Related papers: P-positions in Modular Extensions to Nim
A multi-player competitive Dynkin stopping game is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single…
Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is…
Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
In this paper, we consider hybrid uplink nonorthogonal multiple access (NOMA) that can support more users by exploiting the notion of power-domain NOMA. In hybrid uplink NOMA, we do not consider centralized power control as a base station…
Enemy strategies in turn-based games should be surprising and unpredictable. This study introduces Mirror Mode, a new game mode where the enemy AI mimics the personal strategy of a player to challenge them to keep changing their gameplay. A…
The game of memory is played with a deck of n pairs of cards. The cards in each pair are identical. The deck is shuffled and the cards laid face down. A move consists of flipping over first one card then another. The cards are removed from…
We investigate a class of reinforcement learning dynamics where players adjust their strategies based on their actions' cumulative payoffs over time - specifically, by playing mixed strategies that maximize their expected cumulative payoff…
Complexity develops via the incorporation of innovative properties. Chess is one of the most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
A \emph{bidding} game is played on a graph as follows. A token is placed on an initial vertex and both players are allocated budgets. In each turn, the players simultaneously submit bids that do not exceed their available budgets, the…
We calculated a fixed strategy that minimizes the average number of guesses (minimum strategy) for the number-guessing game MOO by exhaustive search. Although the minimum strategy for a similar game, mastermind, has been reported, this…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
This paper develops a mathematical framework for building a position in a stock over a fixed period of time while in competition with one or more other traders doing the same thing. We develop a game-theoretic framework that takes place in…
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by…
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…
This paper introduces a simulation algorithm for evaluating the log-likelihood function of a large supermodular binary-action game. Covered examples include (certain types of) peer effect, technology adoption, strategic network formation,…
We introduce a new model involving TU-games and exogenous structures. Specifically, we consider that each player in a population can choose an element in a strategy set and that, for every possible strategy profile, a TU-game is associated…