Related papers: A Cartography for 2x2 Symmetric Games
As Aumann stated, cooperation and non-cooperation are different ways of viewing the same game, with the main difference being whether players can reach a binding cooperative agreement. In the real world, many games often coexist competition…
In this paper, we introduce an agent-based representation of games, in order to propose a compact representation for multi-party games in game theory. Our method is inspired by concepts in process theory and process algebra. In addition, we…
We introduce the notion of exchangeable equilibria of a symmetric bimatrix game, defined as those correlated equilibria in which players' strategy choices are conditionally independently and identically distributed given some hidden…
We compare four different `game-spaces' in terms of their usefulness in characterising multi-player tabletop games, with a particular interest in any underlying change to a game's characteristics as the number of players changes. In each…
Cooperative 2-matching games are a generalization of cooperative matching games, where the value function is given by maximum-weight b-matchings, for a vertex capacity vector $b \leq 2$. We show how to separate over the core of 2-matching…
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…
The rank of a bimatrix game is defined as the rank of the sum of the payoff matrices of the two players. The rank of a game is known to impact both the most suitable computation methods for determining a solution and the expressive power of…
Evolutionary game theory has been a successful tool to combine classical game theory with learning-dynamical descriptions in multiagent systems. Provided some symmetric structures of interacting players, many studies have been focused on…
How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model…
We present new data structures for representing symmetric normal-form games. These data structures are optimized for efficiently computing the expected utility of each unilateral pure-strategy deviation from a symmetric mixed-strategy…
This paper identifies a manifold in the space of bimatrix games which contains games that are strategically equivalent to rank-1 games through a positive affine transformation. It also presents an algorithm that can compute, in polynomial…
Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We…
Dynamic game theory offers a toolbox for formalizing and solving for both cooperative and non-cooperative strategies in multi-agent scenarios. However, the optimal configuration of such games remains largely unexplored. While there is…
We introduce new theoretical insights into two-population asymmetric games allowing for an elegant symmetric decomposition into two single population symmetric games. Specifically, we show how an asymmetric bimatrix game (A,B) can be…
Symmetric quantum games for 2-player, 2-qubit strategies are analyzed in detail by using a scheme in which all pure states in the 2-qubit Hilbert space are utilized for strategies. We consider two different types of symmetric games…
This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
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…
A second quantization procedure for the field-theoretic description of interactive games is analyzed. Its relation to the dynamical inverse problem of representation theory is emphasized.