Working Papers

Storage Games (with Guillaume Roger)

We study a long-horizon, oligopolistic market with random shocks to demand that can be arbitraged by two large storage operators with finite capacity. The application we speak to is electricity but our results extend to any storable commodity — that is, most commodities. Because the arbitrage spread is so sensitive to market power, storage operators face strong incentives to restrain quantities by tacitly colluding. This cooperation takes new forms thanks to the multiplicity of actions they must take: selling, buying or both. We construct payoff-maximizing equilibria of this stochastic game, and uncover a new form of Partial Cooperation that trades off quantities and delay. Head-on competition is not always an equilibrium of the long-horizon game, unlike many standard games, when market power becomes large enough. We present some robustness checks. We also draw implications for policy and suggest poorly competitive storage is a negative externality to the development of the underlying commodity — for example, renewable energy.

Near-optimal Storage Strategies in Electricity Markets (with Guillaume Roger)

Storing electricity is completely essential to the energy transition. It also deeply disrupts the manner in which electricity markets operate, for it introduces delay. In this paper, we consider a dynamic model of an oligopolistic market with demand shocks, in which a storage unit buys and sells energy subject to a capacity constraint. To make progress in this stochastic game, we restrict attention to simple heuristics, and we can characterise the optimal policy of a storage unit in this restricted class of heuristics. The heuristics, the exogenous stochastic process and the capacity constraint interact to induce rich dynamics. The optimal policy is sensitive to the nature of demand shocks and to storage capacity. Capacity utilisation decreases with capacity size for two reasons. First, the storage unit internalises its unilateral market power, yet has to remain large enough to not render the arbitrage trade trivial. Second, uncertainty is costly: a storage operator does not want to be stuck empty or full, and so limits the quantities traded in any interval. Too large a capacity nullifies the arbitrage spread, even with the optimal trading policy. We construct an equilibrium, in which electricity arbitrage is never profitable, and so conclude that successful entry is not a foregone conclusion. This work informs market participants as well as the design of electricity markets with storage. It is particularly relevant to major markets with rapid penetration of renewable energy sources, like California or Australia. It can also be applied to trading securities.

Application Costs as a Screening Instrument in Decentralized Matching

We consider decentralized matching in a two-sided market of employers and employees (universities and students) with application costs and limited budgets. Students choose whether they should take the risk of applying to more prestigious school (with some probability of rejection) or make a safe choice. We show that application costs set by universities may be treated as a screening instrument in order to attract only strong students or to avoid the competition. Also, we find conditions for equilibria when costs are negligible, costs are a substantial part of the budget or even the entire budget, in addition to other equilibria.

Decentralized Dynamic Matching with Signaling

We consider multi-period decentralized matching in a two-sided market of employers and employees. Because of dynamics, asymmetry, and private information, we always observe delays and coordination failures with nonzero probability even in a simple case of two agents from each side. For this, we obtain conditions for different strategies to be in equilibrium. We show that problems of miscoordination and delay may be solved by signaling or by incentivizing immediate response that turn a dynamic problem into a static one and make the matching stable. In the general case, we obtain sufficient conditions for assortative matching to be and not to be in equilibrium.

Iterated Regret Minimization in Games with Nonoptimal Nash Equilibria

The concept of iterated regret minimization (IRM) provides solutions that are more reasonable than ones offered by Nash equilibrium (NE) for many games of interest, such as the Traveler's Dilemma, the Centipede Game, and many others. For them, we analyzed new data — the IRM approach prescribes the most profitable strategy better than NE. Also, we apply the IRM to the games with continuous strategy sets, such as Colonel Blotto game and Bertrand-Edgeworth duopoly, and obtain reasonable pricing and allocating policies.

Work in Progress

Information Flows on Network Structures (with Dan Levin and Jaromir Kovarik)

We study how the structure of a network in terms of number of agents, feasible actions, and absorbability of actions of others affects the agent's trade-off between the incentive to delay actions in order to infer information by observing actions of others and the incentive to move early to avoid costs of delay.

Congestion on the Bottom: Matching with Limited Capacity

We consider decentralized matching in a two-sided market of employers and employees, where each side has two types of agents, high and low. With limited capacity of employers and if both employees' types are weak enough, we observe an interesting result: in order to avoid competition with high-type employees, low-type employees send applications to high-type employers.

Dynamic Choice with Noisy Information: Would Overconfidence Help?

We analyze the dynamic application process where the probability of success is determined by the type of an applicant. In the case the type is private and may be revealed to jury only with some random noise, we prove that agents maximize their profits by aiming higher in the first rounds. However, this strategy may change if an applicant herself misinterprets her type with a positive (overconfidence) or a negative (underconfidence) bias.

Selected Publications in Math (in English)

2013 Stochastic Model of Digit Transfer in Computing. Numerical Analysis and Applications 6(1) 71-76 with L. Savelyev
2011 A Combinatorial Approach to Calculation of Moments of Characteristics of Runs in Ternary Markov Sequences. Discrete Mathematics and Applications 21(1) 47-67 with L. Savelyev
2009 Special Operator Equations. Journal of Applied and Industrial Mathematics 3(2) 1-16 with M.M. Lavrentyev and L. Savelyev
2008 Matrix Operator Equations. Journal of Applied and Industrial Mathematics 2(4) 1-23 with M.M. Lavrentyev and L. Savelyev
2004 The joint distribution of the number of ones and the number of 1-runs in binary Markov sequences. Discrete Mathematics and Applications 14(4) 353-372 with L. Savelyev
2003 Covering runs in binary Markov sequences. Discrete Mathematics and Applications 13(2) 111-139 with L. Savelyev and B. Khromov