Related papers: Infinitely many absolute universes
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
In set theory without the axiom of regularity, we consider a game in which two players choose in turn an element of a given set, an element of this element, etc.; a player wins if its adversary cannot make any next move. Sets that are…
Attack--defense trees are used to describe security weaknesses of a system and possible countermeasures. In this paper, the connection between attack--defense trees and game theory is made explicit. We show that attack--defense trees and…
The aim of this of this paper is to study infinite games and to prove formally some properties in this framework. As a consequence we show that the behavior (the madness) of people which leads to speculative crashes or escalation can be…
This note will address the issue of the existence of God from a game theoretic perspective. We will show that, under certain assumptions, man cannot simultaneously be (i) rational and (ii) believe that an infinitely powerful God exists.…
We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…
We introduce a misere quotient semigroup construction in impartial combinatorial game theory, and argue that it is the long-sought natural generalization of the normal-play Sprague-Grundy theory to misere play. Along the way, we illustrate…
This paper introduces a new solution concept for non-cooperative games in normal form with no ties and pure strategies: the Perfectly Transparent Equilibrium. The players are rational in all possible worlds and know each other's strategies…
LP-duality theory has played a central role in the study of the core, right from its early days to the present time. However, despite the extensive nature of this work, basic gaps still remain. We address these gaps using the following…
In this work, we discuss a number game that develops in a manner similar to that on which Gilbreath's conjecture on iterated absolute differences between consecutive primes is formulated. In our case the action occurs at the exponent level…
We prove that chess played on the infinite chessboard $\mathbb{Z}^2$ with infinitely many pieces is as powerful as it could possibly be, by showing that every open Gale-Stewart game with draws is strategically equivalent to some infinite…
The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…
We propose a model for games in which the players have shared access to a blockchain that allows them to deploy smart contracts to act on their behalf. This changes fundamental game-theoretic assumptions about rationality since a contract…
Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its…
We formulate and analyze game-theoretic problems for systems governed by integral equations. For Volterra integral equations, we obtain and prove necessary and sufficient conditions for linear-quadratic problems, and for problems that are…
Games, in their mathematical sense, are everywhere (game industries, economics, defense, education, chemistry, biology, ...).Search algorithms in games are artificial intelligence methods for playing such games. Unfortunately, there is no…
We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…
We prove the almost equivalence of the minimax theorem and the strong duality theorem for a large class of games and conic programs. The previous fundamental results on the equivalence of linear programming and two-player zero-sum games…