Related papers: Linear Representation of Symmetric Games
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…
Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…
Parsimonious games are a subset of constant sum homogeneous weighted majority games unequivocally described by their free type representation vector. We show that the minimal winning quota of parsimonious games satisfies a second order,…
We recast move generators for solving board games as operations on compressed sets of strings. We aim for compressed representations with space sublinear in the number of game positions for interesting sets of positions, move generation in…
Strategic interactions between a group of individuals or organisations can be modelled as games played on networks, where a player's payoff depends not only on their actions but also on those of their neighbours. Inferring the network…
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…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
A supremum-of-quadratics representation for convex barrier-type constraints is developed and applied within the context of a class of continuous time state constrained linear regulator problems. Using this representation, it is shown that a…
In this paper, we introduce an agent-based representation of games, in order to propose a compact representation for multi-party games in game theory. Our method is inspired by concepts in process theory and process algebra. In addition, we…
Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into…
According to Shapley's game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
Coalitional games serve the purpose of modeling payoff distribution problems in scenarios where agents can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. In the classical Transferable Utility…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
In cooperative game theory, games in partition function form are real-valued function on the set of so-called embedded coalitions, that is, pairs $(S,\pi)$ where $S$ is a subset (coalition) of the set $N$ of players, and $\pi$ is a…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
Optimization under uncertainty is a fundamental problem in learning and decision-making, particularly in multi-agent systems. Previously, Feldman, Kalai, and Tennenholtz [2010] demonstrated the ability to efficiently compete in repeated…
Network congestion games are a well-understood model of multi-agent strategic interactions. Despite their ubiquitous applications, it is not clear whether it is possible to design information structures to ameliorate the overall experience…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…