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In trick-taking card games, a two-step process of state sampling and evaluation is widely used to approximate move values. While the evaluation component is vital, the accuracy of move value estimates is also fundamentally linked to how…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…
Reasoning is not just about solving problems -- it is also about evaluating which problems are worth solving at all. Evaluations of artificial intelligence (AI) systems primarily focused on problem solving, historically by studying how…
In this paper, we examine team ball sports to investigate how the likelihood of weaker teams winning against stronger ones, referred to as underdog achievement, is influenced by inherent randomness factors that affect match outcomes in such…
Game theory provides an effective way to model strategic interactions among rational agents. In the context of formal verification, these ideas can be used to produce guarantees on the correctness of multi-agent systems, with a diverse…
Commuters looking for the shortest path to their destinations, the security of networked computers, hedge funds trading on the same stocks, governments and populations acting to mitigate an epidemic, or employers and employees agreeing on a…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
People can evaluate features of problems and their potential solutions well before we can effectively solve them. When considering a game we have never played, for instance, we might infer whether it is likely to be challenging, fair, or…
Utilitarian games such as dictator games to measure fairness have been studied in the social sciences for decades. These games have given us insight into not only how humans view fairness but also in what conditions the frequency of…
Efforts to promote equitable public policy with algorithms appear to be fundamentally constrained by the "impossibility of fairness" (an incompatibility between mathematical definitions of fairness). This technical limitation raises a…
In each round of a Swiss-system tournament, players of similar score are paired against each other. An intentional early loss therefore might lead to weaker opponents in later rounds and thus to a better final tournament result - a…
An analysis of several important aspects of competition or conflict in games, social choice and decision theory is presented. Inherent difficulties and complexities in cooperation are highlighted. These have over the years led to a certain…
Simple stochastic games are turn-based 2.5-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a…
We review recent numerical results on the role of talent and luck in getting success by means of a schematic agent-based model. In general the role of luck is found to be very relevant in order to get success, while talent is necessary but…
The rationalizability concept was introduced in \cite{Ber84} and \cite{Pea84} to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number…
Using game and probability theories, I study the French popular game 421, a perfect information stochastic stage game. The problem is to find strategies maximizing the probability of some expected utility. I only solve a player's round…
Tanking, the act of deliberately dropping points or losing a game in order to gain some other advantage, is usually seen as being against the spirit of sports. It can be even more serious if playing a draw is a (weakly) dominant strategy…
The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk…