Arup Daripa

A Dynamic Mechanism and Surplus Extraction Under Ambiguity

In the standard independent private values (IPV)model, each bidder’s beliefs about the values of any other bidder is represented by a unique prior. In this paper we relax this assumption and study the question of auction design in an IPV setting characterized by ambiguity: bidders have an imprecise knowledge of the distribution of values of others, and are faced with a set of priors. We also assume that their preferences exhibit ambiguity aversion; in particular, they are represented by the epsilon-contamination model. We show that a simple variation of a discrete Dutch auction can extract almost all surplus. This contrasts with optimal auctions under IPV without ambiguity as well as with optimal static auctions with ambiguity - in all of these, types other than the lowest participating type obtain a positive surplus. An important point of departure is that the modified Dutch mechanism we consider is dynamic rather than static, establishing that under ambiguity aversion – even when the setting is IPV in all other respects – a dynamic mechanism can have additional bite over its static counterparts.

Subsidizing Inventory: A Theory of Trade Credit and Pre-Payment

We propose a simple theory of trade credit and prepayment. A downstream firm trades off inventory holding costs against lost sales. Lost final sales impose a negative externality on the upstream firm. We show that allowing the downstream firm to pay with a delay, an arrangement known as “trade credit,” is precisely the solution to the problem. Solving a reverse externality accounts for the use of prepayment for inputs, even in the absence of any risk of default by the downstream firm. We clarify previously unexplained facts including the universal presence of a zerointerest component in trade credit terms, and the non-responsiveness of interest charges to fluctuations in the bank rate as well as market demand. We explain why trade credit is short term credit and why the level of provision is negatively related to sales and profit and inventory, but positively related to the profit margin. Finally, we show that under trade credit, inventory investment is invariant to the real interest rate for a wide range of parameters, explaining the puzzle posed by Blinder and Maccini (1991). This implies that standard empirical inventory models would gain explanatory power by including the subsidy effect of accounts payable.

Shills and Snipes

Online auctions with a fixed end-time often experience a sharp increase in bidding towards the end despite using a proxy-bidding format. We provide a novel explanation of this phenomenon under private values. We study a correlated private values environment in which the seller bids in her own auction (shill bidding). Bidders selected randomly from some large set arrive randomly in an auction, then decide when to bid (possibly multiple times) over a continuous time interval. A submitted bid arrives over a continuous time interval according to some stochastic distribution. The auction is a continuous-time game where the set of players is not commonly known, a natural setting for online auctions. We show that there is a late-bidding equilibrium in which bids are delayed to the latest instance involving no sacrifice of probability of bid arrival, but shill bids fail to arrive with positive probability, and in this sense optimal late bidding serves to snipe the shill bids. We show conditions under which the equilibrium outcome is unique. Our results suggest that under private values, the case against shill-bidding might be weak.

Eliciting Ambiguous Beliefs Under alpha-Maxmin Preference

We study the problem of elicitation of subjective beliefs of an agent when the beliefs are ambiguous (the set of beliefs is a non-singleton set) and the agent’s preference exhibits ambiguity aversion; in particular, as represented by alpha-maxmin preferences. We construct a direct revelation mechanism such that truthful reporting of beliefs is the agent’s unique best response. The mechanism uses knowledge of the preference parameter alpha and we construct a mechanism that truthfully elicits alpha. Finally, using the two as ingredients, we construct a grand mechanism that elicits ambiguous beliefs and alpha concurrently.