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Duncan P. Brumby - One of the best experts on this subject based on the ideXlab platform.
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Dividing Attention Between Tasks: Testing Whether Explicit Payoff Functions Elicit Optimal Dual‐Task Performance
Cognitive science, 2017Co-Authors: George D. Farmer, Christian P. Janssen, Anh T. Nguyen, Duncan P. BrumbyAbstract:We test people's ability to optimize performance across two concurrent tasks. Participants performed a number entry task while controlling a randomly moving cursor with a joystick. Participants received explicit feedback on their performance on these tasks in the form of a single combined score. This Payoff Function was varied between conditions to change the value of one task relative to the other. We found that participants adapted their strategy for interleaving the two tasks, by varying how long they spent on one task before switching to the other, in order to achieve the near maximum Payoff available in each condition. In a second experiment, we show that this behavior is learned quickly (within 2-3 min over several discrete trials) and remained stable for as long as the Payoff Function did not change. The results of this work show that people are adaptive and flexible in how they prioritize and allocate attention in a dual-task setting. However, it also demonstrates some of the limits regarding people's ability to optimize Payoff Functions.
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A Cognitively Bounded Rational Analysis Model of Dual-Task Performance Trade-Offs
2010Co-Authors: Christian P. Janssen, Duncan P. Brumby, John Dowell, Nick ChaterAbstract:The process of interleaving two tasks can be described as making trade-offs between performance on each of the tasks. This can be captured in performance operating characteristic curves. However, these curves do not describe what, given the specific task circumstances, the optimal strategy is. In this paper we describe the results of a dual-task study in which participants performed a tracking and typing task under various experimental conditions. An objective Payoff Function was used to describe how participants should trade-off performance between the tasks. Results show that participants' dual-task interleaving strategy was sensitive to changes in the difficulty of the tracking task, and resulted in differences in overall task performance. To explain the observed behavior, a cognitively bounded rational analysis model was developed to understand participants' strategy selection. This analysis evaluated a variety of dual-task interleaving strategies against the same Payoff Function that participants were exposed to. The model demonstrated that in three out of four conditions human performance was optimal; that is, participants adopted dual-task strategies that maximized the Payoff that was achieved.
Hugo Gimbert - One of the best experts on this subject based on the ideXlab platform.
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Two-Player Perfect-Information Shift-Invariant Submixing Stochastic Games Are Half-Positional
2014Co-Authors: Hugo Gimbert, Edon KelmendiAbstract:We consider zero-sum stochastic games with perfect information and finitely many states and actions. The Payoff is computed by a Payoff Function which associates to each infinite sequence of states and actions a real number. We prove that if the the Payoff Function is both shift-invariant and submixing, then the game is half-positional, i.e. the first player has an optimal strategy which is both deterministic and stationary. This result relies on the existence of $\epsilon$-subgame-perfect equilibria in shift-invariant games, a second contribution of the paper.
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Limits of Multi-Discounted Markov Decision Processes
2007Co-Authors: Hugo Gimbert, Wieslaw ZielonkaAbstract:Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. The Payoff received by the controller can be evaluated in different ways, depending on the Payoff Function the MDP is equipped with. For example a \emph{mean--Payoff} Function evaluates average performance, whereas a \emph{discounted} Payoff Function gives more weights to earlier performance by means of a discount factor. Another well--known example is the \emph{parity} Payoff Function which is used to encode logical specifications~\cite{dagstuhl}. Surprisingly, parity and mean--Payoff MDPs share two non--trivial properties: they both have pure stationary optimal strategies~\cite{CourYan:1990,neyman} and they both are approximable by discounted MDPs with multiple discount factors (multi--discounted MDPs)~\cite{dealf:2003,neyman}. In this paper we unify and generalize these results. We introduce a new class of Payoff Functions called the priority weighted Payoff Functions, which are generalization of both parity and mean--Payoff Functions. We prove that priority weighted MDPs admit optimal strategies that are pure and stationary, and that the priority weighted value of an MDP is the limit of the multi--discounted value when discount factors tend to $0$ simultaneously at various speeds.
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Pure Stationary Optimal Strategies in Markov Decision Processes
2007Co-Authors: Hugo GimbertAbstract:Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. Performances of an MDP are evaluated by a Payoff Function. The controller of the MDP seeks to optimize those performances, using optimal strategies. There exists various ways of measuring performances, i.e. various classes of Payoff Functions. For example, average performances can be evaluated by a mean-Payoff Function, peak performances by a limsup Payoff Function, and the parity Payoff Function can be used to encode logical specifications. Surprisingly, all the MDPs equipped with mean, limsup or parity Payoff Functions share a common non-trivial property: they admit pure stationary optimal strategies. In this paper, we introduce the class of prefix-independent and submixing Payoff Functions, and we prove that any MDP equipped with such a Payoff Function admits pure stationary optimal strategies. This result unifies and simplifies several existing proofs. Moreover, it is a key tool for generating new examples of MDPs with pure stationary optimal strategies.
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LICS - Limits of Multi-Discounted Markov Decision Processes
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), 2007Co-Authors: Hugo Gimbert, Wiesław ZielonkaAbstract:Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. The Payoff received by the controller can be evaluated in different ways, depending on the Payoff Function the MDP is equipped with. For example a mean-Payoff Function evaluates average performance, whereas a discounted Payoff Function gives more weights to earlier performance by means of a discount factor. Another well-known example is the parity Payoff Function which is used to encode logical specifications. Surprisingly, parity and mean-Payoff MDPs share two non-trivial properties: they both have pure stationary optimal strategies and they both are approximable by discounted MDPs with multiple discount factors (multi- discounted MDPs). In this paper we unify and generalize these results. We introduce a new class of Payoff Functions called the priority weighted Payoff Functions, which are generalization of both parity and mean-Payoff Functions. We prove that priority weighted MDPs admit optimal strategies that are pure and stationary, and that the priority weighted value of an MDP is the limit of the multi-discounted value when discount factors tend to 0 simultaneously at various speeds.
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STACS - Pure stationary optimal strategies in Markov decision processes
STACS 2007, 1Co-Authors: Hugo GimbertAbstract:Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. Performances of an MDP are evaluated by a Payoff Function. The controller of the MDP seeks to optimize those performances, using optimal strategies. There exists various ways of measuring performances, i.e. various classes of Payoff Functions. For example, average performances can be evaluated by a mean-Payoff Function, peak performances by a limsup Payoff Function, and the parity Payoff Function can be used to encode logical specifications. Surprisingly, all the MDPs equipped with mean, limsup or parity Payoff Functions share a common non-trivial property: they admit pure stationary optimal strategies. In this paper, we introduce the class of prefix-independent and submixing Payoff Functions, and we prove that any MDP equipped with such a Payoff Function admits pure stationary optimal strategies. This result unifies and simplifies several existing proofs. Moreover, it is a key tool for generating new examples of MDPs with pure stationary optimal strategies.
Sudipta Sarangi - One of the best experts on this subject based on the ideXlab platform.
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A note on local spillovers, convexity, and the strategic substitutes property in networks
Theory and Decision, 2013Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:We provide existence results in a game with local spillovers where the Payoff Function satisfies both convexity and the strategic substitutes property. We show that there always exists a stable pairwise network in this game, and provide a condition which ensures the existence of pairwise equilibrium networks.
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Existence of Nash Networks and Partner Heterogeneity
Mathematical Social Sciences, 2012Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:In this paper, we pursue the line of research initiated by Haller and Sarangi (2005). We examine the existence of equilibrium networks called Nash networks in the non-cooperative two-way flow model by [Bala and Goyal, 2000a] and [Bala and Goyal, 2000b] in the presence of partner heterogeneity. First, we show through an example that Nash networks in pure strategies do not always exist in such model. We then impose restrictions on the Payoff Function to find conditions under which Nash networks always exist. We provide two properties--increasing differences and convexity in the first argument of the Payoff Function that ensure the existence of Nash networks. Note that the commonly used linear Payoff Function satisfies these two properties.
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Existence of Nash Networks and Partner Heterogeneity
SSRN Electronic Journal, 2011Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:In this paper, we pursue the work of H. Haller and al. (2005, [10]) and examine the existence of equilibrium networks, called Nash networks, in the noncooperative two-way flow model (Bala and Goyal, 2000, [1]) with partner heterogeneous agents. We show through an example that Nash networks do not always exist in such a context. We then restrict the Payoff Function, in order to find conditions under which Nash networks always exist. We give two properties: increasing differences and convexity in the first argument of the Payoff Function, that ensure the existence of Nash networks. It is worth noting that linear Payoff Functions satisfy the previous properties.
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Local Spillovers, Convexity and the Strategic Substitutes Property in Networks
2011Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:We provide existence results in a game with local spillovers where the Payoff Function satisfies both convexity and the strategic substitutes property. We show that there always exists a stable pairwise network in this game, and provide a condition which ensures the existence of pairwise equilibrium networks. Moreover, our existence proof allows us to characterize a pairwise equilibrium of these networks.
George D. Farmer - One of the best experts on this subject based on the ideXlab platform.
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Dividing Attention Between Tasks: Testing Whether Explicit Payoff Functions Elicit Optimal Dual‐Task Performance
Cognitive science, 2017Co-Authors: George D. Farmer, Christian P. Janssen, Anh T. Nguyen, Duncan P. BrumbyAbstract:We test people's ability to optimize performance across two concurrent tasks. Participants performed a number entry task while controlling a randomly moving cursor with a joystick. Participants received explicit feedback on their performance on these tasks in the form of a single combined score. This Payoff Function was varied between conditions to change the value of one task relative to the other. We found that participants adapted their strategy for interleaving the two tasks, by varying how long they spent on one task before switching to the other, in order to achieve the near maximum Payoff available in each condition. In a second experiment, we show that this behavior is learned quickly (within 2-3 min over several discrete trials) and remained stable for as long as the Payoff Function did not change. The results of this work show that people are adaptive and flexible in how they prioritize and allocate attention in a dual-task setting. However, it also demonstrates some of the limits regarding people's ability to optimize Payoff Functions.
Pascal Billand - One of the best experts on this subject based on the ideXlab platform.
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A note on local spillovers, convexity, and the strategic substitutes property in networks
Theory and Decision, 2013Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:We provide existence results in a game with local spillovers where the Payoff Function satisfies both convexity and the strategic substitutes property. We show that there always exists a stable pairwise network in this game, and provide a condition which ensures the existence of pairwise equilibrium networks.
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Existence of Nash Networks and Partner Heterogeneity
Mathematical Social Sciences, 2012Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:In this paper, we pursue the line of research initiated by Haller and Sarangi (2005). We examine the existence of equilibrium networks called Nash networks in the non-cooperative two-way flow model by [Bala and Goyal, 2000a] and [Bala and Goyal, 2000b] in the presence of partner heterogeneity. First, we show through an example that Nash networks in pure strategies do not always exist in such model. We then impose restrictions on the Payoff Function to find conditions under which Nash networks always exist. We provide two properties--increasing differences and convexity in the first argument of the Payoff Function that ensure the existence of Nash networks. Note that the commonly used linear Payoff Function satisfies these two properties.
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Existence of Nash Networks and Partner Heterogeneity
SSRN Electronic Journal, 2011Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:In this paper, we pursue the work of H. Haller and al. (2005, [10]) and examine the existence of equilibrium networks, called Nash networks, in the noncooperative two-way flow model (Bala and Goyal, 2000, [1]) with partner heterogeneous agents. We show through an example that Nash networks do not always exist in such a context. We then restrict the Payoff Function, in order to find conditions under which Nash networks always exist. We give two properties: increasing differences and convexity in the first argument of the Payoff Function, that ensure the existence of Nash networks. It is worth noting that linear Payoff Functions satisfy the previous properties.
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Local Spillovers, Convexity and the Strategic Substitutes Property in Networks
2011Co-Authors: Pascal Billand, Christophe Bravard, Sudipta SarangiAbstract:We provide existence results in a game with local spillovers where the Payoff Function satisfies both convexity and the strategic substitutes property. We show that there always exists a stable pairwise network in this game, and provide a condition which ensures the existence of pairwise equilibrium networks. Moreover, our existence proof allows us to characterize a pairwise equilibrium of these networks.
