Related papers: Impartial Scoring Play Games
In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify…
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…
Estimating discrete games of complete information is often computationally difficult due to partial identification and the absence of closed-form moment characterizations. This paper proposes computationally tractable approaches to…
The Sprague-Grundy (SG) theory reduces the sum of impartial games to the classical game of $NIM$. We generalize the concept of sum and introduce $\cH$-combinations of impartial games for any hypergraph $\cH$. In particular, we introduce the…
This paper analyses Escard\'o and Oliva's generalisation of selection functions over a strong monad from a game-theoretic perspective. We focus on the case of the nondeterminism (finite nonempty powerset) monad $\mathcal{P}$. We use these…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD…
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and intensional variants of the type theory with dependent function,…
We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
AlphaZero-style reinforcement learning (RL) algorithms have achieved superhuman performance in many complex board games such as Chess, Shogi, and Go. However, we showcase that these algorithms encounter significant and fundamental…
We analyze inertial coordination games: dynamic coordination games with an endogenously changing state that depends on (i) a persistent fundamental players privately learn about over time; and (ii) past play. The speed of learning…
In this work, we consider the design of Non-Obviously Manipulable (NOM) mechanisms, mechanisms that bounded rational agents may fail to recognize as manipulable, for two relevant classes of succinctly representable Hedonic Games: Additively…
Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation is an important tool to…
We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which…
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…
Strategic interactions between competitive entities are generally considered from the perspective of complete revelation of benefits achieved from those interactions, in the form of public payoff functions and/or beliefs, in the announced…
We propose the study of mathematical ludology, which aims to formally interrogate questions of interest to game studies and game design in particular. The goal is to extend our mathematical understanding of complex games beyond…
Game-theoretic characterizations of process equivalences traditionally form a central topic in concurrency; for example, most equivalences on the classical linear-time / branching-time spectrum come with such characterizations. Recent work…