Nikolai S. Kukushkin

Bio: Nikolai S. Kukushkin is an academic researcher from Russian Academy of Sciences. The author has contributed to research in topics: Nash equilibrium & Best response. The author has an hindex of 12, co-authored 64 publications receiving 502 citations. Previous affiliations of Nikolai S. Kukushkin include Moscow Institute of Physics and Technology.

Acyclicity of improvements in finite game forms

Abstract: Game forms are studied where the acyclicity, in a stronger or weaker sense, of (coalition or individual) improvements is ensured in all derivative games. In every game form generated by an “ordered voting” procedure, individual improvements converge to Nash equilibria if the players restrict themselves to “minimal” strategy changes. A complete description of game forms where all coalition improvement paths lead to strong equilibria is obtained: they are either dictatorial, or voting (or rather lobbing) about two outcomes. The restriction to minimal strategy changes ensures the convergence of coalition improvements to strong equilibria in every game form generated by a “voting by veto” procedure.

Congestion games revisited

Abstract: Strategic games are considered where the players derive their utilities from participation in certain “processes” Two subclasses consisting exclusively of potential games are singled out In the first, players choose where to participate, but there is a unique way of participation, the same for all players In the second, the participation structure is fixed, but each player may have an arbitrary set of strategies In both cases, the players sum up the intermediate utilities; thus the first class essentially coincides with that of congestion games The necessity of additivity in each case is proven

Dynamic Mechanism Design: A Myersonian Approach

Abstract: We study mechanism design in dynamic quasilinear environments where private information arrives over time and decisions are made over multiple periods. We make three contributions. First, we provide a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent's equilibrium expected payoff with respect to his current type. It combines the familiar marginal effect of types on payoffs with novel marginal effects of the current type on future ones that are captured by �impulse response functions.� The formula yields an expression for dynamic virtual surplus that is instrumental to the design of optimal mechanisms and to the study of distortions under such mechanisms. Second, we characterize the transfers that satisfy the envelope formula and establish a sense in which they are pinned down by the allocation rule (�revenue equivalence�). Third, we characterize perfect Bayesian equilibrium-implementable allocation rules in Markov environments, which yields tractable sufficient conditions that facilitate novel applications. We illustrate the results by applying them to the design of optimal mechanisms for the sale of experience goods (�bandit auctions�).

Aggregative games and best-reply potentials

Abstract: This paper introduces quasi-aggregative games and establishes conditions under which such games admit a best-reply potential. This implies existence of a pure strategy Nash equilibrium without any convexity or quasi-concavity assumptions. It also implies convergence of best-reply dynamics under some additional assumptions. Most of the existing literature’s aggregation concepts are special cases of quasi-aggregative games, and many new situations are allowed for. An example is payoff functions that depend on own strategies as well as a linear combination of the mean and the variance of players’ strategies.