Related papers: A brief conversation about subtraction games

We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games to a concurrent setting where the two players choose moves simultaneously and independently at each state. For…

Matthew Baker investigated, in previous work, an elegant, infinite-length game that may be used to study subsets of real numbers. We present two accessible examples of how an important technique from set theory, or a different technique…

In view of the complexity of the dynamics of learning in games, we seek to decompose a game into simpler components where the dynamics' long-run behavior is well understood. A natural starting point for this is Helmholtz's theorem, which…

A new class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is proposed and examined. Our games cover as a very special case the classic two-person…

Last-iterate behaviors of learning algorithms in repeated two-player zero-sum games have been extensively studied due to their wide applications in machine learning and related tasks. Typical algorithms that exhibit the last-iterate…

For a family of multidimensional gambler models we provide formulas for the winning probabilities (in terms of parameters of the system) and for the distribution of game duration (in terms of eigenvalues of underlying one-dimensional…

An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…

Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…

We extend the study of the iterated elimination of strictly dominated strategies (IESDS) from Nash strategic games to a class of qualitative games. Also in this case, the IESDS process leads us to a kind of 'rationalizable' result. We…

We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…

We present a general way of defining various reduction games on \omega\ which "represent" corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for…

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,…

We analyze Coquand's game-theoretic interpretation of Peano Arithmetic through the lens of elementary descent recursion. In Coquand's game semantics, winning strategies correspond to infinitary cut-free proofs and cut elimination…

Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with perfect information, TARK21], we studied well-founded games, a natural extension of finite extensive games with perfect information in which all plays are finite. We…

Subtraction games have a rich literature as normal-play combinatorial games (e.g., Berlekamp, Conway, and Guy, 1982). Recently, the theory has been extended to zero-sum scoring play (Cohensius et al. 2019). Here, we take the approach of…

Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…

In this thesis we introduce quantum refereed games, which are quantum interactive proof systems with two competing provers. We focus on a restriction of this model that we call "short quantum games" and we prove an upper bound and a lower…

The famous theorem of R.Aumann and M.Maschler states that the sequence of values of an N-stage zero-sum game G_N with incomplete information on one side converges as N tends to infinity, and the error term is bounded by a constant divided…

We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem…

We determine the full nim-value structure of additive subtraction games in the {\em primitive quadratic} regime. The problem appears in Winning Ways by Berlekamp et al. in 1982; it includes a closed formula, involving Beatty-type {\em…