Campaigners, advertisers and activists are increasingly turning to social recommendation mechanisms, provided by social media, for promoting their products, services, brands and even ideas. However, many times, such social network based campaigns perform poorly in practice because the intensity of the recommendations drastically reduces beyond a few hops from the source. A natural strategy for maintaining the intensity is to provide incentives. In this paper, we address the problem of minimizing the cost incurred by the campaigner for incentivizing a fraction of individuals in the social network, while ensuring that the campaign message reaches a given expected fraction of individuals. We also address the dual problem of maximizing the campaign penetration for a resource constrained campaigner. To help us understand and solve the above mentioned problems, we use percolation theory to formally state them as optimization problems. These problems are not amenable to traditional approaches because of a fixed point equation that needs to be solved numerically. However, we use results from reliability theory to establish some key properties of the fixed point, which in turn enables us to solve these problems using algorithms that are linearithmic in maximum node degree. Furthermore, we evaluate the efficacy of the analytical solution by performing simulations on real world networks.
The problem of computing the optimal referral payment mechanisms that maximize profit was studied in @cite_20 , by modelling the referral process as a network game. The authors in @cite_20 conclude that a combination of linear payment mechanism (linear in the number of referrals) and threshold payment mechanism (payment only when number of referral exceeds a threshold) approximates the optimal pricing scheme. In this paper, we focus on the set of nodes to be incentivized while assuming that a pricing scheme, which can be computed based on the results in @cite_20 , is provided by the campaigner. Similar problems involving the computation of referral rewards in real time, for maximizing the campaign spread, were studied using the theory of optimal control in @cite_13 @cite_21 @cite_14 @cite_16 @cite_24 .
@cite_14 @cite_21 @cite_24 @cite_16 @cite_13 @cite_20
2084685902 2077124610 1495768673 2136041258
We revisit the classic problem of fair division from a mechanism design perspective and provide an elegant truthful mechanism that yields surprisingly good approximation guarantees for the widely used solution of Proportional Fairness. This solution, which is closely related to Nash bargaining and the competitive equilibrium, is known to be not implementable in a truthful fashion, which has been its main drawback. To alleviate this issue, we propose a new mechanism, which we call the Partial Allocation mechanism, that discards a carefully chosen fraction of the allocated resources in order to incentivize the agents to be truthful in reporting their valuations. This mechanism introduces a way to implement interesting truthful outcomes in settings where monetary payments are not an option. For a multi-dimensional domain with an arbitrary number of agents and items, and for the very large class of homogeneous valuation functions, we prove that our mechanism provides every agent with at least a 1 e ≈ 0.368 fraction of her Proportionally Fair valuation. To the best of our knowledge, this is the first result that gives a constant factor approximation to every agent for the Proportionally Fair solution. To complement this result, we show that no truthful mechanism can guarantee more than 0.5 approximation, even for the restricted class of additive linear valuations. In addition to this, we uncover a connection between the Partial Allocation mechanism and VCG-based mechanism design. We also ask whether better approximation ratios are possible in more restricted settings. In particular, motivated by the massive privatization auction in the Czech republic in the early 90s we provide another mechanism for additive linear valuations that works really well when all the items are highly demanded. We study the classic mathematical economics problem of Bayesian optimal mechanism design where a principal aims to optimize expected revenue when allocating resources to self-interested agents with preferences drawn from a known distribution. In single parameter settings (i.e., where each agent's preference is given by a single private value for being served and zero for not being served) this problem is solved [20]. Unfortunately, these single parameter optimal mechanisms are impractical and rarely employed [1], and furthermore the underlying economic theory fails to generalize to the important, relevant, and unsolved multi-dimensional setting (i.e., where each agent's preference is given by multiple values for each of the multiple services available) [25]. In contrast to the theory of optimal mechanisms we develop a theory of sequential posted price mechanisms, where agents in sequence are offered take-it-or-leave-it prices. We prove that these mechanisms are approximately optimal in single-dimensional settings. These posted-price mechanisms avoid many of the properties of optimal mechanisms that make the latter impractical. Furthermore, these mechanisms generalize naturally to multi-dimensional settings where they give the first known approximations to the elusive optimal multi-dimensional mechanism design problem. In particular, we solve multi-dimensional multi-unit auction problems and generalizations to matroid feasibility constraints. The constant approximations we obtain range from 1.5 to 8. For all but one case, our posted price sequences can be computed in polynomial time. This work can be viewed as an extension and improvement of the single-agent algorithmic pricing work of [9] to the setting of multiple agents where the designer has combinatorial feasibility constraints on which agents can simultaneously obtain each service. In this paper, we introduce a novel approach for reducing the k-item n-bidder auction with additive valuation to k-item 1-bidder auctions. This approach, called the Best-Guess reduction, can be applied to address several central questions in optimal revenue auction theory such as the relative strength of simple versus complex mechanisms, the power of randomization, and Bayesian versus dominant-strategy implementations. First, when the items have independent valuation distributions, we present a deterministic mechanism called Deterministic Best-Guess that yields at least a constant fraction of the optimal revenue by any randomized mechanism. This also gives the first simple mechanism that achieves constant fraction optimal revenue for such multi-buyer multi-item auctions. Second, if all the nk valuation random variables are independent, the optimal revenue achievable in dominant strategy incentive compatibility (DSIC) is shown to be at least a constant fraction of that achievable in Bayesian incentive compatibility (BIC). Third, when all the nk values are identically distributed according to a common one-dimensional distribution F, the optimal revenue is shown to be expressible in the closed form Θ(k(r + ∫0mr(1 − F(x)n)dx)) where r = supx≥0 x(1 − F(x)n) and m = lk nr; this revenue is achievable by a simple mechanism called 2nd-Price Bundling. All our results apply to arbitrary distributions, regular or irregular. We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers who are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumer's usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolist's optimal pricing strategy may involve offering discounts to certain agents who have a central position in the underlying network. Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive a 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 consists of three components: (i) a nominal term that is independent of the network structure, (ii) a discount term proportional to the influence that this agent exerts over the rest of the social network (quantified by the agent's Bonacich centrality), and (iii) a markup term proportional to the influence that the network exerts on the agent. In the second part of the paper, we discuss the optimal strategy of a monopolist who 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. Third, we assume that the monopolist can offer the good in two prices, full and discounted, and we 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 who 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 who does not take into account the network effects when choosing her pricing policy to those of a monopolist who uses this information optimally.