(SUB-)Optimal entry fees

We extend Myerson's (1981) model by allowing for uncertainty about the number of bidders. In such extension the Revenue Equivalence Theorem still holds and the optimal allocation rule remains the same. Hence, the optimal auction can be implemented with an appropriate reserve price. Nonetheless, we show that entry fees are sub-optimal. The reasons are heterogeneity in bidders' beliefs about the number of bidders, and auctioneer's uncertainty about the optimum entry fee, if any. Our result implies a reversal of the revenue ranking by Milgrom and Weber (1982) which is consistent with many real life situations: auction houses, internet auctions,..

Successful uninformed bidding

This paper provides some striking results that arise in the unique symmetric equilibrium of common value multiunit auction in which some bidders are better informed than others. We show that bidders with worse information can do surprisingly well: They can win with higher probability than better informed bidders, and sometimes, even with higher expected utility. We also find a positive relationship between the success of worse informed bidders and the number of units for sale. Finally we argue that the correct intuitive explanation of these results relies on the balance of the winner’s curse and the loser’s curse effects

Competition among auctioneers

In this paper, we analyse a multistage game of competition among auctioneers. In a first stage, auctioneers commit to some publicly announced reserve prices, and in a second stage, bidders choose to participate in one of the auctions. We prove existence of Nash equilibria in mixed strategies for the whole game. We also show that one property of the equilibrium set is that when the numbers of auctioneers and bidders tend to infinity, almost all auctioneers with production cost low enough to trade announce a reserve price equal to their production costs. Our paper confirms previous results for some "limit" versions of the model by McAfee [9], Peters [13], and Peters and Severinov [18]

COMPETITION AMONG AUCTIONEERS

In this paper, we analyse a multistage game of competition among auctioneers. In a first stage, auctioneers commit to some publicly announced reserve prices, and in a second stage, bidders choose to participate in one of the auctions. We prove existence of Nash equilibria in mixed strategies for the whole game. We also show that one property of the equilibrium set is that when the numbers of auctioneers and bidders tend to infinity, almost all auctioneers with production cost low enough to trade announce a reserve price equal to their production costs. Our paper confirms previous results for some "limit" versions of the model by McAfee [9], Peters [13], and Peters and Severinov [18].Auctions; Perfect Competition; Large Markets.

Large deviations sum-queue optimality of a radial sum-rate monotone opportunistic scheduler

A centralized wireless system is considered that is serving a fixed set of users with time varying channel capacities. An opportunistic scheduling rule in this context selects a user (or users) to serve based on the current channel state and user queues. Unless the user traffic is symmetric and/or the underlying capacity region a polymatroid, little is known concerning how performance optimal schedulers should tradeoff "maximizing current service rate" (being opportunistic) versus "balancing unequal queues" (enhancing user-diversity to enable future high service rate opportunities). By contrast with currently proposed opportunistic schedulers, e.g., MaxWeight and Exp Rule, a radial sum-rate monotone (RSM) scheduler de-emphasizes queue-balancing in favor of greedily maximizing the system service rate as the queue-lengths are scaled up linearly. In this paper it is shown that an RSM opportunistic scheduler, p-Log Rule, is not only throughput-optimal, but also maximizes the asymptotic exponential decay rate of the sum-queue distribution for a two-queue system. The result complements existing optimality results for opportunistic scheduling and point to RSM schedulers as a good design choice given the need for robustness in wireless systems with both heterogeneity and high degree of uncertainty.Comment: Revised version. Major changes include addition of details/intermediate steps in various proofs, a summary of technical steps in Table 1, and correction of typos

SUCCESSFUL UNINFORMED BIDDING

This paper provides some striking results that arise in the unique symmetric equilibrium of common value multiunit auction in which some bidders are better informed than others. We show that bidders with worse information can do surprisingly well: They can win with higher probability than better informed bidders, and sometimes, even with higher expected utility. We also find a positive relationship between the success of worse informed bidders and the number of units for sale. Finally we argue that the correct intuitive explanation of these results relies on the balance of the winner's curse and the loser's curse effects.asymmetric bidders, common value, winner¿s curse, loser¿s curse.

(SUB-)OPTIMAL ENTRY FEES

We extend Myerson's (1981) model by allowing for uncertainty about the number of bidders. In such extension the Revenue Equivalence Theorem still holds and the optimal allocation rule remains the same. Hence, the optimal auction can be implemented with an appropriate reserve price. Nonetheless, we show that entry fees are sub-optimal. The reasons are heterogeneity in bidders' beliefs about the number of bidders, and auctioneer's uncertainty about the optimum entry fee, if any. Our result implies a reversal of the revenue ranking by Milgrom and Weber (1982) which is consistent with many real life situations: auction houses, internet auctions,...Optimal Auction; Random Number of Bidders; Reserve Price; Entry Fee.

Bidding markets with financial constraints

We develop a model of bidding markets with financial constraints a la Che and Gale (1998b) in which two firms optimally choose their budgets. First, we provide an alternative explanation for the dispersion of markups and “money left on the table” across procurement auctions. Interestingly, this explanation does not hinge on significant private information but on differences, both endogenous and exogenous, in the availability of financial resources. Second, we explain why the empirical analysis of the size of markups may be biased downwards or upwards with a bias positively correlated with the availability of financial resources when the researcher assumes that the data are generated by the standard auction model. Third, we show that large concentration and persistent asymmetries in market shares together with occasional leadership reversals can arise as a consequence of the firms internal financial decisions even in the absence of exogenous shocks