Budget allocation in competitive search advertisements

This paper proposes a novel budget model based on differential game to deal with budget allocation in competitive search advertisements under a finite time horizon, with consideration of budget constraints. We extend the advertising response function with the dynamical advertising effort u and quality score q to fit search advertising scenarios. We also discuss Nash equilibriums of our model, and study some desirable properties of two kinds of equilibriums in the case with budget constraints: "budget-stable" open-loop Nash equilibrium (BS-OLNE) and "budget-unstable" open-loop Nash equilibrium (BUS-OLNE). We have evaluated our budget model and identified properties with computational experiments. Experimental results show that budget strategies with dynamical advertising elasticity are superior to those with fixed one and our findings on OLNEs are helpful for advertisers to make budget decisions.