Related papers: On numbers and endgames: Combinatorial game theory…
Rex, short for Reverse Hex, is a set coloring game in which players try to avoid connecting terminals of their color. Combinatorial game theory (CGT) is the study of perfect strategy games. Until recently, both Rex and Hex were not examined…
This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems…
This paper introduces constrained correlated equilibrium, a solution concept combining correlation and coupled constraints in finite non-cooperative games. In the general case of an arbitrary correlation device and coupled constraints in…
This paper studies a single-suit version of the card game War on a finite deck of cards. There are varying methods of how players put the cards that they win back into their hands, but we primarily consider randomly putting the cards back…
The known results regarding two-player zero-sum games are naturally generalized in complex space and are presented through a complete compact theory. The payoff function is defined by the real part of the payoff function in the real case,…
This compendium features advances in Game Theory, to include: Classical Game Theory: Cooperative and non-cooperative. Zero-sum and non-zero sum games. Potential and Congestion games. Mean Field games. Nash Equilibrium, Correlated Nash…
In the game theory literature, there appears to be little research on equilibrium selection for normal-form games with an infinite strategy space and discontinuous utility functions. Moreover, many existing selection methods are not…
In cooperative game theory, the social configurations of players are modeled by balanced collections. The Bondareva-Shapley theorem, perhaps the most fundamental theorem in cooperative game theory, characterizes the existence of solutions…
Consider equipping an alphabet $\mathcal{A}$ with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for the Penney's game on patterns and show non-transitivity for…
This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections…
We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the…
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.
We present and study a variant of the mean payoff games introduced by A. Ehrenfeucht and J. Mycielski. In this version, the second player makes an infinite sequence of moves only after the first player's sequence of moves has been decided…
This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of fiinite-player games, the limit of…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. In this…
Coordination and cooperation are among the most important issues of game theory. Recently, the attention turned to game theory on graphs and social networks. Encouraged by interesting results obtained in quantum evolutionary game analysis,…
We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…
In this paper, we introduce an abstract fuzzy economy (generalized fuzzy game) model with a countable space of actions and we study the existence of the fuzzy equilibrium. As applications, two types of results are obtained. The first ones…
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…
The theory of mean field games aims at studying deterministic or stochastic differential games (Nash equilibria) as the number of agents tends to infinity. Since very few mean field games have explicit or semi-explicit solutions, numerical…