While page views are often sold instantly through real-time auctions when users visit websites, they can also be sold in advance via guaranteed contracts. In this paper, we present a dynamic programming model to study how an online publisher should optimally allocate and price page views between guaranteed and spot markets. The problem is challenging because the allocation and pricing of guaranteed contracts affect advertisers' purchase between the two markets, and the terminal value of the model is endogenously determined by the updated dual force of supply and demand in auctions. We take the advertisers' purchasing behaviour into consideration, i.e., risk aversion and stochastic demand arrivals, and present a scalable and efficient algorithm for the optimal solution. The model is also empirically validated with a commercial dataset. The experimental results show that selling page views via both guaranteed contracts and auctions can increase the publisher's expected total revenue, and the optimal pricing and allocation strategies are robust to different market and advertiser types.
Existing literature has also studied selling products or services via both auctions and posted prices. For example, @cite_2 discussed a problem of two channels selling, where the products can be sold through either an auction or an alternative channel with a posted price. They considered two scenarios of this dual-channel optimisation problem: in the first scenario, the posted price is an external channel run by another company; in the second scenario, the seller manages both auction and posted price channels. The second scenario is similar to our model setting. However, their discussion is mainly about the static posted price and they assume that the original values are uniformly distributed and there is no penalty cost. @cite_14 studied a hybrid model that unifies both future and spot markets for dynamic spectrum access, in which buyers can purchase under-utilized licensed spectrum either through predefined contracts or through spot transactions with a VCG-like auction model. Their work is similar to ours, however, the seller does not optimise the contract price dynamically.
@cite_14 @cite_2
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Dynamic spectrum access is a new paradigm of secondary spectrum utilization and sharing. It allows unlicensed secondary users (SUs) to exploit the opportunistically underutilized licensed spectrum. Market mechanism is a widely used promising means to regulate the consuming behaviours of users and, hence, achieve the efficient allocation and consumption of limited resources. In this paper, we propose and study a hybrid secondary spectrum market consisting of both the futures market and the spot market, in which SUs (buyers) purchase underutilized licensed spectrum from a spectrum regulator (SR), either through predefined contracts via the futures market, or through spot transactions via the spot market. We focus on the optimal spectrum allocation among SUs in an exogenous hybrid market that maximizes the secondary spectrum utilization efficiency. The problem is challenging because of the stochasticity and asymmetry of network information. To solve this problem, we first derive an off-line optimal allocatio... We analyze a revenue management problem in which a seller facing a Poisson arrival stream of consumers operates an online multiunit auction. Consumers can get the product from an alternative list price channel. We consider two variants of this problem: In the first variant, the list price is an external channel run by another firm. In the second one, the seller manages both the auction and the list price channels. Each consumer, trying to maximize his own surplus, must decide either to buy at the posted price and get the item at no risk, or to join the auction and wait until its end, when the winners are revealed and the auction price is disclosed. Our approach consists of two parts. First, we study structural properties of the problem, and show that the equilibrium strategy for both versions of this game is of the threshold type, meaning that a consumer will join the auction only if his arrival time is above a function of his own valuation. This consumer's strategy can be computed using an iterative algorithm in a function space, provably convergent under some conditions. Unfortunately, this procedure is computationally intensive. Second, and to overcome this limitation, we formulate an asymptotic version of the problem, in which the demand rate and the initial number of units grow proportionally large. We obtain a simple closed-form expression for the equilibrium strategy in this regime, which is then used as an approximate solution to the original problem. Numerical computations show that this heuristic is very accurate. The asymptotic solution culminates in simple and precise recipes of how bidders should behave, as well as how the seller should structure the auction, and price the product in the dual-channel case.