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Hedonic Games
TLDR
This chapter considers coalition formation games with hedonic preferences, which are used to model many interesting settings, such as research team formation, scheduling group activities, formation of coalition governments, clusterings in social networks, and distributed task allocation for wireless agents. Expand
Lenient Multi-Agent Deep Reinforcement Learning
TLDR
It is found that Lenient-DQN agents are more likely to converge to the optimal policy in a stochastic reward CMOTP compared to standard and scheduled-HDZN agents. Expand
Enumeration of Nash equilibria for two-player games
This paper describes algorithms for finding all Nash equilibria of a two-player game in strategic form. We present two algorithms that extend earlier work. Our presentation is self-contained, andExpand
Computing Stable Outcomes in Hedonic Games
TLDR
This work considers several natural stability requirements defined in the economics literature, and develops polynomial-time algorithms for finding stable outcomes in symmetric additively-separable hedonic games. Expand
Hard‐to‐Solve Bimatrix Games
The Lemke-Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even inExpand
The Complexity of the Simplex Method
TLDR
This paper uses the known connection between Markov decision processes (MDPs) and linear programming, and an equivalence between Dantzig's pivot rule and a natural variant of policy iteration for average-reward MDPs to prove that it is PSPACE-complete to find the solution that is computed by the simplex method using Dantzes' pivot rule. Expand
Power Indices in Spanning Connectivity Games
TLDR
It is proved that Banzhaf indices can be computed in polynomial time for graphs with bounded treewidth and answered an open question of whether computing Shapley-Shubik indices for a simple game represented by the set of minimal winning coalitions is NP-hard. Expand
Computing Approximate Nash Equilibria in Polymatrix Games
TLDR
Inspired by the algorithm of Tsaknakis and Spirakis [28], the algorithm uses gradient descent style approach on the maximum regret of the players and can be applied to efficiently find a 0.5+δ)-Nash equilibrium in a two-player Bayesian game. Expand
Exponentially many steps for finding a Nash equilibrium in a bimatrix game
  • Rahul Savani, B. Stengel
  • Mathematics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of…
  • 17 October 2004
TLDR
A class of bimatrix games for which the Lemke-Howson algorithm takes, even in the best case, exponential time in the dimension d of the game, requiring /spl Omega/((/spl theta//sup 3/4/)/sup d/) many steps, where /spl theTA/ is the golden ratio. Expand
The Complexity of the Homotopy Method, Equilibrium Selection, and Lemke-Howson Solutions
TLDR
It is PSPACE-complete to compute any of the equilibria that could be found via the classical Lemke-How son algorithm, a complexity-theoretic strengthening of the result in [24]. Expand
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