Related papers: When to Quit Gambling, if You Must!
Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, $U$ and $D$. A gambler gains 1 point for each occurrence of $U$ (including overlapping occurrences) and loses 1 point for each…
We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…
We study zero-sum games, a variant of the classical combinatorial Subtraction games (studied for example in the monumental work "Winning Ways", by Berlekamp, Conway and Guy), called Cumulative Subtraction (CS). Two players alternate in…
In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…
When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…
We study a novel variant of the multi-armed bandit problem, where at each time step, the player observes an independently sampled context that determines the arms' mean rewards. However, playing an arm blocks it (across all contexts) for a…
Game theory has grown into a major field over the past few decades, and poker has long served as one of its key case studies. Game-Theory-Optimal (GTO) provides strategies to avoid loss in poker, but pure GTO does not guarantee maximum…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
We carry out a game-theoretic analysis of the recursive game "Guts," a variant of poker featuring repeated play with possibly growing stakes. An interesting aspect of such games is the need to account for funds lost to all players if…
In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…
Using results from neurobiology on perceptual decision making and value-based decision making, the problem of decision making between lotteries is reformulated in an abstract space where uncertain prospects are mapped to corresponding…
We consider various probabilistic games with piles for one player or two players. In each round of the game, a player randomly chooses to add $a$ or $b$ chips to his pile under the condition that $a$ and $b$ are not necessarily positive. If…
In this paper, we propose a probabilistic game-theoretic model to study the properties of the worst-case regret of the greedy strategy under complete (Knightian) uncertainty. In a game between a decision-maker (DM) and an adversarial agent…
We study a sequential coin-flipping game in which a player starts with~$n$ coins, each landing heads independently with probability~$p$. In each round the player flips all remaining coins and must set aside at least one coin showing heads;…
We consider a variant of sequential testing by betting where, at each time step, the statistician is presented with multiple data sources (arms) and obtains data by choosing one of the arms. We consider the composite global null hypothesis…
Composition theory can be used to analyze and enumerate the number of ways a dealer in Blackjack can reach any given point total. The rules of Blackjack provide several restrictions on the number of compositions of a given number. While…
In this paper we consider stopping problems with partial observation under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. Our aim is to maximize the certainty equivalent of the stopping…
While traditional economics assumes that humans are fully rational agents who always maximize their expected utility, in practice, we constantly observe apparently irrational behavior. One explanation is that people have limited…
A gambler moves between the vertices $1, \ldots, n$ of a graph using the probability distribution $p_{1}, \ldots, p_{n}$. Multiple cops pursue the gambler on the graph, only being able to move between adjacent vertices. We investigate the…
Decision-making problems can be modeled as combinatorial optimization problems with Constraint Programming formalisms such as Constrained Optimization Problems. However, few Constraint Programming formalisms can deal with both optimization…