Related papers: Trapping the Ultimate Success
The concept of intransitiveness for games, which is the condition for which there is no first-player winning strategy can arise surprisingly, as happens in the Penney game, an extension of the heads or tails. Since a game can be converted…
We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer.…
We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the…
Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic…
A multi-player competitive Dynkin stopping game is constructed. Each player can either exit the game for a fixed payoff, determined a priori, or stay and receive an adjusted payoff depending on the decision of other players. The single…
We introduce and analyze a natural game formulated as follows. In this one-person game, the player is given a random permutation $A=(a_1,\dots, a_n)$ of a multiset $M$ of $n$ reals that sum up to $0$, where each of the $n!$ permutation…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
Acting as a goalkeeper in a video-game, a participant is asked to predict the successive choices of the penalty taker. The sequence of choices of the penalty taker is generated by a stochastic chain with memory of variable length. It has…
This paper investigates a partial-information pursuit evasion game in which the Pursuer has a limited-range sensor to detect the Evader. Given a fixed final time, we derive the optimal evasion strategy for the Evader to maximize its…
The technique of ``testing by betting" frames nonparametric sequential hypothesis testing as a multiple-round game, where a player bets on future observations that arrive in a streaming fashion, accumulates wealth that quantifies evidence…
When a game involves many agents or when communication between agents is not possible, it is useful to resort to distributed learning where each agent acts in complete autonomy without any information on the other agents' situations.…
Our research is closely related to ontological studies in mathematics. It provides crucial insights into the nature of decisions and strategies characterized by Markov moments. In a stopping game, a holistic decision-maker would evaluate…
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…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
Information uncertainty is one of the major challenges facing applications of game theory. In the context of Stackelberg games, various approaches have been proposed to deal with the leader's incomplete knowledge about the follower's…
Large parts of professional human communication proceed in a request-reply fashion, whereby requests contain specifics of the information desired while replies can deliver the required information. However, time limitations often force…
Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be…
We study a modification of the so-called Parrondo's paradox where a large number of individuals choose the game they want to play by voting. We show that it can be better for the players to vote randomly than to vote according to their own…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
To take advantage of strategy commitment, a useful tactic of playing games, a leader must learn enough information about the follower's payoff function. However, this leaves the follower a chance to provide fake information and influence…