Related papers: A Linear Programming Approach to Estimate the Core…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…
We study fair allocation of profit (or cost) for three central problems from combinatorial optimization: Max-Flow, MST and $b$-matching. The essentially unequivocal choice of solution concept for this purpose would be the core, because of…
Cooperative interval game is a cooperative game in which every coalition gets assigned some closed real interval. This models uncertainty about how much the members of a coalition get for cooperating together. In this paper we study…
We propose a parametric family of measures of fairness in allocations of TU-cooperative games. Their definition is based on generalized Renyi Entropy, is related to the Cowell-Kuga generalized entropy indices in welfare economics, and aims…
Linear complementarity programming is a generalization of linear programming which encompasses the computation of Nash equilibria for bimatrix games. While the latter problem is PPAD-complete, we show that the tropical analogue of the…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We analyze the core of a cooperative Cournot game. We assume that when contemplating a deviation, the members of a coalition assign positive probability over all possible coalition structures that the non-members can form. We show that when…
Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…
Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we…
The recent breakthrough paper by Calude et al. has given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly subexponential. We devise an alternative quasi-polynomial time…
This paper introduces a systematic methodological framework to design and analyze distributed algorithms for optimization and games over networks. Starting from a centralized method, we identify an aggregation function involving all the…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
We consider game-theoretically secure distributed protocols for coalition games that approximate the Shapley value with small multiplicative error. Since all known existing approximation algorithms for the Shapley value are randomized, it…
In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
We propose a numerical algorithm for computing approximately optimal solutions of the matching for teams problem. Our algorithm is efficient for problems involving large number of agent categories and allows for non-discrete agent type…
In this paper, we consider a network allocation problem motivated by peer-to-peer cloud storage models. The setting is that of a network of units (e.g. computers) that collaborate and offer each other space for the back up of the data of…
Unsatisfiable cores (UCs) are a well established means for debugging in a declarative setting. Still, there are few tools that perform automated extraction of UCs for LTL. Existing tools compute a UC as an unsatisfiable subset of the set of…
In this paper we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with a priori unions. In the case of the equal…