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Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
Neural Combinatorial Optimization attempts to learn good heuristics for solving a set of problems using Neural Network models and Reinforcement Learning. Recently, its good performance has encouraged many practitioners to develop neural…
We present a general framework to model strategic aspects and stable and fair resource allocations in networks via variants and generalizations of path coalitional games. In these games, a coalition of edges or vertices is successful if it…
We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
We consider concurrent games played by two-players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study a…
We introduce a new class of population games that we call monotropic; these are games characterized by the presence of a unique globally neutrally stable Nash equilibrium. Monotropic games generalize strictly concave potential games and…
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…
In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…
We study the problem of finding robust equilibria in multiplayer concurrent games with mean payoff objectives. A $(k,t)$-robust equilibrium is a strategy profile such that no coalition of size $k$ can improve the payoff of one its member by…
We study a simple adaptive model in the framework of an N -player normal form game. The model consists of a repeated game where the players only know their own action space and their own payoff scored at each stage, not those of the other…
We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…
We study mean field games and corresponding $N$-player games in continuous time over a finite time horizon where the position of each agent belongs to a finite state space. As opposed to previous works on finite state mean field games, we…
We study a tropical linear regression problem consisting in finding the best approximation of a set of points by a tropical hyperplane. We establish a strong duality theorem, showing that the value of this problem coincides with the maximal…
We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…
A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population…
In settings where full incentive-compatibility is not available, such as core-constraint combinatorial auctions and budget-balanced combinatorial exchanges, we may wish to design mechanisms that are as incentive-compatible as possible. This…
Replicator dynamics have been widely used in evolutionary game theory to model how strategy frequencies evolve over time in large populations. The so-called payoff matrix encodes the pairwise fitness that each strategy obtains when…
We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…
A long-standing open problem in algorithmic game theory asks whether or not there is a polynomial time algorithm to compute a Nash equilibrium in a random bimatrix game. We study random win-lose games, where the entries of the $n\times n$…