相关论文: Multistep Bayesian strategy in coin-tossing games …

Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…

We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…

A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation…

We study the problem of learning a most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses until we identify a coin i* whose posterior probability of being most biased is at least…

Strategies for sustaining cooperation and preventing exploitation by selfish agents in repeated games have mostly been restricted to Markovian strategies where the response of an agent depends on the actions in the previous round. Such…

We study the problem of designing consistent sequential two-sample tests in a nonparametric setting. Guided by the principle of testing by betting, we reframe this task into that of selecting a sequence of payoff functions that maximize the…

Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…

We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…

This paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of…

The velocity-jump model is a specific type of piecewise deterministic Markov process in which an individual's velocity is constant except at times that form the events of some point process. It represents an interpretable continuous-time…

This paper investigates the dynamics of gambling and how they can affect risk-taking behavior in regions not explored by Kahneman and Tversky's Prospect Theory. Specifically, it questions why extreme outcomes do not fit the theory and…

Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or…

An important challenge in non-cooperative game theory is coordinating on a single (approximate) equilibrium from many possibilities - a challenge that becomes even more complex when players hold private information. Recommender mechanisms…

Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the…

In this paper we propose an investing strategy based on neural network models combined with ideas from game-theoretic probability of Shafer and Vovk. Our proposed strategy uses parameter values of a neural network with the best performance…

We introduce a new non-zero-sum game of optimal stopping with asymmetric exercise opportunities. Given a stochastic process modelling the value of an asset, one player observes and can act on the process continuously, while the other player…

In the multiarmed bandit problem a gambler chooses an arm of a slot machine to pull considering a tradeoff between exploration and exploitation. We study the stochastic bandit problem where each arm has a reward distribution supported in a…

In 1996, Mallozzi and Morgan [33] proposed a new model for Stackelberg games which we refer here to as the Bayesian approach. The leader has only partial information about how followers select their reaction among possibly multiple optimal…

In this paper, we consider zero-sum repeated games in which the maximizer is restricted to strategies requiring no more than a limited amount of randomness. Particularly, we analyze the maxmin payoff of the maximizer in two models: the…

The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games) has mostly been studied under the unrealistic assumption that we live in a continuous…