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The Parrondo's paradox is a counterintuitive phenomenon where individually-losing strategies can be combined in producing a winning expectation. In this paper, the issues surrounding the Parrondo's paradox are investigated. The focus is…

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability…

Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other…

According to one of its founders, game theory would soon be a little over a hundred years old . A well-known theory in the academic and strategic fields, it is often the subject of criticism and, for many, seems too simplistic to be truly…

We have previously presented a critique of the standard Marshallian theory of the firm, and developed an alternative formulation that better agreed with the results of simulation. An incorrect mathematical fact was used in our previous…

In this article, we consider some simple combinatorial game and a winning strategy in this game. This game is then used to prove several known results about non-repetitive sequences and approximations with denominators from a lacunary…

We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by a n-player generalization trough the quantum minority games, and…

In this paper a new multiple access algorithm for cognitive radio networks based on game theory is presented. We address the problem of a multiple access system where the number of users and their types are unknown. In order to do this, the…

Research in adversarial machine learning (AML) has shown that statistical models are vulnerable to maliciously altered data. However, despite advances in Bayesian machine learning models, most AML research remains concentrated on classical…

We solve the game of Babylon when played with chips of two colors, giving a winning strategy for the second player in all previously unsolved cases.

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…

Consider a multiplayer game, and assume a system level objective function, which the system wants to optimize, is given. This paper aims at accomplishing this goal via potential game theory when players can only get part of other players'…

An infinite game on the set of real numbers appeared in Matthew Baker's work [Math. Mag. 80 (2007), no. 5, pp. 377--380] in which he asks whether it can help characterize countable subsets of the reals. This question is in a similar spirit…

The game theoretic concepts of rationalizability and iterated dominance are closely related and provide characterizations of each other. Indeed, the equivalence between them implies that in a two player finite game, the remaining set of…

This work lies in the fusion of experimental economics and data mining. It continues author's previous work on mining behaviour rules of human subjects from experimental data, where game-theoretic predictions partially fail to work.…

I give a simple analysis of the game that I previously published in Scientific American which shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled on a random walk, requires only…

A Bayesian player acting in an infinite multi-player game learns to predict the other players' strategies if his prior assigns positive probability to their play (or contains a grain of truth). Kalai and Lehrer's classic grain of truth…

In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial game is a two-player game with no chance and no hidden information, such as Go or Chess. In…

With the rise of advanced reasoning capabilities, large language models (LLMs) are receiving increasing attention. However, although reasoning improves LLMs' performance on downstream tasks, it also introduces new security risks, as…