Many problem contexts give rise to competitive decision situations in which players must make repeated decisions along with or in response to competitors' decisions. Choice models used in transportation generally assume that trip makers make decisions independently. Auction-based electronic marketplaces for freight service procurement are an example of such environments, and they provide the motivating application context for the models presented in this paper. The specific focus is on the decisions of carriers as bidders for the loads tendered by shippers in spot market situations. The paper considers the player's choice of strategy of how much to bid in an auction-based marketplace with repeated auctions involving the same set of players. A dynamic strategy choice model structure is formulated, with alternative specifications corresponding to different levels of cognition capacity. The model is intended to describe how a player or agent in a noncooperative game with no perfect information and bounded rationality chooses a bidding strategy. The paper addresses econometric issues that arise in estimating such models given a time series of auction bids and outcomes, and it formulates error structures appropriate to the highly interactive, dynamic nature of competitive auction-based marketplaces. Estimation results are presented for data obtained from hypothetical experiments designed to illustrate the model structure and alternative specifications.