436,461 research outputs found

    Compositional game theory

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    We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which standard economic tools are not practical. An open game represents a game played relative to an arbitrary environment and to this end we introduce the concept of coutility, which is the utility generated by an open game and returned to its environment. Open games are the morphisms of a symmetric monoidal category and can therefore be composed by categorical composition into sequential move games and by monoidal products into simultaneous move games. Open games can be represented by string diagrams which provide an intuitive but formal visualisation of the information flows. We show that a variety of games can be faithfully represented as open games in the sense of having the same Nash equilibria and off-equilibrium best responses.Comment: This version submitted to LiCS 201

    A Lyapunov Optimization Approach to Repeated Stochastic Games

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    This paper considers a time-varying game with NN players. Every time slot, players observe their own random events and then take a control action. The events and control actions affect the individual utilities earned by each player. The goal is to maximize a concave function of time average utilities subject to equilibrium constraints. Specifically, participating players are provided access to a common source of randomness from which they can optimally correlate their decisions. The equilibrium constraints incentivize participation by ensuring that players cannot earn more utility if they choose not to participate. This form of equilibrium is similar to the notions of Nash equilibrium and correlated equilibrium, but is simpler to attain. A Lyapunov method is developed that solves the problem in an online \emph{max-weight} fashion by selecting actions based on a set of time-varying weights. The algorithm does not require knowledge of the event probabilities and has polynomial convergence time. A similar method can be used to compute a standard correlated equilibrium, albeit with increased complexity.Comment: 13 pages, this version fixes an incorrect statement of the previous arxiv version (see footnote 1, page 5 in current version for the correction

    Dynamic Product Assembly and Inventory Control for Maximum Profit

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    We consider a manufacturing plant that purchases raw materials for product assembly and then sells the final products to customers. There are M types of raw materials and K types of products, and each product uses a certain subset of raw materials for assembly. The plant operates in slotted time, and every slot it makes decisions about re-stocking materials and pricing the existing products in reaction to (possibly time-varying) material costs and consumer demands. We develop a dynamic purchasing and pricing policy that yields time average profit within epsilon of optimality, for any given epsilon>0, with a worst case storage buffer requirement that is O(1/epsilon). The policy can be implemented easily for large M, K, yields fast convergence times, and is robust to non-ergodic system dynamics.Comment: 32 page

    Implementation of complex interactions in a Cox regression framework

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    The standard Cox proportional hazards model has been extended by functionally describable interaction terms. The first of which are related to neural networks by adopting the idea of transforming sums of weighted covariables by means of a logistic function. A class of reasonable weight combinations within the logistic transformation is described. Apart from the standard covariable product interaction, a product of logistically transformed covariables has also been included in the analysis of performance of the new terms. An algorithm combining likelihood ratio tests and AIC criterion has been defined for model choice. The critical values of the likelihood ratio test statistics had to be corrected in order to guarantee a maximum type I error of 5% for each interaction term. The new class of interaction terms allows interpretation of functional relationships between covariables with more flexibility and can easily be implemented in standard software packages

    Knowledge creation and visualisation by using trade-off curves to enable set-based concurrent engineering

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    The increased international competition forces companies to sustain and improve market share through the production of a high quality product in a cost effective manner and in a shorter time. Set‑based concurrent engineering (SBCE), which is a core element of lean product development approach, has got the potential to decrease time‑to‑market as well as enhance product innovation to be produced in good quality and cost effective manner. A knowledge‑based environment is one of the important requ irements for a successful SBCE implementation. One way to provide this environment is the use of trade‑off curves (ToC). ToC is a tool to create and visualise knowledge in the way to understand the relationships between various conflicting design parame ters to each other. This paper presents an overview of different types of ToCs and the role of knowledge‑based ToCs in SBCE by employing an extensive literature review and industrial field study. It then proposes a process of generating and using knowledg e‑based ToCs in order to create and visualise knowledge to enable the following key SBCE activities: (1) Identify the feasible design space, (2) Generate set of conceptual design solutions, (3) Compare design solutions, (4) Narrow down the design sets, (5) Achieve final optimal design solution. Finally a hypothetical example of a car seat structure is presented in order to provide a better understanding of using ToCs. This example shows that ToCs are effective tools to be used as a knowledge sou rce at the early stages of product development process
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