Related papers: Mis\`ere Greedy Nim and Mis\`ere Bounded Greedy Ni…

Let A be a finite subset of $\nat$. Then NIM(A;n) is the following 2-player game: initially there are $n$ stones on the board and the players alternate removing $a\in A$ stones. The first player who cannot move loses. This game has been…

A group of students in 7-9 grades are inventing combinatorial impartial games. The games are played on graphs, piles, and grids. We found winning positions, optimal strategies, and other interesting facts about the games.

We consider two-player random extensive form games where the payoffs at the leaves are independently drawn uniformly at random from a given feasible set C. We study the asymptotic distribution of the subgame perfect equilibrium outcome for…

Public goods games study the incentives of individuals to contribute to a public good and their behaviors in equilibria. In this paper, we examine a specific type of public goods game where players are networked and each has binary actions,…

In the classical Binary Networked Public Goods (BNPG) game, a player can either invest in a public project or decide not to invest. Based on the decisions of all the players, each player receives a reward as per his/her utility function.…

We study a new class of games which generalizes congestion games and its bottleneck variant. We introduce congestion games with mixed objectives to model network scenarios in which players seek to optimize for latency and bandwidths alike.…

We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…

We introduce a novel multi-armed bandit framework, where each arm is associated with a fixed unknown credal set over the space of outcomes (which can be richer than just the reward). The arm-to-credal-set correspondence comes from a known…

In many applications, we want to influence the decisions of independent agents by designing incentives for their actions. We revisit a fundamental problem in this area, called GAME IMPLEMENTATION: Given a game in standard form and a set of…

We study a stopping game of preemption type between two players who both act under uncertain competition. In this framework we introduce, and study the effect of, (i) asymmetry of payoffs, allowing e.g. for different investment costs, and…

We give a weak solution for an impartial game we called ``Inverse Treblecross''. We have determined which of its starting positions are $\mathscr{P}$-position and give a reasonable strategy.

Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games…

We study multi-strategies in multiplayer reachability games played on finite graphs. A multi-strategy prescribes a set of possible actions, instead of a single action as usual strategies: it represents a set of all strategies that are…

We consider two-player games played on finite graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses. Both conditions…

In this paper, we considered impartial games on a simplicial complex. Each vertex of a given simplicial complex acts as a position of an impartial game. Each player in turn chooses a face of the simplicial complex and, for each position on…

These lecture notes are based on a short course on mis\`ere quotients offered at the Weizmann Institute of Science in Rehovot, Israel, in November 2006. They include an introduction to impartial games, starting from the beginning; the basic…

For impartial games $\Gamma$ and $\Gamma'$, the Sprague-Grundy function of the disjunctive sum $\Gamma + \Gamma'$ is equal to the Nim-sum of their Sprague-Grundy functions. In this paper, we introduce $p$-calm subtraction games, and show…

We propose a sorting-based greedy algorithm called SortedGreedy[m] for approximately solving the offline version of the d-choice weighted balls-into-bins problem where the number of choices for each ball is equal to the number of bins. We…

We analyze the Sprague-Grundy functions for a class of almost disjoint selective compound games played on Nim heaps. Surprisingly, we find that these functions behave chaotically for smaller Sprague-Grundy values of each component game yet…