Affiliated Values Research Articles

Auctions in which losers set the price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the kth price auction generates higher revenue than the second-price auction, for all k > 2 . If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the ( t + 1 )st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the kth price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.

Sequential vs. single-round uniform-price auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k 1 objects are sold in the first round and k 2 in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces the first-round price. Total revenue is greater in a single-round, uniform auction for k = k 1 + k 2 objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify a positive informational effect on the second-round price. Total expected revenue in a sequential uniform auction with winning-bids announcement may be greater or smaller than in a single-round uniform auction, depending on the model's parameters.

Takeover auctions with actively participating targets

This paper provides an analysis of takeover auctions in which target firms actively participate by changing their reserve prices. It considers a takeover auction as an affiliated value English auction with flexible reserve price and discusses how the degree of value affiliation affects the bidding strategies and the degree of competition in takeover auctions. It makes comparative analysis of three different designs of English auctions and shows that a takeover auction is dominated by one of the English auctions with fixed reserve price.

Auctions in Which Losers Set the Price

We study auctions of a single asset among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers' bids. In particular, we show that the k-th price auction generates higher revenue than the second-price auction, for all k > 2. If rationing is allowed, with shares of the asset rationed among the t highest bidders, then the (t + 1)-st price auction yields the lowest revenue among all auctions with rationing in which only the winners pay and the unit price only depends on the losers' bids. Finally, we compute bidding functions and revenue of the k-th price auction, with and without rationing, for an illustrative example much used in the experimental literature to study first-price, second-price and English auctions.

Equilibrium in the Two Player, k-Double Auction with Affiliated Private Values

We present sufficient conditions for the existence of an increasing equilibrium in the two player k-double auction with affiliated private values. In the case k ∈ {0, 1} there exists a unique equilibrium in non-dominated strategies. Applying this equilibrium, we provide a detailed example illustrating how dependence level affects strategic bidding. In the case k ∈ (0, 1) we prove existence of a continuum of strictly increasing equilibria, and illustrate them using an example. Furthermore, we show that equilibria in the case of independent private values are pointwise limits of equilibria with strictly affiliated private values.

Implementing the efficient auction: initial results from the lab

The efficient auction is designed to induce truthful bidding for bidders with affiliated values. Herein we implement the auction in the lab, and observe that inexperienced people can bid systematically in this more complex environment, albeit yielding a flatter bid function than the truthful.

Implementing the efficient auction: initial results from the lab

The efficient auction is designed to induce truthful bidding for bidders with affiliated values. Herein we implement the auction in the lab, and observe inexperienced people can bid systematically in this more complex environment, albeit yielding a flatter bid function than the truthful one.

The symmetric solutions of affiliated value model

In a symmetric affiliated value model, this paper analyses High-Technology industrial firms’ competitive strategy in research and development. (R&D). We obtain the symmetric Bayesian Nash Equilibrium functions with or without government’s prize: b1(x)=v(x,)Fn-1\( - \int_0^X {F_{n - 1} } (y|y)dv(y,y),b_2 (x) = \int_0^X {[v(y,y) + v_0 } ]dF_{n - 1} \)(y∣y), and b3(x)=\(\int_0^x {v(y,y)\frac{{f_{n - 1} (y|y)}}{{1 - F_{n - 1} (y|y)}}} dy\). We find the firm’s investment level will increase in prize, only when the constant prize V0≥v(y,y)\(\frac{{f_{n - 1} (y|y)}}{{1 - F_{n - 1} (y|y)}}\), does the firm invest more aggressively with constant prize than with variable prize.

Sequential vs. Single-Round Uniform-Price Auctions

We study sequential and single-round uniform-price auctions with affiliated values. We derive symmetric equilibrium for the auction in which k1 objects are sold in the first round and k2 in the second round, with and without revelation of the first-round winning bids. We demonstrate that auctioning objects in sequence generates a lowballing effect that reduces first-round revenue. Thus, revenue is greater in a single-round, uniform auction for k = k1 + k2 objects than in a sequential uniform auction with no bid announcement. When the first-round winning bids are announced, we also identify two informational effects: a positive effect on second-round price and an ambiguous effect on first-round price. The expected first-round price can be greater or smaller than with no bid announcement, and greater or smaller than the expected price in a single-round uniform auction. As a result, total expected revenue in a sequential uniform auction with winning-bids announcement can be greater or smaller than in a single-round uniform auction.

Equilibrium of Affiliated Value Second Price Auctions with Financially Constrained Bidders: The Two-Bidder Case

We study affiliated value second price auctions with two financially constrained bidders. We prove the existence of a symmetric equilibrium under quite general conditions. Comparative static results are provided. Journal of Economic Literature Classification Number: D44.

Auctions combined with ex post taxation—expected revenue when three parties want a piece of the cake

In order to exploit their natural resources efficiently, states are normally obliged to rely on private mining companies (lessees), which in turn must rely on e.g. hired labour and different suppliers of equipment. This third party will try to exploit any negotiating power that might arise when the right to exploit the resource has been allocated to the lessee. If this succeeds, the size of the rent available to the resource owner and the lessee will be reduced. This paper focusses on rent sharing between the state, the lessee and labour under various combinations of ex ante and ex post rent taxation. In the paper it is shown that in a setting with affiliated values, cash bonus bidding combined with a royalty results in a double dividend: The state’s share of the pie increases and the wage pressure decreases. This result is of particular relevance to nations where the extractive sector represents a relatively large share of the economy.

First?price auctions when the ranking of valuations is common knowledge

We consider a first–price auction when the ranking of bidders' private valuations is common knowledge among bidders. This new informational framework is motivated by several applications, from procurement to privatization. It induces a particular asymmetric auction model with affiliated private values that has several interesting properties but raises serious technical complications. We prove existence and uniqueness of equilibrium in pure strategies and show that the seller's reven generally higher in a first–price than in second–price and English auctions, in contrast to the ranking in the affiliated values model by Milgrom and Weber. This also implies that in first–price auctions, providing information concerning the ranking of valuations among bidders tends to increase the seller's expected revenue.

Strategic Jump Bidding in English Auctions

This paper solves for equilibria of sequential bid (or English) auctions with affiliated values when jump bidding strategies may be employed to intimidate one’s opponents. In these equilibria, jump bids serve as correlating devices which select asymmetric bidding functions to be played subsequently. Each possibility of jump bidding provides a Pareto improvement for the bidders from the symmetric equilibrium of a sealed bid, secondprice auction. The expanded set of equilibria can approximate either first or second-price outcomes and produce exactly the set of expected prices between those two bounds. These results contrast with standard conclusions that equate English and second-price auctions.

Single Crossing Properties And The Existence Of Pure Strategy Equilibria In Games Of Incomplete Information

This paper derives sufficient conditions for a class of games of incomplete information, such as first price auctions, to have pure strategy Nash equilibria (PSNE). The paper treats games between two or more heterogeneous agents, each with private information about his own type (for example, a bidder's value for an object of a firm's marginal cost of production), and the types are drawn from an atomless joint probability distribution which potentially allows for correlation between types. Agents' utility may depend directly on the realizations of other agents' types, as in Milgrom and Weber's (1982) formulation of the auction. The restriction we consider is that each player's expected payoffs satisfy the following single crossing condition: whenever each opponent uses a nondecreasing strategy (that is, an opponent who has a higher type chooses a higher action), then a player's best response strategy is also nondecreasing in her type. The paper has two main results. The first result shows that, when players are restricted to choose among a finite set of actions (for example, bidding or pricing where the smallest unit is a penny), games where players' objective functions satisfy this single crossing condition will have PSNE. The second result demonstrates that when players' utility functions are continuous, as well as in mineral rights auction games and other games where winning creates a discontinuity in payoffs, the existence result can be extended to the case where players choose from a continuum of actions. The paper then applies the theory to several classes of games, providing conditions on utility functions and joint distributions over types under which each class of games satisfies the single crossing condition. In particular, the single crossing condition is shown to hold in all first-price, private value auctions with potentially heterogeneous, risk-averse bidders, with either independent or affiliated values, and with reserve prices which may differ across bidders; mineral rights auctions with two heterogeneous bidders and affiliated values; a class of pricing games with incomplete information about costs; a class of all-pay auction games; and a class of noisy signaling games. Finally, the formulation of the problem introduced in this paper suggests a straightforward algorithm for numerically computing equilibrium bidding strategies in games such as first price auctions, and we present numerical analyses of several auctions under alternative assumptions about the joint distribution of types.

Withdrawable Bids as Winner's Curse Insurance

When bidders have a common value or strongly affiliated values for an object or contract being auctioned by sealed bids, it is possible that the maker of a rational and apparently winning bid would, upon learning the competing bids, prefer losing the auction to honoring his bid. The ability to withdraw a bid, perhaps at a cost, in such circumstances provides a form of “winner's curse insurance.” Bidding with such insurance is analyzed, obtaining the general condition for rational bid withdrawal and sufficient conditions for the existence of an equilibrium with more aggressive bidding. Next, we define a “compensation penalties” bid withdrawal penalty scheme and show that with it the bid-taker is better off on the average than if bid withdrawal is impossible. Finally, we find equilibrium bidding and withdrawal strategies in a multiplicative model as a function of the magnitude of the bid withdrawal penalty and of the bid-taker's likelihood, after a withdrawal, of honoring the second-best bid. This model has cases in which allowing withdrawal at a cost is in the bid-taker's interest and ones in which it is not.