arXiv subjects

Anisse Ismaili

Publications and source records attributed to Anisse Ismaili.

6 recordsLinked to original sources

arXiv2019

The Complexity of Student-Project-Resource Matching-Allocation Problems

I settle the computational complexity of student-project-resource matching-allocation problems, in which students and resources are assigned to projects \citep{pc2017}. A project's capacity for students is endogenously determined by the resources allocated to it. I show that finding a nonwasteful matching is $\text{FP}^{\text{NP}}[\text{log}]$-hard, and deciding a stable matching is $\text{NP}^{\text{NP}}$-complete. To obtain these results, I introduce two new problems: (i) \textsc{ParetoPartition}, shown $\text{FP}^{\text{NP}}[\text{poly}]$-hard and also strongly $\text{FP}^{\text{NP}}[\text{log}]$-hard, and (ii) \textsc{$\forall\exists$-4-Partition}, shown strongly $\text{NP}^{\text{NP}}$-complete.

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arXiv2019

The Complexity of Max-Min $k$-Partitioning

In this paper we study a max-min $k$-partition problem on a weighted graph, that could model a robust $k$-coalition formation. We settle the computational complexity of this problem as complete for class $Σ_2^P$. This hardness holds even for $k=2$ and arbitrary weights, or $k=3$ and non-negative weights, which matches what was known on \textsc{MaxCut} and \textsc{Min-3-Cut} one level higher in the polynomial hierarchy.

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arXiv2018

The Complexity of Sequential Routing Games

We study routing games where every agent sequentially decides her next edge when she obtains the green light at each vertex. Because every edge only has capacity to let out one agent per round, an edge acts as a FIFO waiting queue that causes congestion on agents who enter. Given $n$ agents over $|V|$ vertices, we show that for one agent, approximating a winning strategy within $n^{1-\varepsilon}$ of the optimum for any $\varepsilon>0$, or within any polynomial of $|V|$, are PSPACE-hard. Under perfect information, computing a subgame perfect equilibrium (SPE) is PSPACE-hard and in FPSPACE. Under imperfect information, deciding SPE existence is PSPACE-complete.

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arXiv2018

On Existence, Mixtures, Computation and Efficiency in Multi-objective Games

In a multi-objective game, each individual's payoff is a \emph{vector-valued} function of everyone's actions. Under such vectorial payoffs, Pareto-efficiency is used to formulate each individual's best-response condition, inducing Pareto-Nash equilibria as the fundamental solution concept. In this work, we follow a classical game-theoretic agenda to study equilibria. Firstly, we show in several ways that numerous pure-strategy Pareto-Nash equilibria exist. Secondly, we propose a more consistent extension to mixed-strategy equilibria. Thirdly, we introduce a measurement of the efficiency of multiple objectives games, which purpose is to keep the information on each objective: the multi-objective coordination ratio. Finally, we provide algorithms that compute Pareto-Nash equilibria and that compute or approximate the multi-objective coordination ratio.

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arXiv2017

Routing Games over Time with FIFO policy

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a \emph{first-in-first-out} queue and may wait: an edge is associated with a capacity, which defines how many agents-per-time-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.

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arXiv2015

Efficiency in Multi-objective Games

In a multi-objective game, each agent individually evaluates each overall action-profile on multiple objectives. I generalize the price of anarchy to multi-objective games and provide a polynomial-time algorithm to assess it. This work asserts that policies on tobacco promote a higher economic efficiency.

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