On Joint Distribution of Bids in Some k-th Price Auction Model

In the era of increasingly widespread use of electronic communication tools, constant growth of e-commerce turnover is hardly surprising. One of its mechanisms are online auctions whose turnover, on a global scale, is enormous. Consequently, there is a need for theoretical research to facilitate effective modeling of online auctions. This paper proposes a stochastic model of the value of subsequent actual bids appearing in the course of a dynamic internet k-th price auction. This model was naturally defined by conditional probability distributions. On this basis, it was possible to determine theoretical, unconditional joint probability distributions, as well as univariate marginal distributions of successive bids appearing in the course of the auction type under consideration. The presented approach is a novelty comparing to bid value models that appear in the literature