Bid distributions of competing agents in simple models of auctions

Models of auctions or tendering processes are introduced. In every round of bidding the players select their bid from a probability distribution and whenever a bid is unsuccessful, it is discarded and replaced. For simple models, the probability distributions evolve to a stationary power law with the exponent dependent only on the number of players. For most situations, the system converges towards a state where all players are identical. A number of variations of this model are introduced and the application of these models to the dynamics of market makers is discussed. The effect of price uncertainty on bid distributions is presented. An underlying market structure generates heterogenous agents which do not have power law bid distribution in general.