Related papers: Beyond Parrondo's paradox
Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…
This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same…
In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce…
One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma, namely the Prisoner's Dilemma. Specifically, for a…
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…
Public Goods Games represent one of the most useful tools to study group interactions between individuals. However, even if they could provide an explanation for the emergence and stability of cooperation in modern societies, they are not…
In this work we reexamine the EPR paradox for composite systems with a finite number of levels. The analysis emphasizes the connection between measurements and conditional probabilities. This connection implies that when a measurement is…
We investigate how Simpson's paradox affects analysis of trends in social data. According to the paradox, the trends observed in data that has been aggregated over an entire population may be different from, and even opposite to, those of…
This paper discusses the dual interpretation of the Jeffreys--Lindley's paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to…
An optical model of classical photons propagating through array of many beam splitters is developed to give a physical analogy of Parrondo's game and Parrondo-Harmer-Abbott game. We showed both the two games are reasonable game without…
I think we can agree that dealing with uncertainty is not easy. Probability is the main tool for dealing with uncertainty, and we know there are many probability-related puzzles and paradoxes. Here I describe a rather idiosyncratic…
Recently there has been much interest in discrete forms of Brownian ratchets, using a game-theoretic formalism. Using the approach pioneered by Parrondo, we develop a new method for obtaining the stationary probabilities and probability…
A strategy for playing the game of roulette is presented in this paper. The strategy is based on the same probabilistic argument that leads to the well-known Birthday Paradox in Probability theory. Following the strategy, a player will have…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
In game theory, the notion of a player's beliefs about the game players' beliefs about other players' beliefs arises naturally. In this paper, we present a non-self-referential paradox in epistemic game theory which shows that completely…
The Perron-Frobenius theorem plays an important role in many areas of management science and operations research. This paper provides a probabilistic perspective on the theorem, by discussing a proof that exploits a probabilistic…
We study the mathematical properties of probabilistic processes in which the independent actions of $n$ players (`causes') can influence the outcome of each player (`effects'). In such a setting, each pair of outcomes will generally be…
In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which…
We introduce a betting game, where the gambler aims to guess the last success epoch from past observed data. The player may bet on the event that no further successes occur, or choose a `trap' which is any span of future times. In the…
The General Lotto game is a popular variant of the famous Colonel Blotto game, in which two opposing players allocate limited resources over many battlefields. In this paper, we consider incomplete and asymmetric information formulations…