Related papers: Choice Structures in Games
A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players uses a finite set of ad hoc strategies to make their decision, based on the past record. The…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…
Alan Turing proposed in 1950 a framework called an imitation game to decide if a machine could think. Using mathematics developed largely after Turing -- category theory -- we analyze a broader class of universal imitation games (UIGs),…
We explore the connections between selection games on Hausdorff spaces and their corresponding Vietoris space of compact subsets. These considerations offer a similar relationship as the well-known relationship between $\omega$-covers of…
The application of the methods of quantum mechanics to game theory provides us with the ability to achieve results not otherwise possible. Both linear superpositions of actions and entanglement between the players' moves can be exploited.…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
The study focuses on strategic-form games extended in the Eisert-Wilkens-Lewenstein scheme by two unitary operations. Conditions are determined under which the pair of unitary operators, along with classical strategies, form a game…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
In this paper we consider positional games where the winning sets are tree universal graphs. Specifically, we show that in the unbiased Maker-Breaker game on the complete graph $K_n$, Maker has a strategy to occupy a graph which contains…
When applied to the same game, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the…
Behavioral experiments on the Ultimatum Game have shown that we human beings have remarkable preference in fair play, contradicting the predictions by the game theory. Most of the existing models seeking for explanations, however, strictly…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…
The game theory techniques are used to find the equilibrium of a market. Game theory refers to the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents,…
Different constructions in the recursion theory use the so-called priority arguments. A general scheme was suggested by A.~Lachlan. Based on his work, we define the notion of a priority-closed class of requirements. Then, for a specific…
We investigate a game-theoretic model of a social system where both the rules of the game and the interaction structure are shaped by the behavior of the agents. We call this type of model, with several types of feedback couplings from the…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…