buyer's bid for a successful purchase. Bidders have strong incentives to learn more about the secret reserve price in these auctions, thereby relying on their own network of friends or digital networks of users with similar interests and information needs. Information-sharing and flow in digital networks, both person-to-person and via communities, can change bidding behavior and thus can have important implications for buyers and sellers in secret reserve price auctions. This paper uses a multiparadigm approach to analyze the impact of information diffusion in social networks on bidding behavior in secret reserve price auctions. We first develop an analytical model for the effect of shared information on individual bidding behavior ...

Journal ArticleDOI
TL;DR: In this article, the authors explore the consequences of neglecting nonsalient information when making such inferences and show that bidders herd into auctions with more existing bids, even if these are a signal of no longer available lower starting prices rather than of higher quality.
Abstract: People often observe others' decisions before deciding themselves. Using eBay data for DVD auctions we explore the consequences of neglecting nonsalient information when making such inferences. We show that bidders herd into auctions with more existing bids, even if these are a signal of no-longer-available lower starting prices rather than of higher quality. Bidders bidding a given dollar amount are less likely to win low starting price auctions, and pay more for them when they do win. Experienced bidders are less likely to bid on low starting price auctions. Remarkably, the seller side of the market is in equilibrium, because expected revenues are nearly identical for high and low starting prices.

Journal Article
TL;DR: Managers can minimize the potential for competitive arousal and the harm it can inflict by avoiding certain types of interaction and targeting the causes of a win-at-all-costs approach to decision making.
Abstract: In the heat of competition, executives can easily become obsessed with beating their rivals. This adrenaline-fueled emotional state, which the authors call competitive arousal, often leads to bad decisions. Managers can minimize the potential for competitive arousal and the harm it can inflict by avoiding certain types of interaction and targeting the causes of a win-at-all-costs approach to decision making. Through an examination of companies such as Boston Scientific and Paramount, and through research on auctions, the authors identified three principal drivers of competitive arousal: intense rivalry, especially in the form of one-on-one competitions; time pressure, found in auctions and other bidding situations, for example; and being in the spotlight--that is, working in the presence of an audience. Individually, these factors can seriously impair managerial decision making; together, their consequences can be dire, as evidenced by many high-profile business disasters. It's not possible to avoid destructive competitions and bidding wars completely. But managers can help prevent competitive arousal by anticipating potentially harmful competitive dynamics and then restructuring the deal-making process. They can also stop irrational competitive behavior from escalating by addressing the causes of competitive arousal. When rivalry is intense, for instance, managers can limit the roles of those who feel it most. They can reduce time pressure by extending or eliminating arbitrary deadlines. And they can deflect the spotlight by spreading the responsibility for critical competitive decisions among team members. Decision makers will be most successful when they focus on winning contests in which they have a real advantage--and take a step back from those in which winning exacts too high a cost.

Journal ArticleDOI
TL;DR: A web-based sub-contractor evaluation system called WEBSES is proposed by which the SCs can be evaluated based on a combined criterion to enable general contractors to select the most appropriate SCs for their relevant sub-works, speed up the selection process and gain time and cost savings during the bidding process.

Journal ArticleDOI
TL;DR: In this article, a dynamic forecasting system is proposed to predict the price of an ongoing online auction and update its prediction based on newly arriving information, which can account for unequal spacing of bids and changing dynamics of price and bidding throughout the auction.
Abstract: Online auctions have become increasingly popular in recent years, and as a consequence there is a growing body of empirical research on this topic. Most of that research treats data from online auctions as cross-sectional, and consequently ignores the changing dynamics that occur during an auction. In this article we take a different look at online auctions and propose to study an auction's price evolution and associated price dynamics. Specifically, we develop a dynamic forecasting system to predict the price of an ongoing auction. By dynamic, we mean that the model can predict the price of an auction “in progress” and can update its prediction based on newly arriving information. Forecasting price in online auctions is challenging because traditional forecasting methods cannot adequately account for two features of online auction data: (1) the unequal spacing of bids and (2) the changing dynamics of price and bidding throughout the auction. Our dynamic forecasting model accounts for these special featur...

Journal ArticleDOI
TL;DR: In this article, the economic properties of the economic demand-response (DR) program in the PJM electricity market in the United States using DR market data were analyzed, and the largest economic effect is wealth transfers from generators to non-price responsive loads.

Journal ArticleDOI
TL;DR: In this paper, the authors compare the value effects of large bank merger announcements in Europe and the US and find an inverse relationship between the level of investor protection prevalent in the target country and abnormal returns that bidders realize during the announcement period.
Abstract: Investor protection regimes have been shown to partly explain why the same type of corporate event may attract different investor reactions across countries. We compare the value effects of large bank merger announcements in Europe and the US and find an inverse relationship between the level of investor protection prevalent in the target country and abnormal returns that bidders realize during the announcement period. Accordingly, bidding banks realize higher returns when targeting low protection economies (most European economies) than bidders targeting institutions which operate under a high investor protection regime (the US). We argue that bidding bank shareholders need to be compensated for an increased risk of expropriation by insiders which they face in a low protection environment where takeover markets are illiquid and there are high private benefits of control.

Journal ArticleDOI
TL;DR: This paper proposes a methodology for optimising supply-chain configurations to cope with customer demand over a period of time, using a multi-agent system to model resource options available in a supply chain as well as dynamic changes taking place at the resources and their operational environment.

Patent
09 Dec 2008
TL;DR: In this article, a method and system for auctioning or sales of deliverable prepared food via the Internet permit customers to purchase or bid on prepared food items, with an estimated time of arrival (ETA).
Abstract: A method and system for auctioning or sales of deliverable prepared food via the Internet permit customers to purchase or bid on prepared food items. A food preparation and delivery portion of the system includes a delivery vehicle, which may have a mobile kitchen for the preparation of food items en-route. The location of the delivery vehicle is determined from a global positioning system (GPS) receiver in the vehicle or via another location-finding mechanism. Food items with an estimated time of arrival (ETA) is displayed on a web page that provides an interface for purchase or bidding. Bidding may be made for the actual food item purchase or for a scheduled delivery time. Items may be re-auctioned, causing the delivery of a food item to be transferred to another bidder. Audio and/or visual communication with an ordering point and/or delivery vehicle may be provided in the user interface.

Journal ArticleDOI
TL;DR: In this article, the relationship between spectrum policy (including license auctions) and efficiency in output markets has been investigated, and empirical estimates suggest that countries allocating greater bandwidth to licensed operators and achieving more competitive market structures realize demonstrable social welfare benefits.
Abstract: Economic analysis of spectrum allocation policies focuses on competitive bidding for wireless licenses Auctions generating high bids, as in Germany and the UK, are identified as successful, while those producing lower receipts, as in Switzerland and the Netherlands, are deemed fiascoes Yet, even full and costless extraction of license rents does not map directly to social welfare, because spectrum policies creating rents impose social costs For example, rules favoring monopoly market structure predictably increase license values, but reduce welfare This paper attempts to shift analytical focus to the relationship between spectrum policy (including license auctions) and efficiency in output markets In cross-country comparisons of performance metrics in mobile telephone service markets, empirical estimates suggest that countries allocating greater bandwidth to licensed operators and achieving more competitive market structures realize demonstrable social welfare benefits These gains generally dominate efficiencies associated with license sales Spectrum policies and rules intended to increase auction receipts (eg reserve prices and subsidies for weak bidders), should be evaluated in this light

Posted Content
TL;DR: This paper conducted a controlled field experiment on eBay and examined to what extent both social and competitive laboratory behavior is robust to institutionally complex real world markets with experienced traders, who selected themselves into these markets.
Abstract: We conducted a controlled field experiment on eBay and examined to what extent both social and competitive laboratory behavior is robust to institutionally complex real world markets with experienced traders, who selected themselves into these markets. EBay's natural trading system provides bridges between lab and field environment that can be exploited to explore differences in behavior in the two environments. We find that many sellers do not make use of their commitment power as predicted by standard theories of both selfish and social behavior. However, a concern for equity strongly affects outcomes and reputation building in bilateral bargaining, while buyer competition effectively masks this concern and robustly yields equilibrium outcomes. The dichotomy of behaviors mirrors observations in laboratory research. Furthermore, we find that behavioral patterns in the field experiment mirror fully naturally occurring trading patterns in the market.

Journal ArticleDOI
TL;DR: In this paper, the authors take advantage of bidding data from two auction designs to identify nonparametrically the bidders' utility function within a private value framework, which leads to a nonparametric estimator.
Abstract: Estimating bidders’ risk aversion in auctions is a challeging problem because of identification issues. This paper takes advantage of bidding data from two auction designs to identify nonparametrically the bidders’ utility function within a private value framework. In particular, ascending auction data allow us to recover the latent distribution of private values, while first-price sealed-bid auction data allow us to recover the bidders’ utility function. This leads to a nonparametric estimator. An application to the US Forest Service timber auctions is proposed. Estimated utility functions display concavity, which can be partly captured by constant relative risk aversion.

Journal ArticleDOI
TL;DR: In this article, a stochastic midterm risk-constrained hydrothermal scheduling algorithm in a generation company (GENCO) is presented, where the objective is to maximize payoffs and minimize financial risks when scheduling its midterm generation of thermal, cascaded hydro, and pumped storage units.
Abstract: This paper presents a stochastic midterm risk-constrained hydrothermal scheduling algorithm in a generation company (GENCO). The objective of a GENCO is to maximize payoffs and minimize financial risks when scheduling its midterm generation of thermal, cascaded hydro, and pumped-storage units. The proposed schedule will be used by the GENCO for bidding purposes to the ISO. The optimization model is based on stochastic price-based unit commitment. The proposed GENCO solution may be used to schedule midterm fuel and natural water inflow resources for a few months to a year. The proposed stochastic mixed-integer programming solution considers random market prices for energy and ancillary services, as well as the availability of natural water inflows and generators in Monte Carlo scenarios. Financial risks associated with uncertainties are considered by applying expected downside risks which are incorporated explicitly as constraints. Variable time-steps are adopted to avoid the exponential growth in solution time and memory requirements when considering midterm constraints. A single water-to-power conversion function is used instead of several curves for representing water head and discharge parameters. Piecewise linearized head-dependant water-to-power conversion functions are used for computational efficiency. Illustrative examples examine GENCOs' midterm generation schedules, risk levels, fuel and water usage, and hourly generation dispatches for bidding in energy and ancillary services markets. The paper shows that GENCOs could decrease their financial risks by adjusting expected payoffs.

Journal ArticleDOI
TL;DR: This paper proposes a distance between two realizations of a random process where for each realization only sparse and irregularly spaced measurements with additional measurement errors are available, and applies distance-based clustering methods to eBay online auction data.
Abstract: We propose a distance between two realizations of a random process where for each realization only sparse and irregularly spaced measurements with additional measurement errors are available. Such data occur commonly in longitudinal studies and online trading data. A distance measure then makes it possible to apply distance-based analysis such as classification, clustering and multidimensional scaling for irregularly sampled longitudinal data. Once a suitable distance measure for sparsely sampled longitudinal trajectories has been found, we apply distance-based clustering methods to eBay online auction data. We identify six distinct clusters of bidding patterns. Each of these bidding patterns is found to be associated with a specific chance to obtain the auctioned item at a reasonable price.

Journal ArticleDOI
TL;DR: This paper proposes a low-complexity auction framework to distribute spectrum in real-time among a large number of wireless users with dynamic traffic with a compact and highly expressive bidding format, and develops analytical bounds on algorithm performance and complexity to verify the efficiency.

Journal ArticleDOI
TL;DR: In this paper, the authors examined and classified more than 60 risk models for contractors that are published in journals and conducted exploratory interviews with five UK contractors and documentary analyses on how contractors price work generally and risk specifically to help in comparing the propositions from the literature to what contractors actually do.
Abstract: Formal and analytical models that contractors can use to assess and price project risk at the tender stage have proliferated in recent years. However, they are rarely used in practice. Introducing more models would, therefore, not necessarily help. A better understanding is needed of how contractors arrive at a bid price in practice, and how, and in what circumstances, risk apportionment actually influences pricing levels. More than 60 proposed risk models for contractors that are published in journals were examined and classified. Then exploratory interviews with five UK contractors and documentary analyses on how contractors price work generally and risk specifically were carried out to help in comparing the propositions from the literature to what contractors actually do. No comprehensive literature on the real bidding processes used in practice was found, and there is no evidence that pricing is systematic. Hence, systematic risk and pricing models for contractors may have no justifiable basis. Contra...

Journal ArticleDOI
TL;DR: In this paper, demand is categorized into two groups: one that highly values reliability and one that does not, and the two types are modeled separately and a new optimal bidding function is developed and tested based on this model.
Abstract: Problems such as price volatility have been observed in electric power markets. Demand-side participation is frequently offered as a potential solution by promising to increase market efficiency when hockey-stick-type offer curves are present. However, the individual end-consumer will surely value electricity differently, which makes demand-side participation difficult as a group and at a bus. In this paper demand is categorized into two groups: one that highly values reliability and one that does not. The two types are modeled separately and a new optimal bidding function is developed and tested based on this model.