Related papers: An estimation method for game complexity
Without further ado, we present the P_3-game. The P_3-game is decidable for elementary classes of graphs such as paths and cycles. From an algorithmic point of view, the connected P_3-game is fascinating. We show that the connected P_3-game…
Video games, just like any other media have both explicit and implicit messages, and they can have impact on physical and mental health of the users. These impacts can be positive or negative. The impacts, the implications and the meanings…
We propose the following question: what game-like interactive system would provide a good environment for measuring the impact and success of a co-creative, cooperative agent? Creativity is often formulated in terms of novelty, value,…
We initiate the study of structured Stackelberg games, a novel form of strategic interaction between a leader and a follower where contextual information can be predictive of the follower's (unknown) type. Motivated by applications such as…
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…
We prove that it is PPAD-hard to compute a Nash equilibrium in a tree polymatrix game with twenty actions per player. This is the first PPAD hardness result for a game with a constant number of actions per player where the interaction graph…
In this paper we argue that Massively Multiplayer Online Games (MMOGs), also known as Large Games are an interesting research tool for policy experimentation. One of the major problems with lawmaking is that testing the laws is a difficult…
We introduce a novel and extensible benchmark for large language models (LLMs) through grid-based games such as Tic-Tac-Toe, Connect Four, and Gomoku. The open-source game simulation code, available on GitHub, allows LLMs to compete and…
Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require…
Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not…
In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter. Thus, the problem of deciding whether a…
Quantitative measures of randomness in games are useful for game design and have implications for gambling law. We treat the outcome of a game as a random variable and derive a closed-form expression and estimator for the variance in the…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of two-player parity games over graphs of bounded tree-width, where updates may add or delete edges,…
Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm.…
We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which…
This is a theoretical and computational strategy exploration of the visually attractive game IQ-Link. Not all games which are visually appealing are worthy of your time as a puzzlist. This analysis gives a would-be addict some idea of what…
We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences…
We study the problem of approximating the value of a Unique Game instance in the streaming model. A simple count of the number of constraints divided by $p$, the alphabet size of the Unique Game, gives a trivial $p$-approximation that can…
In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…