BIDDING WITH A BUDGET CONSTRAINT (AUCTIONS, NON-COOPERATIVE GAMES, UNCERTAINTY, PRICING, PURE STRATEGIES)

The bidding behavior of players in a perfectly divisible good auction is examined under the assumption that the players are constrained by their capital endowments. The purpose of this paper is to derive and compare the optimal bidding behavior under the rules of the discriminatory price and the competitive price auctioning procedures given this constraint.Because of the possibility of a partial payoff to the low bidder, the optimal price bidding strategy for the discriminatory price auction is everywhere lower than that for the unconstrained first price auction given that the bidders are effectively constrained. When the players are not constrained the two functions are identical. Similarly, the optimal price bidding strategy in the competitive price auction is everywhere lower than that for the unconstrained second price auction but converging to that strategy as the budget increases.From a comparison of the optimal constrained price bidding strategies derived for the discriminatory price and the competitive price auctions we conclude that the mean and variance of the bids are greater under the competitive price procedure. It is also shown that the expected revenue to the seller is greater under the discriminatory price method.The model developed in this paper is applied to the Treasury Auctions and corporate Dutch auctions. From the results of the model it is concluded that the use of the discriminatory price procedure by the Treasury is consistent with expected revenue maximization. The use of the fixed price method and even the Dutch auction in corporate self tender offers is concluded to be inconsistent with cost minimization.In order to address this question the homogeneous rectangular game introduced by Vickrey is generalized by assuming the good to be perfectly divisible and by assuming the bidders to be constrained by their budgets. A Nash equilibrium analysis is employed to determine the optimal bidding strategies for the participants.