This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic expectation for lower semicontinuous positive functionals. We consider a new broad de…
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48 results for “game-theoretic probability”
In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas…
We consider the game-theoretic scenario of testing the performance of Forecaster by Sceptic who gambles against the forecasts. Sceptic's current capital is interpreted as the amount of evidence he has found against Forecaster. Reporting the maximum of Sceptic's capital so far exaggerates the evidence. We characterize t…
This paper establishes a non-stochastic analogue of the celebrated result by Dubins and Schwarz about reduction of continuous martingales to Brownian motion via time change. We consider an idealized financial security with continuous price path, without making any stochastic assumptions. It is shown that typical price …
This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain a simple expression for the equity premium and derive a version of the capital a…
We propose a betting strategy based on Bayesian logistic regression modeling for the probability forecasting game in the framework of game-theoretic probability by Shafer and Vovk (2001). We prove some results concerning the strong law of large numbers in the probability forecasting game with side information based on …
We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be …
We give an exposition and numerical studies of upper hedging prices in multinomial models from the viewpoint of linear programming and the game-theoretic probability of Shafer and Vovk. We also show that, as the number of rounds goes to infinity, the upper hedging price of a European option converges to the solution of…
This work shows how evaluation metrics can be seen as fair gambles.
problem The relationship and evaluation of machine learning forecasts.
method Using game-theoretic probability, the authors show evaluation metrics as fair gambles.
result Standard evaluation metrics are fair gambler outcomes, with calibration and regret metrics on two dimensions.
The paper explores game-theoretic alignment of LLMs with human preferences, finding limitations and conditions.
problem Aligning LLMs with human preferences using game theory.
method Systematic study of payoff choices in a two-player zero-sum game for desirable alignment properties.
result Impossibility of preference matching in game-theoretic LLM alignment under standard assumptions.
A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness. This paper concentrates on "qualitative" results, stated in terms of order (or or…
Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we propose an actor-critic reinforcement learning algorithm that provably converges t…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to compute equilibria in games where the payoffs are probability distributions. Our appr…
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 until the previous round (trading day) for deciding the investment in the curren…
Game-theoretic models predict asset prices in financial markets.
problem Understanding price formation in financial markets with limited liquidity.
method Developed game-theoretic models for many-person and mean-field games, derived analytical formulas, and numerically assessed results.
result The derived price converges to the mean-field counterpart under specific conditions.
We investigate upper and lower hedging prices of multivariate contingent claims from the viewpoint of game-theoretic probability and submodularity. By considering a game between "Market" and "Investor" in discrete time, the pricing problem is reduced to a backward induction of an optimization over simplexes. For Europe…
Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by dr…
We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit arbitrary patterns of deviations of nature's moves from independent Bernoulli trial…
Game-theoretic model captures investor interactions for stock price forecasting.
problem Complex market dynamics driving stock price movements.
method Game-theoretic modeling of heterogeneous investor interactions in a dynamic graph structure.
result Our method outperforms state-of-the-art stock price forecasting methods.
Paper introduces metrics for evaluating multi-agent policies using best response dynamics.
problem Evaluation and ranking of multi-agent policies in reinforcement learning.
method Adopting strict best response dynamics (SBRD) to model selfish behaviors, proposing perturbed SBRD for dynamic and non-stationary settings.
result Proposed perturbed SBRD can observe policies with maximum metrics and differ from optimal by any given tolerance.
Optimization methods are used to determine equilibria of investment in cryptocurrencies. The basic assumptions involve existence of a core group (the "wealthy") that fears the loss of substantial assets through government seizure. Speculators constitute another group that tends to introduce volatility and risk for the …
One often finds in the literature connections between measures of fairness and measures of feature importance employed to interpret trained classifiers. However, there seems to be no study that compares fairness measures and feature importance measures. In this paper we propose ways to evaluate and compare such measure…
A game-theoretic framework identifies influential hyperparameters for neural networks.
problem Understanding which hyperparameters are most important for neural network performance.
method Employing Shapley Effects for global sensitivity analysis and Pareto front sets for identifying effective configurations.
result Reveals which hyperparameters are most influential for different objectives in neural networks.
We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk \cite{sv}. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergen…
In this article we consider a game theoretic approach to the Risk-Sensitive Benchmarked Asset Management problem (RSBAM) of Davis and Lleo \cite{DL}. In particular, we consider a stochastic differential game between two players, namely, the investor who has a power utility while the second player represents the market …
Paper proposes a game-theoretic approach to generate unlearnable examples.
problem Generating imperceptible perturbations to degrade deep learning models.
method Formulated as a Stackelberg game, proposing a novel attack method GUE.
result GUE effectively poisons models with minimal training data and generalizes well.
We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can dep…
GT-DDP optimizer trains residual networks using game theory.
problem Applying DDP to residual networks.
method Game-theoretic DDP optimizer for residual networks.
result Improved training convergence and variance reduction.
In this paper, we propose a gamification approach as a novel framework for smart building infrastructure with the goal of motivating human occupants to reconsider personal energy usage and to have positive effects on their environment. Human interaction in the context of cyber-physical systems is a core component and c…
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From t…
Energy game-theoretic frameworks have emerged to be a successful strategy to encourage energy efficient behavior in large scale by leveraging human-in-the-loop strategy. A number of such frameworks have been introduced over the years which formulate the energy saving process as a competitive game with appropriate incen…
We study the origins of the effect in finance and SDE. In particular, we show, in the game-theoretic framework, that market volatility is a consequence of the absence of riskless opportunities for making money and that too high volatility is also incompatible with such opportunities. More precisely, riskles…
Predicting the outcomes of integrating Unmanned Aerial Systems (UAS) into the National Aerospace (NAS) is a complex problem which is required to be addressed by simulation studies before allowing the routine access of UAS into the NAS. This thesis focuses on providing 2D and 3D simulation frameworks using a game theore…
Mind the Gap in the Mining Gameq-fin.GN
Game-theoretic analysis of mining gaps in blockchain systems.
problem Strategic mining behavior and its impact on blockchain stability.
method Game-theoretic model and Nash equilibrium analysis.
result Mining gaps can destabilize blockchain systems, especially with decreasing block rewards.
New method for evaluating LLMs reduces bias in open-ended evaluations.
problem Bias in Elo-based ratings of LLMs due to data redundancies.
method Proposes evaluation as a 3-player game and introduces novel solution concepts.
result Novel method leads to more robust and intuitive ratings.
The paper improves dropout's utility by reducing interactions in deep neural networks.
problem Over-fitting problem in deep learning.
method Game-theoretic interactions analysis and interaction loss.
result Interaction loss improves dropout's utility and boosts DNN performance.
This paper studies two important signal processing aspects of equilibrium behavior in non-cooperative games arising in social networks, namely, reinforcement learning and detection of equilibrium play. The first part of the paper presents a reinforcement learning (adaptive filtering) algorithm that facilitates learning…
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem is seen as a two-players zero-sum game. An algorithm is proposed to incremental…
We solve a continuous-time game-theoretic problem for Kihlstrom-Mirman preferences.
problem Dynamic inconsistency in preferences due to multiattribute utility theory.
method Formalized an equilibrium control theory for continuous-time Markov processes.
result Equilibrium strategy and value function as solution to extended HJB system.
The paper solves investment problems with uncertain factors using game theory.
problem Optimal forward investment in an incomplete market with model uncertainty.
method Combining stochastic differential games and ergodic BSDE approach.
result Representation of robust forward performance processes in factor form.
The paper analyzes how mutable blockchain protocols affect miner behavior and strategic stability.
problem The mutability of blockchain protocols undermines long-term planning and cooperative equilibria.
method Integrates Austrian capital theory with repeated game theory to examine miner behavior under different institutional conditions.
result Effective time preference increases when protocol rules are mutable, leading to political rent-seeking and undermining strategic coherence.
End-to-end model predicts multiagent trajectories using game theory and neural nets.
problem Predicting trajectories of interacting agents in complex scenarios.
method Hybrid neural net with game-theoretic reasoning, using implicit layers to map preferences to Nash equilibria.
result Trains an interpretable model that predicts future trajectories and transfers to decision making.
Unsupervised domain adaptation (UDA) amounts to assigning class labels to the unlabeled instances of a dataset from a target domain, using labeled instances of a dataset from a related source domain. In this paper, we propose to cast this problem in a game-theoretic setting as a non-cooperative game and introduce a ful…
Paper analyzes adversarial attacks and defenses using game theory.
problem Unclear conditions for optimal attacks and defenses in adversarial learning.
method Game-theoretic framework with locally linear decision boundary model.
result Fast Gradient Method attack and Randomized Smoothing defense form a Nash Equilibrium.
For a monotonically advancing front, the arrival time is the time when the front reaches a given point. We show that it is twice differentiable everywhere with uniformly bounded second derivative. It is smooth away from the critical points where the equation is degenerate. We also show that the critical set has finite …
Proposes CoPO, a new policy optimization method for competitive games.
problem Designing efficient optimization methods for competitive Markov decision processes.
method Competitive policy optimization (CoPO) approach that exploits game-theoretic nature of competitive games.
result Stable optimization, convergence to sophisticated strategies, and higher scores compared to baseline methods.
Decentralised optimisation tasks are important components of multi-agent systems. These tasks can be interpreted as n-player potential games: therefore game-theoretic learning algorithms can be used to solve decentralised optimisation tasks. Fictitious play is the canonical example of these algorithms. Nevertheless fic…
It is now well known that decentralised optimisation can be formulated as a potential game, and game-theoretical learning algorithms can be used to find an optimum. One of the most common learning techniques in game theory is fictitious play. However fictitious play is founded on an implicit assumption that opponents' …