Buffered Simulation Games for B\"uchi Automata

Simulation relations are an important tool in automata theory because they provide efficiently computable approximations to language inclusion. In recent years, extensions of ordinary simulations have been studied, for instance multi-pebble and multi-letter simulations which yield better approximations and are still polynomial-time computable. In this paper we study the limitations of approximating language inclusion in this way: we introduce a natural extension of multi-letter simulations called buffered simulations. They are based on a simulation game in which the two players share a FIFO buffer of unbounded size. We consider two variants of these buffered games called continuous and look-ahead simulation which differ in how elements can be removed from the FIFO buffer. We show that look-ahead simulation, the simpler one, is already PSPACE-hard, i.e. computationally as hard as language inclusion itself. Continuous simulation is even EXPTIME-hard. We also provide matching upper bounds for solving these games with infinite state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527

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

Modeling the Psychology of Consumer and Firm Behavior with Behavioral Economics

Marketing is an applied science that tries to explain and influence how firms and consumers actually behave in markets. Marketing models are usually applications of economic theories. These theories are general and produce precise predictions, but they rely on strong assumptions of rationality of consumers and firms. Theories based on rationality limits could prove similarly general and precise, while grounding theories in psychological plausibility and explaining facts which are puzzles for the standard approach. Behavioral economics explores the implications of limits of rationality. The goal is to make economic theories more plausible while maintaining formal power and accurate prediction of field data. This review focuses selectively on six types of models used in behavioral economics that can be applied to marketing. Three of the models generalize consumer preference to allow (1) sensitivity to reference points (and loss-aversion); (2) social preferences toward outcomes of others; and (3) preference for instant gratification (quasi-hyperbolic discounting). The three models are applied to industrial channel bargaining, salesforce compensation, and pricing of virtuous goods such as gym memberships. The other three models generalize the concept of gametheoretic equilibrium, allowing decision makers to make mistakes (quantal response equilibrium), encounter limits on the depth of strategic thinking (cognitive hierarchy), and equilibrate by learning from feedback (self-tuning EWA). These are applied to marketing strategy problems involving differentiated products, competitive entry into large and small markets, and low-price guarantees. The main goal of this selected review is to encourage marketing researchers of all kinds to apply these tools to marketing. Understanding the models and applying them is a technical challenge for marketing modelers, which also requires thoughtful input from psychologists studying details of consumer behavior. As a result, models like these could create a common language for modelers who prize formality and psychologists who prize realism

Thinking about Attention in Games: Backward and Forward Induction

Behavioral economics improves economic analysis by using psychological regularity to suggest limits on rationality and self-interest (e.g. Camerer and Loewenstein 2003). Expressing these regularities in formal terms permits productive theorizing, suggests new experiments, can contribute to psychology, and can be used to shape economic policies which make normal people better off

Routing Games with Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived