Crowdfunding is quickly emerging as an alternative to traditional methods of funding new products. In a crowdfunding campaign, a seller solicits financial contributions from a crowd, usually in the form of pre-buying an unrealized product, and commits to producing the product if the total amount pledged is above a certain threshold. We provide a model of crowdfunding in which consumers arrive sequentially and make decisions about whether to pledge or not. Pledging is not costless, and hence consumers would prefer not to pledge if they think the campaign will not succeed. This can lead to cascades where a campaign fails to raise the required amount even though there are enough consumers who want the product. The paper introduces a novel stochastic process-anticipating random walksto analyze this problem. The analysis helps explain why some campaigns fail and some do not, and provides guidelines about how sellers should design their campaigns in order to maximize their chances of success.

Motivated by applications in online advertising, we consider a class of maximization problems where the objective is a function of the sequence of actions as well as the running duration of each action. For these problems, we introduce the concepts of sequence-submodularity and sequence-monotonicity which extend the notions of submodularity and monotonicity from functions defined over sets to functions defined over sequences. We establish that if the objective function is sequence-submodular and sequence-non-decreasing, then there exists a greedy algorithm that achieves 1 − 1/e of the optimal solution.We apply our algorithm and analysis to two applications in online advertising: online ad allocation and query rewriting. We first show that both problems can be formulated as maximizing non-decreasing sequence-submodular functions. We then apply our framework to these two problems, leading to simple greedy approaches with guaranteed performances. In particular, for online ad allocation problem the performance of our algorithm is 1 − 1/e, which matches the best known existing performance, and for query rewriting problem the performance of our algorithm is 1 − 1/e 1−1/e which improves upon the best known existing performance in the literature.

Crowdfunding is quickly emerging as an alternative to traditional methods of funding new products. In a crowdfunding campaign, a seller solicits financial contributions from a crowd, usually in the form of pre-buying an unrealized product, and commits to producing the product if the total amount pledged is above a certain threshold. We provide a model of crowdfunding in which consumers arrive sequentially and make decisions about whether to pledge or not. Pledging is not costless, and hence consumers would prefer not to pledge if they think the campaign will not succeed. This can lead to cascades where a campaign fails to raise the required amount even though there are enough consumers who want the product. The paper introduces a novel stochastic process-anticipating random walksto analyze this problem. The analysis helps explain why some campaigns fail and some do not, and provides guidelines about how sellers should design their campaigns in order to maximize their chances of success.

Two sided matching markets are among the most studied models in market design. There is a vast literature on the structure of competitive equilibria in these markets, yet most of it is focused on quasilinear settings. General (non-quasilinear) utilities can, for instance, model smooth budget constraints as a special case. Due to the difficulty of dealing with arbitrary non-quasilinear utilities, most of the existing work on non-quasilinear utilities is limited to the special case of hard budget constraints in which the utility of each agent is quasilinear as long as her payment is within her budget limit and is negative infinity otherwise. Most of the work on competitive equilibria with hard budget constraints rely on some form of ascending auction. For general non-quasilinear utilities, such ascending auctions may not even converge in finite time. As such, almost all of the existing work on general non-quasilinear utilities have resorted to non-constructive proofs based on fixed point theorems or discretization. We present the first direct characterization of competitive equilibria in such markets. Our approach is constructive and solely based on induction. Our characterization reveals striking similarities between the payments at the lowest competitive equilibrium for general utilities and VCG payments for quasilinear utilities. We also show that lowest competitive equilibrium is group strategyproof for the agents on one side of the market (e.g., for buyers).

Motivated by applications in online advertising, we consider a class of maximization problems where the objective is a function of the sequence of actions and the running duration of each action. For these problems, we introduce the concepts of sequence-submodularity and sequence-monotonicity, which extend the notions of submodularity and monotonicity from functions defined over sets to functions defined over sequences. We establish that if the objective function is sequence-submodular and sequence-nondecreasing, then there exists a greedy algorithm that achieves [Formula: see text] of the optimal solution. We apply our algorithm and analysis to two applications in online advertising: online ad allocation and query rewriting. We first show that both problems can be formulated as maximizing nondecreasing sequence-submodular functions. We then apply our framework to these two problems, leading to simple greedy approaches with guaranteed performances. In particular, for the online ad allocation problem, the performance of our algorithm is [Formula: see text], which matches the best known existing performance, and for the query rewriting problem, the performance of our algorithm is [Formula: see text], which improves on the best known existing performance in the literature. This paper was accepted by Chung Piaw Teo, optimization.