Related papers: Erratum to: Lattice point methods for combinatoria…
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain way as diamond-colored modular or distributive lattices. Our…
A straightforward 3-point quadrature formula of closed type is derived that improves on Simpson's rule. Just using the additional information of the integrand's derivative at the two endpoints we show the error is sixth order in grid…
A recent comment highlights a discussion at the PATRAS Workshop on Axions, WIMPs and WISPs relating to a recent publication. We respond to this comment, and detail a calculation error in the original letter.
We present a general theorem for distributed synthesis problems in coordination games with $\omega$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an "essential" winning strategy,…
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge reductions of games to arrive at smaller, solved sub-games…
In this thesis, we survey techniques and results from the study of Complexity Theory and Games. We then apply these techniques to obtain new results for previously unstudied games. Our contributions in the games Hexiom, Cut the Rope, and…
The equations in cond-mat/0011020 and Phys. Rev, Lett. 86, 4652 (2001) are valid but a numerical estimate in the paper is incorrect.
Proposition~6.4 of the author's paper {\origpaper} is incorrect. This invalid proposition was used in the proof of Corollary~6.5, so we provide a new proof of the latter result.
Notes on the Spinpossible puzzle game. We give a mathematical description of the game, prove some elementary bounds on the length of optimal solutions, and consider variations of the game which place restrictions on the set of permitted…
There is an error in the proof (but not the truth) of Theorem 3.2 in the author's 1985 paper "The Double-Wedge Algebra for Quantum Fields on Schwarzschild and Minkowski Spacetimes" in "Communications in Mathematical Physics". The author…
After the publication of [Compos. Math. 156 (2020), no. 4, 822-861], Andrew Putman pointed out a mistake in our paper and helped us fix it. In this note, we will explain what this mistake is and how to fix it.
We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident edges) while Right is able to delete edges. This natural…
We introduce a general and accurate method for determining lattice phase shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices. Our method combines angular momentum projection, spherical wall boundaries and an…
We study a multi-agent decision problem in population games, where agents select from multiple available strategies and continually revise their selections based on the payoffs associated with these strategies. Unlike conventional…
Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether agents have…
This note describes a correct way to perform the inflation procedures claimed in the papers on embedding ellipsoids, Journ. Top. 2 (2009), 1-22 and 589-623. The idea is to inflate along a collection of transversally and positively…
We study the problem of characterizing the set of games that are consistent with observed equilibrium play. Our contribution is to develop and analyze a new methodology based on convex optimization to address this problem for many classes…
This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum describes: 1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak…