The Structure of Equilibria in Market Share Attraction Models

A market share attraction model of competitive effort allocation by two firms is formulated as a constant sum, two-person game. The dependence of optimal competitive effort allocations on factors such as gross profit margins, relative effectiveness of effort, and attraction elasticity of effort is studied. Two versions of the model are developed. In the first version, effort budgets of both competitors are exogenously fixed. In the second, the competitors each choose both budget levels and allocations. In each version of the model, an important function of the parameters, called the competitive advantage ratio, indicates when it is optimal to either increase or decrease effort allocated in a market in response to changes in various measures of effectiveness. Implications of differences in the cost associated with each competitor's budget on equilibrium allocations are derived.