Resource competition problems are often modeled using Colonel Blotto games, where players take simultaneous actions. However, many real-world scenarios involve sequential decision-making rather than simultaneous moves. To model these dynamics, we represent the Lottery Colonel Blotto game as a Stackelberg game, in which one player, the leader, commits to a strategy first, and the other player, the follower, responds. We derive the Stackelberg equilibrium for this game, formulating the leader's strategy as a bi-level optimization problem. To solve this, we develop a constructive method based on iterative game reductions, which allows us to efficiently compute the leader’s optimal commitment strategy in polynomial time. Additionally, we identify the conditions under which the Stackelberg equilibrium coincides with the Nash equilibrium. Specifically, this occurs when the budget ratio between the leader and the follower equals a certain threshold, which we can calculate in closed form. In some instances, we observe that when the leader’s budget exceeds this threshold, both players achieve higher utilities in the Stackelberg equilibrium compared to the Nash equilibrium. Lastly, we show that, in the best case, the leader can achieve an infinite utility improvement by making an optimal first move compared to the Nash equilibrium.

Online advertising has been one of the most important sources for industry's growth, where the demand-side platforms (DSP) play an important role via bidding to the ad exchanges on behalf of their advertiser clients. Since more and more ad exchanges have shifted from second to first price auctions, it is challenging for DSPs to adjust bidding strategy in the volatile environment. Recent studies on bid shading in first-price auctions may have limited performance due to relatively strong hypotheses about winning probability distribution. Moreover, these studies do not consider the incentive of advertiser clients, which can be crucial for a reliable advertising platform. In this work, we consider both the optimization of bid shading technique and the design of internal auction which is ex-post incentive compatible (IC) for the management of a DSP. Firstly, we prove that the joint design of bid shading and ex-post IC auction can be reduced to choosing one monotone bid function for each advertiser without loss of optimality. Then we propose a parameterized neural network to implement the monotone bid functions. With well-designed surrogate loss, the objective can be optimized in an end-to-end manner. Finally, our experimental results demonstrate the effectiveness and superiority of our algorithm.

Online advertising has become a dominant source of revenue of the Internet. In classic auction theory, only the auctioneer (i.e., the platform) and buyers (i.e., the advertisers) are involved, while the advertising audiences are ignored. For ecommerce advertising, however, the platform can provide coupons for the advertising audiences and nudge them into purchasing more products at lower prices (e.g., 2 dollars off the regular price). Such promotions can lead to an increase in amount and value of purchases. In this paper, we jointly design the coupon value computation, slot allocation, and payment of online advertising in an auto-bidding world. Firstly, we propose the auction mechanism, named CFA-auction (i.e., Coupon-For-the-Audiences-auction), which takes advertising audiences into account in the auction design. We prove the existence of pacing equilibrium, and show that CFA-auction satisfies the IC (incentive compatibility), IR (individual rationality) constraints. Then, we study the optimality of CFA-auction, and prove it can maintain an approximation of the optimal. Finally, experimental evaluation results on both offline dataset as well as online A/B test demonstrate the effectiveness of CFA-auction.

We consider a variant of the standard Bayesian mechanism, where players evaluate their outcomes and constraints in an ex-ante manner. Such a model captures a major form of modern online advertising where an advertiser is concerned with her/his expected utility over a time period and her/his type may change over time. We are interested in the incentive compatibility (IC) problem of such Bayesian mechanism. Under very mild conditions on the mechanism environments, we give a full characterization of IC via the taxation principle and show, perhaps surprisingly, that such IC mechanisms are fully characterized by the so-called auto-bidding mechanisms, which are pervasively fielded in the online advertising industry.