Convexity spaces defined in the paper are generated by families of continuous functions. Without imposing any explicitly stated linear structure on the spaces, Browder’s, Brouwer’s and Kakutani’s fixed point theorems are proved and used for deriving generalized Fan inequalities and two-function minimax theorems. The existence of Nash equilibria in noncooperative games is also established under ...

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into so-called “prosumers,” i.e., proactive consumers, which can both produce consume power. To encourage exchange among prosumers, sharing is increasingly adopted, usually formulated as a generalized Nash game (GNG). In this paper, approach pr...

We study a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the lexicographical improvement property (LIP) and show that, in finite games, it is equivalent to the existence of a...

Procedural content generation (PCG) has become a popular research topic in recent years, but not much work has been done in terms of generalized content generators, that is, methods that can generate content for a wide variety of games without requiring hand-tuning. Probabilistic approaches are a promising avenue for creating more general content generators, and specificially map generators. I ...

We show that an optimal counterstrategy against a fixed positional strategy in a generalized discounted payoff game, where edges have individual discounts, can be computed in O(mn logm) strongly polynomial time, where n and m are the number of vertices and edges in the game graph. This results in the best known strongly subexponential time bound for solving two-player generalized discounted pay...