Related papers: Who Wins the Multi-Structural Game?
Scoring play games were first studied by Fraser Stewart for his PhD thesis. He showed that under the disjunctive sum, scoring play games are partially ordered, but do not have the same "nice" structure of normal play games. In this paper I…
The \emph{stationary set splitting game} is a game of perfect information of length $\omega_{1}$ between two players, \unspls and \spl, in which \unspls chooses stationarily many countable ordinals and \spls tries to continuously divide…
We consider a simple streaming game between two players Alice and Bob, which we call the mirror game. In this game, Alice and Bob take turns saying numbers belonging to the set $\{1, 2, \dots,2N\}$. A player loses if they repeat a number…
Combinatorial games are played under two different play conventions: normal play, where the last player to move wins, and \mis play, where the last player to move loses. Combinatorial games are also classified into impartial positions and…
A major open question in algorithmic game theory is whether normal-form correlated equilibria (NFCE) can be computed efficiently in succinct games such as extensive-form games [DFF+25,6PR24,FP23,HvS08,VSF08,PR08]. Motivated by this…
The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…
We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other…
We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…
We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…
We study a game puzzle that has enjoyed recent popularity among mathematicians, computer scientist, coding theorists and even the mass press. In the game, $n$ players are fitted with randomly assigned colored hats. Individual players can…
We study the long-term behavior of the fictitious play process in repeated extensive-form games of imperfect information with perfect recall. Each player maintains incorrect beliefs that the moves at all information sets, except the one at…
A number of model-comparison games central to (finite) model theory, such as pebble and Ehrenfeucht-Fra\"{i}ss\'{e} games, can be captured as comonads on categories of relational structures. In particular, the coalgebras for these comonads…
We introduce and study coverage games - a novel framework for multi-agent planning in settings in which a system operates several agents but does not have full control on them, or interacts with an environment that consists of several…
Projection games constitute an important class of nonlocal games where, for any answer from the first player, there is a unique correct answer for the second player. This class of games captures nonlocal games arising from constraint…
We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…
The security game is a basic model for resource allocation in adversarial environments. Here there are two players, a defender and an attacker. The defender wants to allocate her limited resources to defend critical targets and the attacker…
We study a Stackelberg game to examine how two agents determine to cooperate while competing with each other. Each selects an arrival time to a destination, the earlier one fetching a higher reward. There is, however, an inherent penalty in…
We consider a 2-player permutation game inspired by the celebrated Erd\H{o}s-Szekeres Theorem. The game depends on two positive integer parameters $a$ and $b$ and we determine the winner and give a winning strategy when $a \geq b$ and $b…
Spatial structure has a profound effect on the outcome of evolutionary games. In the ultimatum game, it leads to the dominance of much fairer players than those predicted to evolve in well-mixed settings. Here we show that spatiality leads…
Behavioural equivalences can be characterized via bisimulation, modal logics, and spoiler-duplicator games. In this paper we work in the general setting of coalgebra and focus on generic algorithms for computing the winning strategies of…