Allen and Gale on risk-taking and competition in banking

Using an elegant simple model, Allen and Gale [Comparing Financial Systems, MIT Press, 2001] obtain a result with significant policy implications: portfolio risk of banks increases as competition in banking, measured by the number of banks, increases. That result is, however, lacking in robustness. If banks play a game not all that different from that assumed by Allen and Gale, then, we show, a markedly different result obtains: risk-taking by banks is independent of the number of banks.