Dmitrii V. Pasechnik

The Cost of Stability in Coalitional Games

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the core --the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which is interested in having the players work together, offers a supplemental payment to the grand coalition (or, more generally, a particular coalition structure). This payment is conditional on players not deviating from their coalition(s). The sum of this payment plus the actual gains of the coalition(s) may then be divided among the agents so as to promote stability. We define the cost of stability (CoS) as the minimal external payment that stabilizes the game. We provide general bounds on the cost of stability in several classes of games, and explore its algorithmic properties. To develop a better intuition for the concepts we introduce, we provide a detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings. Finally, we extend our model and results to games with coalition structures.

Improved Bounds for the Crossing Numbers of K m,n and K n

It has been long conjectured that the crossing number

Complexity of Semi-algebraic Proofs

\Cr(K_{m,n})

Computing the nucleolus of weighted voting games

of the complete bipartite graph

Polynomial-time computing over quadratic maps i: sampling in real algebraic sets

K_{m,n}

Erratum: On Semidefinite Programming Relaxations of the Traveling Salesman Problem

equals the Zarankiewicz number

CSS-Like Constructions of Asymmetric Quantum Codes

Z(m,n):= \floor{\frac{m-1}{2}} \floor{\frac{m}{2}} \floor{\frac{n-1}{2}} \floor{\frac{n}{2}}

On the Skeleton of the Metric Polytope

. Another longstanding conjecture states that the crossing number

Extending polar spaces of rank at least 3

\Cr(K_n)

Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials

of the complete graph