Sergei Izmalkov

Rational secure computation and ideal mechanism design

Secure computation essentially guarantees that whatever computation n players can do with the help of a trusted party, they can also do by themselves. Fundamentally, however, this notion depends on the honesty of at least some players. We put forward and implement a stronger notion, rational secure computation, that does not depend on player honesty, but solely on player rationality. The key to our implementation is showing that the ballot-box - the venerable device used throughout the world to tally secret votes securely - can actually be used to securely compute any function. Our work bridges the fields of game theory and cryptography, and has broad implications for mechanism design.

Verifiably secure devices

We put forward the notion of a verifiably secure device, in essence a stronger notion of secure computation, and achieve it in the ballot-box model. Verifiably secure devices 1. Provide a perfect solution to the problem of achieving correlated equilibrium, an important and extensively investigated problem at the intersection of game theory, cryptography and efficient algorithms; and 2. Enable the secure evaluation of multiple interdependent functions.

on efficiency of the English auction

We study efficiency properties of the irrevocable exit English auction in a setting with interdependent values. Maskin (1992) [1] shows that the pairwise single-crossing condition is sufficient for efficiency of the English auction with two bidders and suggests that it is also a necessary condition. This paper clarifies and extends Maskin[modifier letter apostrophe]s results to the case of N bidders. We introduce the generalized single-crossing condition--a fairly intuitive extension of the pairwise single-crossing condition--and prove that it is essentially a necessary and sufficient condition for the existence of an efficient equilibrium of the N-bidder English auction.

English Auctions with Reentry

The English auction is usually modeled as an open continuously ascending price auction in which bidders choose when to drop out but, once they do so, are forbidden from reentering. It is known that this auction allocates a single object efficiently in many but not all circumstances. In particular, if there are three or more bidders with interdependent values, the English auction may not be efficient. This paper considers a modification of the standard model in which bidders can exit and reenter at will. The main result is that the English auction with reentry has an efficient equilibrium under weak conditions. These are much weaker than the conditions under which the standard English auction is efficient. Thus the modification is not only a more realistic model of the real-world auction but has superior theoretical properties. The failure of the English auction to allocate efficiently stems not from some defect in the institution per se but rather from the way it has been traditionally modeled as a game.

Informed Seller in a Hotelling Market

We derive the optimal selling mechanism for a monopolist who is privately informed about the attributes of a horizontally differentiated good. To do so, we set up an informed principal problem in a Hotelling model where the buyers preferences are described in terms of a base consumption value and the distance between the buyers and the sellers locations. To represent different kinds of markets we consider linear, concave, and convex distance costs. We derive the optimal mechanism and offer ways to implement it. For instance, for low (high) base consumption values, it is optimal for the seller to disclose (do not disclose) her type and then set the optimal price. For intermediate values, the optimal mechanism may involve stochastic delivery and can be implemented by multi-item menus that involve selling information or refund options. Under linear distance costs, offering the following two-item menu is optimal: a good with undisclosed attributes (opaque good) or an option to learn information and buy the good later. Under convex and concave costs, the optimal mechanism may involve type-specific probabilistic allocations, which can also be implemented through private transmission of different information to different buyer types.

The Market for Surprises: Selling Substitute Goods Through Lotteries

In this paper we solve the revenue maximization problem of multi-product monopolist when the products are substitutes. We consider a Hotelling model with two horizontally differentiated goods located at the endpoints of the segment. Consumers are located uniformly on the segment, their valuations for each good are equal to base consumption value minus distance costs. We consider different specifications for the distance cost function: linear, concave, and convex. When base consumption value is high, the seller maximizes her expected profit by offering a menu of base and opaque goods. A continuum of type-specific opaque goods is optimal under convex costs, whereas a single half-half lottery over base goods is optimal under concave and linear costs. When base consumption value is low, only base goods are sold. Finally, when base-consumption value is intermediate, the optimal mechanism may entail the offering of lotteries with positive probability of no delivery. Our findings can explain the emergence of opaque goods sales (e.g. hotel bookings without complete description of the hotel by hotwire.com or priceline.com) as the outcome of the industries search for the optimal selling scheme.

Games in the Arctic: applying game theory insights to Arctic challenges

We illustrate the benefits of game theoretic analysis for assisting decision-makers in resolving conflicts and other challenges in a rapidly evolving region. We review a series of salient Arctic issues with global implications—managing open-access fisheries, opening Arctic areas for resource extraction and ensuring effective environmental regulation for natural resource extraction—and provide insights to help reach socially preferred outcomes. We provide an overview of game theoretic analysis in laymans terms, explaining how game theory can help researchers and decision-makers to better understand conflicts, and how to identify the need for, and improve the design of, policy interventions. We believe that game theoretic tools are particularly useful in a region with a diverse set of players ranging from countries to firms to individuals. We argue that the Arctic Council should take a more active governing role in the region by, for example, dispersing information to “players” in order to alleviate conflicts regarding the management of common-pool resources such as open-access fisheries and natural resource extraction. We also identify side payments—that is, monetary or in-kind compensation from one party of a conflict to another—as a key mechanism for reaching a more biologically, culturally and economically sustainable Arctic future. By emphasizing the practical insights generated from an academic discipline, we present game theory as an influential tool in shaping the future of the Arctic—for individual researchers, for inter-disciplinary research and for policy-makers themselves.

Arctic games: an analytical framework for identifying options for sustainable natural resource governance

Abstract Changes in the Arctic are fuelled by a variety of drivers, including global warming, economic growth, improved access to natural resources, technological advances and globalisation processes. Further, the region is characterised by a diverse set of international agreements, national legislations and common pool resources. This presents challenges for actors to suggest, evaluate and agree on sustainable development alternatives. We propose an analytical framework to better understand (1) the types of trade-offs associated with Arctic futures and (2) actors’ incentives for strategic behaviour. In the framework, game theory illuminates incentives and strategies among actors, cost-benefit analysis and economic valuation of ecosystem services help identify socially desirable outcomes and institutional analysis provides insight on how governance structures can support or interfere with policy intervention. We apply the proposed framework by analysing possible oil development futures for Lofoten in Northern Norway. For example, institutional analysis and estimates of costs and benefits of reducing oil spill risk and their distribution among actors are used for discussing incentive structures, including the use of side payments as a mechanism to mitigate conflicting interests.

Multi-Unit Open Ascending Price Efficient Auction

This paper presents an open ascending price mechanism that allocates efficiently M units of the same good among N bidders with interdependent values The mechanism consists of a number of sequential English auctions with reentry and has the following attributes. In each of the individual auctions all the bidders compete simultaneously in the open ascending price format. The most distinctive feature of the mechanism is that winners are determined first, and then additional auxillary auctions are conducted to determine prices. The total number of auctions depends only on the number of goods to be allocated and not on the number of bidders.