This essay theoretically investigates symmetric types of auctions and provides simulation for the different types of statistical distributions that bidders follow in order to determine the maximum bid, Expected revenue for the auctioneer, Expected payment by bidders, Expected utility of the bidders, probability that item is unallocated. In addition, the subject of interest of this paper are three types of auctions: FPA (first price auction, Dutch type, SPA (Second price auction, English

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... Vickrey auction), APA (all-pay auctions) SYMMETRIC AUCTIONS: FINDING NUMERICAL SOLUTIONS BY USING AUCTION SOLVER ∂ζ 32) i.e. , -----= c, where, c is constant. ∂ρ 33) This strategy for value which the player could bid immediately applies only for the beginning of the auction, or in any time between the beginning and the end of the auction.