Related papers: On Potential Equations of Finite Games

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…

We study new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. We say that two games are "strategically equivalent" if, for every…

This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in $NP \cap coNP$ which are not known to be in $P$. However, there are some…

We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of…

We show that it is NP-Complete to decide whether a bimatrix game is degenerate and it is Co-NP-Complete to decide whether a bimatrix game is nondegenerate.

There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of the classical normal play structure. To analyze these games,…

We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant…

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…

This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo methodology based on a sample of 10,000 randomly generated…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

Quantitative extensions of parity games have recently attracted significant interest. These extensions include parity games with energy and payoff conditions as well as finitary parity games and their generalization to parity games with…

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…

We study stochastic games with energy-parity objectives, which combine quantitative rewards with a qualitative $\omega$-regular condition: The maximizer aims to avoid running out of energy while simultaneously satisfying a parity condition.…

In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the…

Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…

In this paper we provide three new results axiomatizing the core of games in characteristic function form (not necessarily having transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is…

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Wald's pick-the-larger-integer game. Several authors have provided conditions for the existence of…

Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…

We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…