Related papers: Sun Bin's Legacy
We consider the problem of a learning agent who has to repeatedly play a general sum game against a strategic opponent who acts to maximize their own payoff by optimally responding against the learner's algorithm. The learning agent knows…
In how many ways can $n$ queens be placed on an $n \times n$ chessboard so that no two queens attack each other? This is the famous $n$-queens problem. Let $Q(n)$ denote the number of such configurations, and let $T(n)$ be the number of…
We introduce a new virtual environment for simulating a card game known as "Big 2". This is a four-player game of imperfect information with a relatively complicated action space (being allowed to play 1,2,3,4 or 5 card combinations from an…
We consider repeated multi-unit auctions with uniform pricing, which are widely used in practice for allocating goods such as carbon licenses. In each round, $K$ identical units of a good are sold to a group of buyers that have valuations…
Spiro, Surya and Zeng (Electron. J. Combin. 2023; arXiv:2207.11272) recently studied a semi-restricted variant of the well-known game Rock, Paper, Scissors; in this variant the game is played for $3n$ rounds, but one of the two players is…
We analyze the following version of the deterministic \hats game. We have a graph $G$, and a sage resides at each vertex of $G$. When the game starts, an adversary puts on the head of each sage a hat of a color arbitrarily chosen from a set…
Challenge the Champ is a simple tournament format, where an ordering of the players -- called a seeding -- is decided. The first player in this order is the initial champ, and faces the next player. The outcome of each match decides the…
In lowest unique bid auctions, $N$ players bid for an item. The winner is whoever places the \emph{lowest} bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium…
In a seminal paper, Meyer [David Meyer, Phys. Rev. Lett. 82, 1052 (1999)] described the advantages of quantum game theory by looking at the classical penny flip game. A player using a quantum strategy can win against a classical player…
In this work a balanced k-way partitioning problem with weight constraints is defined to model the sports team realignment. Sports teams must be partitioned into a fixed number of groups according to some regulations, where the total…
Within the framework of Game Theory, contests study decision-making in those situations or conflicts when rewards depend on the relative rank between contenders rather than their absolute performance. By relying on the formalism of Tullock…
"Guess Who?" is a popular two player game where players ask "Yes"/"No" questions to search for their opponent's secret identity from a pool of possible candidates. This is modeled as a simple stochastic game. Using this model, the optimal…
This paper presents an efficient algorithm to solve the sleeping bandit with multiple plays problem in the context of an online recommendation system. The problem involves bounded, adversarial loss and unknown i.i.d. distributions for arm…
In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with a lower and upper bound. An axiomatic approach is applied to the problem of…
Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team…
In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum ("tragedy of the commons"). Is the routing of traffic a similar problem? In order to address this question, we present…
We consider the manipulability of tournament rules for round-robin tournaments of $n$ competitors. Specifically, $n$ competitors are competing for a prize, and a tournament rule $r$ maps the result of all $\binom{n}{2}$ pairwise matches…
The game of Hex has two players who take turns placing stones of their respective colors on the hexagons of a rhombus-shaped hexagonal grid. Black wins by completing a crossing between two opposite edges, while White wins by completing a…
We study a sequential resource allocation problem between a fixed number of arms. On each iteration the algorithm distributes a resource among the arms in order to maximize the expected success rate. Allocating more of the resource to a…
When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average…