Related papers: The Swiss Gambit
This paper investigates a class of games with large strategy spaces, motivated by challenges in AI alignment and language games. We introduce the hidden game problem, where for each player, an unknown subset of strategies consistently…
A famous result in game theory known as Zermelo's theorem says that "in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all…
A match played in a sports tournament can be called stakeless if at least one team is indifferent to its outcome because it already has qualified or has been eliminated. Such a game threatens fairness since teams may not exert full effort…
Moves in chess games are usually analyzed on a case-by-case basis by professional players, but thanks to the availability of large game databases, we can envision another approach of the game. Here, we indeed adopt a very different point of…
The group draw of a sports tournament requires assigning teams to groups of (almost) the same size. The most important criteria for a draw procedure are balance, randomness, and transparency, which could not be satisfied simultaneously if…
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…
The centipede game is a two-player non-zero-sum game. Each turn, a player can choose whether they want to take or pass a growing reward. The classical, rational solution of this game shows defection in the first round, when in reality,…
In this work the properties of minority games containing agents which try to winning all the time are studied by means of computational simulations. We have considered several ways of introducing above the rules clever players using…
In the last round of the FIFA World Cup group stage, games for which the outcome does not affect the selection of the qualified teams are played with little enthusiasm. Furthermore, a team that has already qualified may take into account…
Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the bracket, these results ignore the prevalent…
In this work the properties of multi choice minority games are studied by means of extensive computational simulations. We have considered several ways of rewarding the strategies of the players and compared the resulting behaviours of the…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
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…
Researchers have explored the performance of Iterated Prisoner's Dilemma strategies for decades, from the celebrated performance of Tit for Tat to the introduction of the zero-determinant strategies and the use of sophisticated learning…
AI agents will be predictable in certain ways that traditional agents are not. Where and how can we leverage this predictability in order to improve social welfare? We study this question in a game-theoretic setting where one agent can pay…
In competitive resource allocation formulations multiple agents compete over different contests by committing their limited resources in them. For these settings, contest games offer a game-theoretic foundation to analyze how players can…
We characterize robust tournament design -- the prize scheme that maximizes the lowest effort in a rank-order tournament where the distribution of noise is unknown, except for an upper bound, $\bar{H}$, on its Shannon entropy. The robust…
Given a mapping from a set of players to the leaves of a complete binary tree (called a seeding), a knockout tournament is conducted as follows: every round, every two players with a common parent compete against each other, and the winner…
We explore a new way to evaluate generative models using insights from evaluation of competitive games between human players. We show experimentally that tournaments between generators and discriminators provide an effective way to evaluate…
The actions of intelligent agents, such as chatbots, recommender systems, and virtual assistants are typically not fully transparent to the user. Consequently, using such an agent involves the user exposing themselves to the risk that the…