相关论文: A game on partial orderings

We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant…

We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…

A word automaton recognizing a language $L$ is good for games (GFG) if its composition with any game with winning condition $L$ preserves the game's winner. While all deterministic automata are GFG, some nondeterministic automata are not.…

In this paper we analyse some questions concerning trees on $\kappa$, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in…

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…

Determining a Nash equilibrium in a $2$-player non-zero sum game is known to be PPAD-hard (Chen and Deng (2006), Chen, Deng and Teng (2009)). The problem, even when restricted to win-lose bimatrix games, remains PPAD-hard (Abbott, Kane and…

In this work we show that the ordering ambiguity on quantization depends on the representation choice. This property is then used to solve unambiguously some particular systems. Finally, we speculate on the consequences for more involved…

For which infinite cardinals $\kappa$ is there a partition of the real line $\mathbb R$ into precisely $\kappa$ Borel sets? Hausdorff famously proved that there is a partition of $\mathbb R$ into $\aleph_1$ Borel sets. But other than this,…

We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the reaping number $\mathfrak{r}$, the bounding number $\mathfrak{b}$, the dominating number $\mathfrak{d}$, and the additivity…

We present an overview of results on the question of whether the non-stationary ideal of an uncountable regular cardinal $\kappa$ can be defined by a $\Pi_1$-formula using parameters of hereditary cardinality at most $\kappa$. These results…

We introduce a new method, involving infinite games and Borel determinacy, which we use to answer several well-known questions in Borel combinatorics.

The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…

We investigate regularity properties derived from tree-like forcing notions in the setting of "generalized descriptive set theory", i.e., descriptive set theory on $\kappa^\kappa$ and $2^\kappa$, for regular uncountable cardinals $\kappa$.

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…

We introduce the game Slow $A$-Nim which generalizes a number of recently studied games. Slow $A$-Nim is played on $n$ stacks of tokens, and the set $A$ indicates the number of stacks a player can play on. Once a player has decided on the…

Game theory relies heavily on the availability of cardinal utility functions, but in fields such as matching markets, only ordinal preferences are typically elicited. The literature focuses on mechanisms with simple dominant strategies, but…

It is well known that artificial neural networks (ANNs) can learn deterministic automata. Learning nondeterministic automata is another matter. This is important because much of the world is nondeterministic, taking the form of…

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…

We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…

We provide game-theoretic proofs of some well-known existence theorems of Friedberg numberings for the class of all partial computable functions, including (1) the existence of two incomparable Friedberg numberings; (2) the existence of a…