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This paper tries to find out a necessary and sufficient condition for the existence of a symmetric and increasing equilibrium bidding strategy for buyers in a standard auction. The paper considers a standard auction with one seller (whose valuation of the object is zero) and shows that an increasing bidding strategy constitutes a symmetric Bayesian Nash equilibrium if and only if the bidding strategy, derived from the first order condition of expected payoff maximization, is increasing in valuations. We also provide two examples to illustrate our results.