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Register a new userOptimal Pricing in Networks with Externalities
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Added by
Ozan Candogan
Publication date
2011
fields
Informatics Engineering
and research's language is
English
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We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers that are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumers usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolists optimal pricing strategy may involve offering discounts to certain agents, who have a central position in the underlying network. First, we consider a setting where the monopolist can offer individualized prices and derive an explicit characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that is proportional to her Bonacich centrality in the social network. In the second part of the paper, we discuss the optimal strategy of a monopolist that can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price. Thirdly, we assume that the monopolist can offer the good in two prices, full and discounted, and study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard, however we provide an explicit characterization of the set of agents that should be offered the discounted price. Next, we describe an approximation algorithm for finding the optimal set of agents. We show that if the profit is nonnegative under any feasible price allocation, the algorithm guarantees at least 88% of the optimal profit. Finally, we highlight the value of network information by comparing the profits of a monopolist that does not take into account the network effects when choosing her pricing policy to those of a monopolist that uses this information optimally.
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A decision-maker is deciding between an active action (e.g., purchase a house, invest certain stock) and a passive action. The payoff of the active action depends on the buyers private type and also an unknown state of nature. An information seller can design experiments to reveal information about the realized state to the decision-maker and would like to maximize profit from selling such information. We fully characterize, in closed-form, the revenue-optimal information selling mechanism for the seller. After eliciting the buyers type, the optimal mechanism charges the buyer an upfront payment and then simply reveals whether the realized state passed a certain threshold or not. The optimal mechanism features both price discrimination and information discrimination. The special buyer type who is a priori indifferent between the active and passive action benefits the most from participating in the mechanism.
Cooperative multihop communication can greatly increase network throughput, yet packet forwarding for other nodes involves opportunity and energy cost for relays. Thus one of the pre-requisite problems in the successful implementation of multihop transmission is how to foster cooperation among selfish nodes. Existing researches mainly adopt monetary stimulating. In this manuscript, we propose instead a simple and self-enforcing forwarding incentive scheme free of indirect monetary remunerating for asymmetric (uplink multihop, downlink single-hop) cellar network based on coalitional game theory, which comprises double compensation, namely, Inter- BEA, global stimulating policy allotting resources among relaying coalitions according to group size, and Intra-BEA, local compensating and allocating rule within coalitions. Firstly, given the global allotting policy, we introduce a fair allocation estimating approach which includes remunerating for relaying cost using Myerson value for partition function game, to enlighten the design of local allocating rules. Secondly, given the inter- and intra-BEA relay fostering approach, we check stability of coalition structures in terms of internal and external stability as well as inductive core. Theoretic analysis and numerical simulation show that our measure can provide communication opportunities for outer ring nodes and enlarge system coverage, while at the same time provide enough motivation with respect to resource allocation and energy saving for nodes in inner and middle ring to relay for own profits.
A patient seller aims to sell a good to an impatient buyer (i.e., one who discounts utility over time). The buyer will remain in the market for a period of time $T$, and her private value is drawn from a publicly known distribution. What is the revenue-optimal pricing-curve (sequence of (price, time) pairs) for the seller? Is randomization of help here? Is the revenue-optimal pricing-curve computable in polynomial time? We answer these questions in this paper. We give an efficient algorithm for computing the revenue-optimal pricing curve. We show that pricing curves, that post a price at each point of time and let the buyer pick her utility maximizing time to buy, are revenue-optimal among a much broader class of sequential lottery mechanisms: namely, mechanisms that allow the seller to post a menu of lotteries at each point of time cannot get any higher revenue than pricing curves. We also show that the even broader class of mechanisms that allow the menu of lotteries to be adaptively set, can earn strictly higher revenue than that of pricing curves, and the revenue gap can be as big as the support size of the buyers value distribution.
We consider the problem of posting prices for unit-demand buyers if all $n$ buyers have identically distributed valuations drawn from a distribution with monotone hazard rate. We show that even with multiple items asymptotically optimal welfare can be guaranteed. Our main results apply to the case that either a buyers value for different items are independent or that they are perfectly correlated. We give mechanisms using dynamic prices that obtain a $1 - Theta left( frac{1}{log n}right)$-fraction of the optimal social welfare in expectation. Furthermore, we devise mechanisms that only use static item prices and are $1 - Theta left( frac{logloglog n}{log n}right)$-competitive compared to the optimal social welfare. As we show, both guarantees are asymptotically optimal, even for a single item and exponential distributions.
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