Related papers: The Gambler's Problem and Beyond
We introduce a method based on the Public Goods Game for solving optimization tasks. In particular, we focus on the Traveling Salesman Problem, i.e. a NP-hard problem whose search space exponentially grows increasing the number of cities.…
We consider a number of questions related to tradeoffs between reward and regret in repeated gameplay between two agents. To facilitate this, we introduce a notion of $\textit{generalized equilibrium}$ which allows for asymmetric regret…
This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the…
Behavioral experiments on the ultimatum game (UG) reveal that we humans prefer fair acts, which contradicts the prediction made in orthodox Economics. Existing explanations, however, are mostly attributed to exogenous factors within the…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
In online betting, the bookmaker can update the payoffs it offers on a particular event many times before the event takes place, and the updated payoffs may depend on the bets accumulated thus far. We study the problem of bookmaking with…
Optimal probabilistic approach in reinforcement learning is computationally infeasible. Its simplification consisting in neglecting difference between true environment and its model estimated using limited number of observations causes…
We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step…
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…
The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions…
Reinforcement learners are agents that learn to pick actions that lead to high reward. Ideally, the value of a reinforcement learner's policy approaches optimality--where the optimal informed policy is the one which maximizes reward.…
This work considers two-player zero-sum semi-Markov games with incomplete information on one side and perfect observation. At the beginning, the system selects a game type according to a given probability distribution and informs to Player…
The purpose of this article is to propose a new "theory," the Strategic Analysis of Financial Markets (SAFM) theory, that explains the operation of financial markets using the analytical perspective of an enlightened gambler. The gambler…
In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the…
A growing body of computational studies shows that simple machine learning agents converge to cooperative behaviors in social dilemmas, such as collusive price-setting in oligopoly markets, raising questions about what drives this outcome.…
This paper is dedicated to the application of reinforcement learning combined with neural networks to the general formulation of user scheduling problem. Our simulator resembles real world problems by means of stochastic changes in…
Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions which focus on policy…
This work considers a repeated principal-agent bandit game, where the principal can only interact with her environment through the agent. The principal and the agent have misaligned objectives and the choice of action is only left to the…
This work introduces a unified framework for analyzing games in greater depth. In the existing literature, players' strategies are typically assigned scalar values, and equilibrium concepts are used to identify compatible choices. However,…