Related papers: When 1+1 does not equal 2: Synergy in games
We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player.…
Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…
Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…
Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht-Fraisse game. We point out the great affinity of these games to…
In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of…
There is currently an intersection in the research of game theory and cryptography. Generally speaking, there are two aspects to this partnership. First there is the application of game theory to cryptography. Yet, the purpose of this paper…
Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…
Balancing is, especially among players, a highly debated topic of video games. Whether a game is sufficiently balanced greatly influences its reception, player satisfaction, churn rates and success. Yet, conceptions about the definition of…
A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…
We define a new concept of "mistake" strategies and actions for strategic-form and extensive-form games, analyze the relationship to prior main game-theoretic solution concepts, study algorithms for computation, and explore practicality.…
Existing efforts to formulate computational definitions of fairness have largely focused on distributional notions of equality, where equality is defined by the resources or decisions given to individuals in the system. Yet existing…
We propose a general definition of perfect equilibrium which is applicable to a wide class of games. A key feature is the concept of completely mixed nets of strategies, based on a more detailed notion of carrier of a strategy. Under…
Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification:…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
According to one of its founders, game theory would soon be a little over a hundred years old . A well-known theory in the academic and strategic fields, it is often the subject of criticism and, for many, seems too simplistic to be truly…
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…