Previous studies have found underestimation of risk, or overconfidence, to be pervasive. In this paper, we model overconfidence as a reduction in perceived variance. We generalize the analysis of Sandmo and examine the effects of competition on firms displaying overconfidence. Cases for both competitive equilibrium and imperfect competition are investigated. We show that overconfidence may strictly dominate rationality in a competitive market by leading risk averse producers to invest greater amounts and produce more. This leads to a higher average profit, and greater variance of profits, leaving the producer a greater probability of surviving competitive pressures. Despite the greater variance of profits, if enough producers underestimate their risk, they should collectively drive more rational decision makers from the market. Our results suggest that overconfidence may be as important a determinant of market behavior as diminishing marginal utility of wealth.