相关论文: Lattice games without rational strategies
We provide an epistemic analysis of arbitrary strategic games based on possibility correspondences. We first establish a generic result that links true common beliefs (and, respectively, common knowledge) of players' rationality defined by…
In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies.…
We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations…
Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z^d}$ which tiles that lattice by translations, in fact tiles periodically. We announce here a disproof of this conjecture for sufficiently large $d$, which…
Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…
A notion of incentive for agents is introduced which leads to a very general notion of an equilibrium for a finite game. Sufficient conditions for the existence of these equilibria are given. Known existence theorems are shown to be…
The assumptions of necessary rationality and necessary knowledge of strategies, also known as perfect prediction, lead to at most one surviving outcome, immune to the knowledge that the players have of them. Solutions concepts implementing…
Let each site of the square lattice $\mathbb{Z}^2$ be independently assigned one of three states: a \textit{trap} with probability $p$, a \textit{target} with probability $q$, and \textit{open} with probability $1-p-q$, where $0<p+q<1$.…
This article investigates an evolutionary game based on the framework of interacting particle systems. Each point of the square lattice is occupied by a player who is characterized by one of two possible strategies and is attributed a…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for…
We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw -- both…
We construct a linear system non-local game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
There are two well-known sufficient conditions for Nash equilibrium in two-player games: mutual knowledge of rationality (MKR) and mutual knowledge of conjectures. MKR assumes that the concept of rationality is mutually known. In contrast,…
We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger…
Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
Refutation calculi are formal systems developed to derive the invalid formulas of a given logic. While the notion of refutation calculi has played a key role in the development of tableaux calculi, a refutation approach to display calculi…