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First-price sealed-bid auctions have been modeled using a utility function that takes into account bidders' regret in case of winning or losing the auctioned item. However, that modeling does not consider bidders' wealth which is an important determinant of bidders' behavior in these auctions. In this paper, we apply an adversarial risk analysis approach for these auctions and find solutions using non-strategic play and level-k thinking solution concepts assuming n bidders. We define new regret parameters and a modified utility function to incorporate the effect of bidders' wealth on their bidding behavior. In our modeling, we assume that the auctioned item is a normal item and has a reserve price. We give numerical examples to illustrate our methodology for each solution concept. [ABSTRACT FROM AUTHOR]

A method to approximate Bayesian posterior by evaluating it on a low discrepancy sequence (LDS) point set has recently been proposed. However, this method does not focus on finding the posterior marginals. Finding posterior marginals when the posterior approximation is obtained using LDS is not straightforward, and as yet, there is no method to approximate one dimensional marginals using an LDS. We propose an approximation method for this problem. This method is based on an s-dimensional integration rule together with fitting a polynomial smoothing function. We state and prove results showing conditions under which this polynomial smoothing function will converge to the true one-dimensional function. We also demonstrate the computational efficiency of the new approach compared to a grid based approach. [ABSTRACT FROM AUTHOR]