Related papers: Three-player impartial games
This paper provides effective methods for the polyhedral formulation of impartial finite combinatorial games as lattice games. Given a rational strategy for a lattice game, a polynomial time algorithm is presented to decide (i) whether a…
Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. This paper defines parametrized parity games and introduces an operation, Justify, that determines a…
We present an algebraic framework for the analysis of combinatorial games. This framework embraces the classical theory of partizan games as well as a number of misere games, comply-constrain games, and card games that have been studied…
Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…
The game theoretic concepts of rationalizability and iterated dominance are closely related and provide characterizations of each other. Indeed, the equivalence between them implies that in a two player finite game, the remaining set of…
Coalition Logic is a central logic in logical research on strategic reasoning. In a recent paper, Li and Ju argued that generally, models of Coalition Logic, concurrent game models, have three too strong assumptions: seriality, independence…
The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…
We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…
Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of "forward induction," because rational agents may use dominated strategies as experiments to learn how opponents play,…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
A traditional assumption in game theory is that players are opaque to one another -- if a player changes strategies, then this change in strategies does not affect the choice of other players' strategies. In many situations this is an…
In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…
The rationalizability concept was introduced in \cite{Ber84} and \cite{Pea84} to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form…
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 classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…
A coalition is blameable for an outcome if the coalition had a strategy to prevent it. It has been previously suggested that the cost of prevention, or the cost of sacrifice, can be used to measure the degree of blameworthiness. The paper…