Optimal Bundle Pricing with Monotonicity Constraint

We consider the problem to price (digital) items in order to maximize the revenue obtainable from a set of bidders. We suggest a natural monotonicity constraint on bundle prices, show that the problem remains NP-hard, and we derive a PTAS. We also discuss a special case, the highway pricing problem.operations research and management science;

Multi-dimensional Virtual Values and Second-degree Price Discrimination

We consider a multi-dimensional screening problem of selling a product with multiple quality levels and design virtual value functions to derive conditions that imply optimality of only selling highest quality. A challenge of designing virtual values for multi-dimensional agents is that a mechanism that pointwise optimizes virtual values resulting from a general application of integration by parts is not incentive compatible, and no general methodology is known for selecting the right paths for integration by parts. We resolve this issue by first uniquely solving for paths that satisfy certain necessary conditions that the pointwise optimality of the mechanism imposes on virtual values, and then identifying distributions that ensure the resulting virtual surplus is indeed pointwise optimized by the mechanism. Our method of solving for virtual values is general, and as a second application we use it to derive conditions of optimality for selling only the grand bundle of items to an agent with additive preferences

Offloading in Software Defined Network at Edge with Information Asymmetry: A Contract Theoretical Approach

The proliferation of highly capable mobile devices such as smartphones and tablets has significantly increased the demand for wireless access. Software defined network (SDN) at edge is viewed as one promising technology to simplify the traffic offloading process for current wireless networks. In this paper, we investigate the incentive problem in SDN-at-edge of how to motivate a third party access points (APs) such as WiFi and smallcells to offload traffic for the central base stations (BSs). The APs will only admit the traffic from the BS under the precondition that their own traffic demand is satisfied. Under the information asymmetry that the APs know more about own traffic demands, the BS needs to distribute the payment in accordance with the APs' idle capacity to maintain a compatible incentive. First, we apply a contract-theoretic approach to model and analyze the service trading between the BS and APs. Furthermore, other two incentive mechanisms: optimal discrimination contract and linear pricing contract are introduced to serve as the comparisons of the anti adverse selection contract. Finally, the simulation results show that the contract can effectively incentivize APs' participation and offload the cellular network traffic. Furthermore, the anti adverse selection contract achieves the optimal outcome under the information asymmetry scenario.Comment: 10 pages, 9 figure

Optimal Bundle Pricing for Homogeneous Items

We consider a revenue maximization problem where we are selling a set of m items, each of which available in a certain quantity (possibly unlimited) to a set of n bidders. Bidders are single minded, that is, each bidder requests exactly one subset, or bundle of items. Each bidder has a valuation for the requested bundle that we assume to be known to the seller. The task is to find an envy-free pricing such as to maximize the revenue of the seller. We derive several complexity results and algorithms for several variants of this pricing problem. In fact, the settings that we consider address problems where the different items are `homogeneous'' in some sense. First, we introduce the notion of affne price functions that can be used to model situations much more general than the usual combinatorial pricing model that is mostly addressed in the literature. We derive fixed-parameter polynomial time algorithms as well as inapproximability results. Second, we consider the special case of combinatorial pricing, and introduce a monotonicity constraint that can also be seen as `global'' envy-freeness condition. We show that the problem remains strongly NP-hard, and we derive a PTAS - thus breaking the inapproximability barrier known for the general case. As a special case, we finally address the notorious highway pricing problem under the global envy-freeness condition.operations research and management science;