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We examine the problem of efficiently learning coarse correlated equilibria (CCE) in polyhedral games, that is, normal-form games with an exponentially large number of actions per player and an underlying combinatorial structure. Prominent…

We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…

Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…

Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…

Lagrangian relaxation and approximate optimization algorithms have received much attention in the last two decades. Typically, the running time of these methods to obtain a $\epsilon$ approximate solution is proportional to…

We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the…

We show that for any given norm ball or proper cone, weak membership in its dual ball or dual cone is polynomial-time reducible to weak membership in the given ball or cone. A consequence is that the weak membership or membership problem…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

We present polynomial-time algorithms as well as hardness results for equilibrium computation in atomic splittable routing games, for the case of general convex cost functions. These games model traffic in freight transportation, market…

We consider cost allocation for set covering problems. We allocate as much cost to the elements (players) as possible without violating the group rationality condition (no subset of players pays more than covering this subset would cost),…

We investigate different aspects of area convexity [Sherman '17], a mysterious tool introduced to tackle optimization problems under the challenging $\ell_\infty$ geometry. We develop a deeper understanding of its relationship with more…

We study bargaining games between suppliers and manufacturers in a network context. Agents wish to enter into contracts in order to generate surplus which then must be divided among the participants. Potential contracts and their surplus…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

The complexity of computing equilibrium refinements has been at the forefront of algorithmic game theory research, but it has remained open in the seminal class of potential games; we close this fundamental gap in this paper. We first show…

Nash equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von…

Dealing with NP-hard problems, kernelization is a fundamental notion for polynomial-time data reduction with performance guarantees: in polynomial time, a problem instance is reduced to an equivalent instance with size upper-bounded by a…

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…

We study the problem of finding Stackelberg equilibria in games with a massive number of players. So far, the only known game instances in which the problem is solved in polynomial time are some particular congestion games. However, a…

For common notions of correlated equilibrium in extensive-form games, computing an optimal (e.g., welfare-maximizing) equilibrium is NP-hard. Other equilibrium notions -- communication (Forges 1986) and certification (Forges & Koessler…

We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…