Related papers: Trapping the Ultimate Success
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…
We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse…
Suppose $N$ independent Bernoulli trials are observed sequentially at random times of a mixed binomial process. The task is to maximise, by using a nonanticipating stopping strategy, the probability of stopping at the last success. We focus…
Given a finite sequence of events and a well-defined notion of events being interesting, the Odds-theorem (Bruss (2000)) gives an online strategy to stop on the last interesting event. It is optimal for independent events. Here we study…
We study a continuous-time stochastic Stackelberg game in which a leader seeks to accomplish a primary objective while inferring a hidden parameter of a rational follower. The follower solves an entropy-regularized tracking problem and…
We provide a general approach to reformulating any continuous-time stochastic Stackelberg differential game under closed-loop strategies as a single-level optimisation problem with target constraints. More precisely, we consider a…
We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…
The Stackelberg equilibrium solution concept describes optimal strategies to commit to: Player 1 (termed the leader) publicly commits to a strategy and Player 2 (termed the follower) plays a best response to this strategy (ties are broken…
We study a game in which one keeps flipping a coin until a given finite string of heads and tails occurs. We find the expected number of coin flips to end the game when the ending string consists of at most four maximal runs of heads or…
We consider the Last-Success-Problem with $n$ independent Bernoulli random variables with parameters $p_i>0$. We improve the lower bound provided by F.T. Bruss for the probability of winning and provide an alternative proof to the one given…
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…
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…
We develop an approach to solve Barberis (2012)'s casino gambling model in which a gambler whose preferences are specified by the cumulative prospect theory (CPT) must decide when to stop gambling by a prescribed deadline. We assume that…
Based on NFL game data we try to predict the outcome of a play in multiple different ways. An application of this is the following: by plugging in various play options one could determine the best play for a given situation in real time.…
In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum…
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
This paper discusses the gambling contest introduced in Seel & Strack (Gambling in contests, Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 375, Mar 2012.) and considers the impact of adding a penalty…
Recent results in the ML community have revealed that learning algorithms used to compute the optimal strategy for the leader to commit to in a Stackelberg game, are susceptible to manipulation by the follower. Such a learning algorithm…
A decision maker observes the evolving state of the world while constantly trying to predict the next state given the history of past states. The ability to benefit from such predictions depends not only on the ability to recognize patters…
We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…