Related papers: Taming the wild in impartial combinatorial games

We introduce a simple extension of the minority game in which the market rewards contrarian (resp. trend-following) strategies when it is far from (resp. close to) efficiency. The model displays a smooth crossover from a regime where…

One common assumption in game theory is that any player optimizes a utility function that takes into account only its own payoff. However, it has long been observed that in real life players may adopt an altruistic or even spiteful…

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum…

Number games play a central role in alternating normal play combinatorial game theory due to their real-number-like properties (Conway 1976). Here we undertake a critical re-examination: we begin with integer and dyadic games and identify…

In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the…

We discuss a set of computational techniques, called Inductive Game Theory, for extracting strategic decision-making rules from time series data and constructing probabilistic social circuits. We construct these circuits by connecting…

This paper introduces a notion of presentation for locally inverse semigroups and develops a graph structure to describe the elements of locally inverse semigroups given by these presentations. These graphs will have a role similar to the…

In combinatorial game theory, the winning player for a position in normal play is analyzed and characterized via algebraic operations. Such analyses define a value for each position, called a game value. A game (ruleset) is called universal…

We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master…

In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…

Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This pa- per suggests an approach to this problem in the framework of a non- cooperative game theory. Definition of…

We propose an abstract approach to coalition formation that focuses on simple merge and split rules transforming partitions of a group of players. We identify conditions under which every iteration of these rules yields a unique partition.…

We apply Game Theory to a mathematical representation of two competing teams of agents connected within a complex network, where the ability of each side to manoeuvre their resource and degrade that of the other depends on their ability to…

Game comonads, introduced by Abramsky, Dawar and Wang, and developed by Abramsky and Shah, give a categorical semantics for model comparison games. We present an axiomatic account of Feferman-Vaught-Mostowski (FVM) composition theorems…

In this note, we investigate combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random). In this model, we provide closed-form expressions for the expected number of turns in a…

Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

The Minority Game is a simple model for the collective behavior of agents in an idealized situation where they have to compete through adaptation for a finite resource. This review summarizes the statistical mechanics community efforts to…

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…

This dissertation highlights connections between the fields of neural networks, game theory and time series generation. The concept of antipredictability is explained, and the properties of time series that are antipredictable for several…