Game theory

An established company has private information about its marginal cost; the potential entrant does not know exactly what that cost is but they do know it is either very low, low, or average with probabilities 0.1, 0.3, and 0.6 respectively. The established company chooses either a high price, a moderate price, or a competitive price (pH > pM > pC ) and is able to commit to that choice. The entrant can enter or not after observing the chosen price.

Carefully and clearly write down appropriate posterior beliefs for

(a) a separating strategy in which the price set is proportional to the marginal cost;

(b) a pooling strategy; and

(c) a semiseparating strategy in which low and very low cost firms choose a competitive price while average cost firms choose a moderate one

Sample Solution

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