Krishnamurthy Iyer

Information aggregation in smooth markets

Recent years have seen extensive investigation of the information aggregation properties of prediction markets. However, relatively little is known about conditions under which a market will aggregate the private information of rational risk averse traders who optimize their portfolios over time; in particular, what features of a market encourage traders to ultimately reveal their private information through trades? We consider a market model involving finitely many informed risk-averse traders interacting with a market maker. Our main result identifies a basic asymptotic smoothness condition on the price in the market that ensures information will be aggregated under a portfolio convergence assumption. Asymptotic smoothness is fairly mild: it requires that, eventually, infinitesimal purchases or sales should see the same per unit price. Notably, we demonstrate that, under some mild conditions, cost function market makers (or, equivalently, market makers based on market scoring rules) satisfy the asymptotic smoothness requirement.

Mean field equilibria of dynamic auctions with learning

Auctions are observed as a market mechanism in a wide range of economic transactions involving repeated interactions among the market participants: sponsored search markets run by Google and Yahoo!, online marketplaces such as eBay and Amazon, crowdsourcing, etc. In many of these markets, the participants typically have incomplete information; for example, the participants may not know the quality of the good being auctioned or their value for the good. In such settings, repeated interactions among the participants give rise to extremely complex bidder behavior due to the presence of learning among the participants.

Information Aggregation and Allocative Efficiency in Smooth Markets

Recent years have seen extensive investigation of the information aggregation properties of markets. However, relatively little is known about conditions under which a market will aggregate the private information of rational risk-averse traders who optimize their portfolios over time; in particular, what features of a market encourage traders to ultimately reveal their private information through trades? We consider a market model involving finitely many informed risk-averse traders interacting with a market maker. Our main result identifies a basic asymptotic smoothness condition on prices in the market that ensures information is aggregated as long as portfolios converge; furthermore, under this assumption, the allocation achieved is ex post Pareto efficient. Asymptotic smoothness is fairly mild: it requires that, eventually, infinitesimal purchases or sales should see the same per-unit price. Notably, we demonstrate that, under some mild conditions, algorithmic markets based on cost functions (or, equivalently, markets based on market scoring rules) aggregate the information of traders. This paper was accepted by Brad M. Barber, finance .

Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models

We consider a discrete time Markov Decision Process (MDP) under the discounted payoff criterion in the presence of additional discounted cost constraints. We study the sensitivity of optimal Stationary Randomized (SR) policies in this setting with respect to the upper bound on the discounted cost constraint functionals. We show that such sensitivity analysis leads to an improved version of the Feinberg–Shwartz algorithm (Math Oper Res 21(4):922–945, 1996) for finding optimal policies that are ultimately stationary and deterministic.

Near-Efficient Allocation Using Artificial Currency in Repeated Settings

We study the design of mechanisms without money for repeated allocation of resources among competing agents. Such mechanisms are gaining widespread use in allocating physical and/or computing resources in universities and companies, and also distributing of public goods like vaccines among hospitals and food donations among food banks. We consider repeated allocation mechanisms based on artificial currencies, wherein we first allot each agent a chosen endowment of credits, which they can then use over time to bid for the item in a chosen auction format. Our main contribution is in showing that a simple mechanism, based on a repeated all-pay auction with personalized endowments and static pricing rules, simultaneously guarantees vanishing gains from non-truthful bidding as well as vanishing loss in efficiency. Our work lies at the intersection of dynamic mechanism design and mechanisms without money, and the techniques we develop here may prove of independent interest in these settings.

When Bribes are Harmless: The Power and Limits of Collusion-Resilient Mechanism Design

Collusion has long been the Achilles heel of mechanism design, as most results break down when participating agents can collude. The issue is more severe when monetary transfers (bribes) between agents are feasible, wherein it is known that truthful revelation and efficient allocation are incompatible. A natural relaxation that circumvents these impossibility results is that of coalitional dominance: replacing truthful revelation with the weaker requirement that all coalitions, whatever they may be, have dominant strategies. When a mechanism satisfies this property and is efficient, we call it collusion resilient. The goal of this paper is to characterize the power and limits of collusion resilient mechanisms. On the positive side, in a general allocation setting, we demonstrate a new mechanism which is collusion-resilient for surplus-submodular settings -- a large-class of problems which includes combinatorial auctions with gross substitutes valuations. We complement this mechanism with two impossibility results: (1) for combinatorial auctions with general submodular valuations, we show that no mechanism can be collusion-resilient, and (2) for the problem of collective decision making, we argue that any non-trivial approximation of welfare is impossible under coalitional dominance. Finally, we make a connection between collusion resilience and false-name-proofness, and show that our impossibility theorems strengthen existing results for false-name-proof mechanisms.

Price competition under linear demand and finite inventories: Contraction and approximate equilibria

Abstract We consider a multi-period price competition among multiple firms with limited inventories of substitutable products, and study two types of equilibrium: with and without recourse. Under a linear demand model, we show that an equilibrium without recourse uniquely exists. In contrast, we show an equilibrium with recourse need not exist, nor be unique. In a low-influence regime, using the equilibrium without recourse, we construct an approximate equilibrium with recourse with the same equilibrium price trajectory.

Information and the value of execution guarantees

In many markets, uncertainty about whether a trade is executed can be removed by paying a price premium. We use financial markets as a particular setting in which to study this trade-off. In particular, we assess the role of information in the choice between certain trade at a price premium in an intermediated dealer market and contingent trade in a dark pool. Our setting consists of intrinsic traders and speculators, each endowed with heterogeneous fine-grained private information as to an assets value, that endogenously decide between these two venues. We solve for an equilibrium in this setting, and address three main questions: First, how does the level of information of a trader and her competitors affect their behavior-i.e., how does the choice between certain and contingent trade depend on information structure? Second, how does the level of premium for certain trade over contingent trade affect the strategic behavior of traders? And finally, how should market makers intermediating certain trade set transaction costs to maximize profit, in the presence of an option for contingent trade? We derive the following implications from our model: (1) Information and the choice between certain and contingent trade. We find that, in general, the dark pool is utilized by uninformed or mildly informed traders, whereas highly informed traders will trade in the open market. Furthermore, there is adverse selection in the dark pool, in the sense that buy (sell) orders are more likely to be filled when the dark pool price is above (resp. below) the true value. (2) The impact of transaction costs on adverse selection. Surprisingly, in the partial equilibrium setting where the transaction costs in the open market are exogenously specified, the fill rate in the dark pool (and therefore adverse selection) is not monotonically related to the bid-offer spread: for example, when the dark pool price is above true value, the fill rate for buyers in the dark pool falls at lower transaction costs, and rises at higher transaction costs. (3) Market making in the open market. We find that a dark pool lowers a monopolists choice of transaction cost in the open market. Further, we find the surprising insight that the monopolists profit also increases as traders become more informed.

Mean field equilibria of dynamic auctions with learning: A dynamic revenue equivalence theorem

Auctions are observed as a market mechanism in a wide range of economic transactions involving repeated interactions among the market participants: sponsored search markets run by Google and Yahoo!, online marketplaces such as eBay and Amazon, crowdsourcing, etc. In many of these markets, the participants typically have incomplete information; for example, the participants may not know the quality of the good being auctioned or their value for the good. In such settings, repeated interactions among the participants give rise to extremely complex bidder behavior due to the presence of learning among the participants.