Evolutionary Multiplayer Games

Evolutionary game theory has become one of the most diverse and far reaching theories in biology. Applications of this theory range from cell dynamics to social evolution. However, many applications make it clear that inherent non-linearities of natural systems need to be taken into account. One way of introducing such non-linearities into evolutionary games is by the inclusion of multiple players. An example is of social dilemmas, where group benefits could e.g.\ increase less than linear with the number of cooperators. Such multiplayer games can be introduced in all the fields where evolutionary game theory is already well established. However, the inclusion of non-linearities can help to advance the analysis of systems which are known to be complex, e.g. in the case of non-Mendelian inheritance. We review the diachronic theory and applications of multiplayer evolutionary games and present the current state of the field. Our aim is a summary of the theoretical results from well-mixed populations in infinite as well as finite populations. We also discuss examples from three fields where the theory has been successfully applied, ecology, social sciences and population genetics. In closing, we probe certain future directions which can be explored using the complexity of multiplayer games while preserving the promise of simplicity of evolutionary games.Comment: 14 pages, 2 figures, review pape

What Drives People's Choices in Turn-Taking Games, if not Game-Theoretic Rationality?

In an earlier experiment, participants played a perfect information game against a computer, which was programmed to deviate often from its backward induction strategy right at the beginning of the game. Participants knew that in each game, the computer was nevertheless optimizing against some belief about the participant's future strategy. In the aggregate, it appeared that participants applied forward induction. However, cardinal effects seemed to play a role as well: a number of participants might have been trying to maximize expected utility. In order to find out how people really reason in such a game, we designed centipede-like turn-taking games with new payoff structures in order to make such cardinal effects less likely. We ran a new experiment with 50 participants, based on marble drop visualizations of these revised payoff structures. After participants played 48 test games, we asked a number of questions to gauge the participants' reasoning about their own and the opponent's strategy at all decision nodes of a sample game. We also checked how the verbalized strategies fit to the actual choices they made at all their decision points in the 48 test games. Even though in the aggregate, participants in the new experiment still tend to slightly favor the forward induction choice at their first decision node, their verbalized strategies most often depend on their own attitudes towards risk and those they assign to the computer opponent, sometimes in addition to considerations about cooperativeness and competitiveness.Comment: In Proceedings TARK 2017, arXiv:1707.0825

A multi-paradigm language for reactive synthesis

This paper proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms, extended with past LTL. The implementation translates Promela to input for the Slugs synthesizer and is written in Python. The AMBA AHB bus case study is revisited and synthesized efficiently, identifying the need to reorder binary decision diagrams during strategy construction, in order to prevent the exponential blowup observed in previous work.Comment: In Proceedings SYNT 2015, arXiv:1602.0078

Solving Stochastic B\"uchi Games on Infinite Arenas with a Finite Attractor

We consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized B\"uchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and associated winning strategies in the case where the arena satisfies the finite-attractor property. From this we directly deduce the decidability of these games on probabilistic lossy channel systems.Comment: In Proceedings QAPL 2013, arXiv:1306.241

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility

Sequentiality vs. Concurrency in Games and Logic

Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc