# Budget Allocation Problem with Multiple Advertisers: A Game Theoretic View

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Takanori Maehara,
Akihiro Yabe,
Ken-ichi Kawarabayashi
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Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:428-437, 2015.

#### Abstract

In marketing planning, advertisers seek to maximize the number of customers by allocating given budgets to each media channel effectively. The budget allocation problem with a bipartite influence model captures this scenario; however, the model is problematic because it assumes there is only one advertiser in the market. In reality, there are many advertisers which are in conflict of advertisement; thus we must extend the model for such a case. By extending the budget allocation problem with a bipartite influence model, we propose a game-theoretic model problem that considers many advertisers. By simulating our model, we can analyze the behavior of a media channel market, e.g., we can estimate which media channels are allocated by an advertiser, and which customers are influenced by an advertiser. Our model has many attractive features. First, our model is a potential game; therefore, it has a pure Nash equilibrium. Second, any Nash equilibrium of our game has 2-optimal social utility, i.e., the price of anarchy is 2. Finally, the proposed model can be simulated very efficiently; thus it can be used to analyze large markets.

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