Related papers: Three-player impartial games
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
There are multiple notions of coalitional responsibility. The focus of this paper is on the blameworthiness defined through the principle of alternative possibilities: a coalition is blamable for a statement if the statement is true, but…
Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial…
This paper introduces a variant of the impartial combinatorial game nim, called tree nim, as well as a particular case of tree nim called tripod nim. A certain existence-uniqueness result and a periodicity result are proven about the…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by a cognitive radio networks application, we assume that players incur a loss upon colliding, and that communication between…
Two-player win/lose games of infinite duration are involved in several disciplines including computer science and logic. If such a game has deterministic winning strategies, one may ask how simple such strategies can get. The answer may…
The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to…
We provide here an epistemic analysis of arbitrary strategic games based on the possibility correspondences. Such an analysis calls for the use of transfinite iterations of the corresponding operators. Our approach is based on Tarski's…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…
We deal with coalitional games possessing strictly positive values. Individually rational allocations of such a game has clear fractional interpretations. Many concepts, including the long-existing core and other stability notions more…
The explicit construction is presented of two-player game satisfying: (i) symmetry with respect to the permutation of the players; (ii) the existence of upper bound on total payoff following from Bell inequality; (iii) the existence of…
The main objective of this work is to describe games which fall under title of Potential and simplify the conditions for class of aggregative games. Games classified as aggregative are ones in which, in addition to the player's own action,…
Admissible strategies, i.e. those that are not dominated by any other strategy, are a typical rationality notion in game theory. In many classes of games this is justified by results showing that any strategy is admissible or dominated by…
It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We…
Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break the alternating play axiom and/or restrict the other…
The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…
Cooperative game theory studies how to allocate the joint value generated by a set of players. These games are typically analyzed using the characteristic function form with transferable utility, which represents the value attainable by…