Game-Theoretic Automata: Foundations, Formalizations, and Open Problems (original) (raw)

The Applications of Automata in Game Theory

Intelligent Technologies and Techniques for Pervasive Computing

In game theory, presenting players with strategies directly affects the performance of the players. Utilizing the power of automata is one way for presenting players with strategies. In this chapter, the authors studied different types of automata and their applications in game theory. They found that finite automata, adaptive automata, and cellular automata are widely adopted in game theory. The applications of finite automata are found to be limited to present simple strategies. In contrast, adaptive automata and cellular automata are intensively applied in complex environment, where the number of interacted players (human, computer applications, etc.) is high, and therefore, complex strategies are needed.

Automata-theoretic decision of timed games

The solution of games is a key decision problem in the context of verification of open systems and program synthesis. We present an automata-theoretic approach to solve timed games. Our solution gives a general framework to solve many classes of timed games via a translation to tree automata, extending to timed games a successful approach to solve discrete games. Our approach relies on translating a timed automaton into a tree automaton that accepts all the trees corresponding to a given strategy of the protagonist. This construction exploits the region automaton introduced by Alur and Dill. We use our framework to solve timed Büchi games in exponential time, timed Rabin games in exponential time, Ctl games in exponential time and Ltl games in doubly exponential time. All these results are tight in the sense that they match the known lower bounds on these decision problems.

A-Games: using game-like representation for representing finite automata

Anais do VI Workshop-Escola de Informática Teórica (WEIT 2021), 2021

Non-determinism in automata theory allows us to model situations where given an input, one or more outputs are possible. Although this decision regarding which state to chose could be random, there are contexts where this decision is not random, for instance when modeling real life situations. Using game theory, we propose the representation of automata as a game of two players. This game is defined for languages of finite size. We characterize that this representation is suited for both deterministic and non-deterministic automata, and relate the former with perfect information games, and the latter with imperfect information games. We argue that this could help us in explaining concurrency in programming, for instance in novice programming environments.

Stochastic Real-Time Games with Qualitative Timed Automata Objectives

Lecture Notes in Computer Science, 2010

We consider two-player stochastic games over real-time probabilistic processes where the winning objective is specified by a timed automaton. The goal of player is to play in such a way that the play (a timed word) is accepted by the timed automaton with probability one. Player aims at the opposite. We prove that whenever player has a winning strategy, then she also has a strategy that can be specified by a timed automaton. The strategy automaton reads the history of a play, and the decisions taken by the strategy depend only on the region of the resulting configuration. We also give an exponential-time algorithm which computes a winning timed automaton strategy if it exists.

The Trembling Hand Approach to Automata in Iterated Games

We consider two state automata playing infinitely iterated two players, two strategies game, where each move can be mis-implemented (or mis-perceived) with a small error probability, and compute the payoff matrix by means of a perturbation approach.

Abstract games for infinite state processes

CONCUR'98 Concurrency Theory, 1998

games for infinite state processes Citation for published version: Stevens, P 1998, 'Abstract games for infinite state processes'. in D Sangiorgi & R de Simone (eds), CONCUR'98

GAMES ON GRAPHS: AUTOMATA, STRUCTURE, AND COMPLEXITY

Proceedings of the 7th and 8th Asian Logic Conferences, 2003

McNaughton in his known paper [7], motivated by the work of Gurevich and Harrington [4], introduced a class of games played on finite graphs. In his paper McNaughton proves that winners in his games have winning strategies that can be implemented by finite state automata. McNaughton games have attracted attention of many experts in the area, partly because the games have close relationship with automata theory, the study of reactive systems, and logic (see, for instance, [12] and [11]). McNaughton games can also be used to develop game-theoretical approach for many important concepts in computer science such as models for concurrency, communication networks, and update networks, and provide natural examples of computational problems. For example, Nerode, Remmel and Yakhnis in a series of papers (e.g., [8], [9]) developed foundations of concurrent programming in which finite state strategies of McNaughton games are identified with distributed concurrent programs.

Reasoning about Games Via Temporal Logics: A Model Checking Approach

2005

This article shows how to use a subset of first-order CTL, namely Game Analysis Logic (GAL), in order to reason about games. A model checking algorithm for GAL is presented. Standard games and solution concepts of Game Theory are described in this context. Taking into account the strong relationship between games and Multi-Agent systems(MAS), the approach described here seems to be completely suitable for MAS formal analysis. Strategic and Coalition games are modelled and formally analyzed as case studies in order to demonstrate this approach.

Infinite-state games with finitary conditions

We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi games, and finite-memory suffices for finitary parity games. We then study pushdown boundedness games, with two contributions. First we prove a collapse result for pushdown ωB games, implying the decidability of solving these games. Second we consider pushdown games with finitary parity along with stack boundedness conditions, and show that solving these games is EXPTIME-complete.