Extending finite-memory determinacy to multi-player games

Roux, Stéphane; Pauly, Arno

doi:10.1016/j.ic.2018.02.024

Cited by 5 publications

(2 citation statements)

References 26 publications

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“…Proving finite-memory determinacy is sometimes difficult (already in deterministic games, e.g., [BHM + 17]), and as opposed to memoryless strategies, there are few widely applicable results. We mention [LPR18], which provides sufficient conditions for finite-memory determinacy in Boolean combinations of finite-memory-determined objectives in deterministic games. Results for multi-player non-zero-sum games are also available [LP18].…”

Section: Introductionmentioning

confidence: 99%

Arena-Independent Finite-Memory Determinacy in Stochastic Games

Bouyer,

Oualhadj,

Randour

et al. 2023

Logical Methods in Computer Science

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We study stochastic zero-sum games on graphs, which are prevalent tools to model decision-making in presence of an antagonistic opponent in a random environment. In this setting, an important question is the one of strategy complexity: what kinds of strategies are sufficient or required to play optimally (e.g., randomization or memory requirements)? Our contributions further the understanding of arena-independent finite-memory (AIFM) determinacy, i.e., the study of objectives for which memory is needed, but in a way that only depends on limited parameters of the game graphs. First, we show that objectives for which pure AIFM strategies suffice to play optimally also admit pure AIFM subgame perfect strategies. Second, we show that we can reduce the study of objectives for which pure AIFM strategies suffice in two-player stochastic games to the easier study of one-player stochastic games (i.e., Markov decision processes). Third, we characterize the sufficiency of AIFM strategies through two intuitive properties of objectives. This work extends a line of research started on deterministic games to stochastic ones.

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Section: Introductionmentioning

confidence: 99%

Arena-Independent Finite-Memory Determinacy in Stochastic Games

Bouyer,

Oualhadj,

Randour

et al. 2023

Logical Methods in Computer Science

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“…Kahneman and others criticized [20] the theory of expected utility and developed alternatives [7]. Moreover, impossibility results were proven [19]. Nevertheless, it still remains the standard theory in game theory [14] and the most common tool in economic reasoning [9].…”

Section: Introductionmentioning

confidence: 99%

Towards Formal Foundations for Game Theory

Parsert

Kaliszyk

2018

Interactive Theorem Proving

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Abstract. Utility functions form an essential part of game theory and economics. In order to guarantee the existence of these utility functions sufficient properties are assumed in an axiomatic manner. In this paper we discuss these axioms and the von-Neumann-Morgenstern Utility Theorem, which names precise assumptions under which expected utility functions exist. We formalize these results in Isabelle/HOL. The formalization includes formal definitions of the underlying concepts including continuity and independence of preferences. We make the dependencies more precise and highlight some consequences for a formalization of game theory.

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Equilibria in multi-player multi-outcome infinite sequential games

Roux

Pauly

2021

Information and Computation

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We investigate the existence of certain types of equilibria (Nash, ε-Nash, subgame perfect, ε-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental approaches: one requires strong topological restrictions on the games, but produces very strong existence results. The other merely requires some very basic determinacy properties to still obtain some existence results. Both results are transfer results: starting with the existence of some equilibria for a small class of games, they allow us to conclude the existence of some type of equilibria for a larger class.To make the abstract results more concrete, we investigate as a special case infinite sequential games with real-valued payoff functions. Depending on the class of payoff functions (continuous, upper semi-continuous, Borel) and whether the game is zero-sum, we obtain various existence results for equilibria.Our results hold for games with two or up to countably many players. * The project was begun while the first author was a postdoctoral researcher at

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Extending finite-memory determinacy to multi-player games

Cited by 5 publications

References 26 publications

Arena-Independent Finite-Memory Determinacy in Stochastic Games

Arena-Independent Finite-Memory Determinacy in Stochastic Games

Towards Formal Foundations for Game Theory

Equilibria in multi-player multi-outcome infinite sequential games

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