Related papers: Repetition in Permutation Wordle

This paper considers repeated games in which one player has more information about the game than the other players. In particular, we investigate repeated two-player zero-sum games where only the column player knows the payoff matrix A of…

Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…

In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. This work is about the complexity behind these proofs: how hard is it to actually…

Iterated coopetitive games capture the situation when one must efficiently balance between cooperation and competition with the other agents over time in order to win the game (e.g., to become the player with highest total utility).…

Applying neural network (NN) methods in games can lead to various new and exciting game dynamics not previously possible. However, they also lead to new challenges such as the lack of large, clean datasets, varying player skill levels, and…

Simulating bipartite games, such as the trust game, is not straightforward due to the lack of a natural way to distinguish roles in a single population. The square lattice topology can provide a simple yet elegant solution by alternating…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

We use replicator dynamics to study an iterated prisoners' dilemma game with memory. In this study, we investigate the characteristics of all 32 possible strategies with a single-step memory by observing the results when each strategy…

Buy low, sell high is one of the basic rules of thumb used in investment, although it is not considered to be a beneficial strategy. In this paper, we show how the appropriate permutation-based representation (i.e., the epistemic form) of a…

We present tournament results and several powerful strategies for the Iterated Prisoner's Dilemma created using reinforcement learning techniques (evolutionary and particle swarm algorithms). These strategies are trained to perform well…

Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…

A comply/constrain game or a game with a Muller twist is a game where the next player is allowed to place constraints on opponent's next move. We develop a closed form formula for the Grundy value of the single-pile subtraction game where…

This work is a contribution to the study of rewrite games. Positions are finite words, and the possible moves are defined by a finite number of local rewriting rules. We introduce and investigate taking-and-merging games, that is, where…

We study the quality of outcomes in repeated games when the population of players is dynamically changing and participants use learning algorithms to adapt to the changing environment. Game theory classically considers Nash equilibria of…

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even…

In this missive, the author goes about ruining an online word guessing game called Wordle, by generally trying to mathify the whole thing. On the other hand, one might consider that the author is trying to spice up mathematics by applying…

We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is riffle-shuffled exactly one time. Given a value $p\in(0{,}1)\setminus\{\frac12\}$, the riffle shuffle is assumed to be…

It is well known that in games with imperfect information, such as poker, bluffing with some probability can be a component of the optimal strategy. However, as far as we know, nobody has ever exhibited a Scrabble position in which the…

We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…

We extend the formalism of Conjectural Variations games to Stackelberg games involving multiple leaders and a single follower. To solve these nonconvex games, a common assumption is that the leaders compute their strategies having perfect…