Related papers: When to Quit Gambling, if You Must!
This paper studies a dynamic discrete-time queuing model where at every period players get a new job and must send all their jobs to a queue that has a limited capacity. Players have an incentive to send their jobs as late as possible;…
Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target…
Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…
In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…
Cumulative prospect theory (CPT) is the first theory for decision-making under uncertainty that combines full theoretical soundness and empirically realistic features [P.P. Wakker - Prospect theory: For risk and ambiguity, Page 2]. While…
There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein, charges an agent for doing costly computation; the second, initiated by Neyman, does not charge for…
I study collective dynamic information acquisition. Players decide when to stop sequential sampling via a collective stopping rule, which specifies decisive coalitions that can terminate information acquisition upon agreement. I develop a…
Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent…
No matter how much some gamblers occasionally win, as long as they continue to gamble, sooner or later they will lose more to the casino, which is the so-called long bet will lose. Our results demonstrate the counter-intuitive phenomenon,…
In this paper, we propose a new multi-armed bandit problem called the Gambler's Ruin Bandit Problem (GRBP). In the GRBP, the learner proceeds in a sequence of rounds, where each round is a Markov Decision Process (MDP) with two actions…
Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth $W_t$ quantifies the evidence against the null hypothesis after $t$ rounds, and the null…
One way to make decisions under uncertainty is to select an optimal option from a possible range of options, by maximizing the expected utilities derived from a probability model. However, under severe uncertainty, identifying precise…
Consider a game consisting of independent turns with even money payoffs in which the player wins with a fixed probability $p \geq 1/3$ and loses with probability $1 - p$. The Labouchere system is a betting strategy which entails keeping a…
In the best choice problem with random arrivals, an unknown number $n$ of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with…
We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We…
We investigate the problem of cumulative regret minimization for individual sequence prediction with respect to the best expert in a finite family of size K under limited access to information. We assume that in each round, the learner can…
In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…
In this article, inspired by Shi, et al. we investigate the optimal portfolio selection with one risk-free asset and one risky asset in a multiple period setting under cumulative prospect theory (CPT). Compared with their study, our novelty…
Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
The setting of the classic prophet inequality is as follows: a gambler is shown the probability distributions of $n$ independent, non-negative random variables with finite expectations. In their indexed order, a value is drawn from each…