State ownership, credit risk and bank competition: a mixed oligopoly approach

Recent events have led many governments to buy equity in banks leading to a situation of mixed oligopoly in banking markets. We model such a case where a partially state-owned bank competes with a private bank in collecting deposits. The government is purely a welfare maximiser while the private bank maximises profits. Both banks face risks in the loan market. We show that if the risk of default is sufficiently high and there is limited liability, then the state-owned bank tries to mitigate depositors' losses by mobilising less deposit leading to contraction of aggregate deposit. This contradicts the standard mixed oligopoly results in the literature.