Related papers: The Complexity of Simple Stochastic Games
Game-theoretic approaches are envisioned to bring human-like reasoning skills and decision-making processes for autonomous vehicles (AVs). However, challenges including game complexity and incomplete information still remain to be addressed…
This paper proves that arrangement of music is NP-hard when subject to various constraints: avoiding musical dissonance, limiting how many notes can be played simultaneously, and limiting transition speed between chords. These results imply…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
In this paper we study the computational complexity of the game of Scrabble. We prove the PSPACE-completeness of a derandomized model of the game, answering an open question of Erik Demaine and Robert Hearn.
Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium…
Coalitional games are mathematical models suited to analyze scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental problem for coalitional games is to single…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…
An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to…
More precise estimation of the greedy algorithm complexity for a special case of the set cover problem is given in this paper.
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
We study the computational complexity of solving mean payoff games. This class of games can be seen as an extension of parity games, and they have similar complexity status: in both cases solving them is in $\textbf{NP} \cap \textbf{coNP}$…
Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…
We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game…
This paper deals with a standard stochastic game model with a continuum of states under the duel-type setup. It newly proposes a hybrid model of game theory and the fluctuation process, which could be applied for various practical decision…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
We study oracle complexity of gradient based methods for stochastic approximation problems. Though in many settings optimal algorithms and tight lower bounds are known for such problems, these optimal algorithms do not achieve the best…
This paper investigates repeated win-lose coordination games (WLC-games). We analyse which protocols are optimal for these games covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected…