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Dynamic Budget Allocation in Competitive Search Advertising

Search advertising marketplace is highly competitive in nature. As such, advertisers have to consider their competitors' responses when making advertising decisions, which concern both bid determination in individual keyword auction instances, and budget allocation over time at the aggregate market level. Although bidding decisions have been extensively treated in competitive auction settings in the literature, competitive budgeting models are yet to be developed. Applying the differential game framework, we propose a dynamic budget allocation model in a duopolistic competitive setting. We first examine the steady-state Nash equilibrium policies for the advertisers, and then investigate the optimal paths of open-loop Nash equilibrium. In addition, we provide an algorithm to compute the optimal path of budget policies. Computational experiments were conducted to derive additional managerial insights. One important finding of this study is that the effects of two advertising factors, quality score and potential market revenue, on the steady-state budget levels are non-monotonic. This finding to some extent challenges the commonly-held view that higher quality scores lead to lower optimal advertising expenditures. Another interesting finding suggests that advertisers should set a budget cap even in a competitive environment to avoid the potential risk of over-spending in sponsored search advertising.