A Market Share Game of Strategic Behaviour

Within a Cournot duopoly game the total market supply equation is [n/n+1] market share. Individual firm output may also be expressed as ½ x [1 - rival output]. The market share game where the market is fixed at 100% is an ideal represenatation of a zero sum game. As one firm gains, the rival firm loses that share of the market. Consider the following pay-off for rival cigarette producers.

Firm B’s strategy are filter tip or unfiltered. Allow each firm to know the strategy of the rival firm, but firm B plays first. There is 50:50 probability from A’s perspective of firm B adopting either strategy, hence we could apply the old guy rule of equal probability.

If A followed this rule and produced Regular, and if B produced filter cigarettes, A’s market share could fall to 10%. The regret matrix for firm B has the payoffs [10, 0, 0, 20], which suggests the minimax strategy of producing filter cigarettes. For firm A, a maximin strategy is to produce King Size brands, with a market share of 20%, if B plays minimax. This represents the best that firm A can do, given B’s minimax strategy. However, if we adopt an old guy rule of thumb which is to apply the strategy which guarantees a mean market share, M*

(a•M1)+((1–a)• M2)=M*

(a = 0.51)

in our example the certainty equivalent market share would be a 45% share.