Cooperative Game Theoretic Bid Optimizer for Sponsored Search Auctions

In this paper, we propose a bid optimizer for sponsored keyword search auctions which leads to better retention of advertisers by yielding attractive utilities to the advertisers without decreasing the revenue to the search engine. The bid optimizer is positioned as a key value added tool the search engine provides to the advertisers. The proposed bid optimizer algorithm transforms the reported values of the advertisers for a keyword into a correlated bid profile using many ideas from cooperative game theory. The algorithm is based on a characteristic form game involving the search engine and the advertisers. Ideas from Nash bargaining theory are used in formulating the characteristic form game to provide for a fair share of surplus among the players involved. The algorithm then computes the nucleolus of the characteristic form game since we find that the nucleolus is an apt way of allocating the gains of cooperation among the search engine and the advertisers. The algorithm next transforms the nucleolus into a correlated bid profile using a linear programming formulation. This bid profile is input to a standard generalized second price mechanism (GSP) for determining the allocation of sponsored slots and the prices to be be paid by the winners. The correlated bid profile that we determine is a locally envyfree equilibrium and also a correlated equilibrium of the underlying game. Through detailed simulation experiments, we show that the proposed bid optimizer retains more customers than a plain GSP mechanism and also yields better long-run utilities to the search engine and the advertisers. Keywords-Bid Optimizer, Sponsored Search, Cooperative Game Theory, Nash bargaining, Nucleolus.