807 research outputs found

    Bounding Rationality by Discounting Time

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    Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the hardness of factoring. We define a new notion of bounded rationality, where the payoffs of players are discounted by the computation time they take to produce their actions. We use this notion to give a direct correspondence between the existence of equilibria where Alice has a winning strategy and the hardness of factoring. Namely, under a natural assumption on the discount rates, there is an equilibriumwhere Alice has a winning strategy iff there is a linear-time samplable distribution with respect to which Factoring is hard on average. We also give general results for discounted games over countable action spaces, including showing that any game with bounded and computable payoffs has an equilibrium in our model, even if each player is allowed a countable number of actions. It follows, for example, that the Largest Integer game has an equilibrium in our model though it has no Nash equilibria or epsilon-Nash equilibria.Comment: To appear in Proceedings of The First Symposium on Innovations in Computer Scienc

    Bounding Rationality by Discounting Time

    Get PDF
    Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the hardness of factoring. We define a new notion of bounded rationality, where the payoffs of players are discounted by the computation time they take to produce their actions. We use this notion to give a direct correspondence between the existence of equilibria where Alice has a winning strategy and the hardness of factoring. Namely, under a natural assumption on the discount rates, there is an equilibriumwhere Alice has a winning strategy iff there is a linear-time samplable distribution with respect to which Factoring is hard on average. We also give general results for discounted games over countable action spaces, including showing that any game with bounded and computable payoffs has an equilibrium in our model, even if each player is allowed a countable number of actions. It follows, for example, that the Largest Integer game has an equilibrium in our model though it has no Nash equilibria or E-Nash equilibria.Bounded rationality; Discounting; Uniform equilibria; Factoring game

    Computable Rationality, NUTS, and the Nuclear Leviathan

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    This paper explores how the Leviathan that projects power through nuclear arms exercises a unique nuclearized sovereignty. In the case of nuclear superpowers, this sovereignty extends to wielding the power to destroy human civilization as we know it across the globe. Nuclearized sovereignty depends on a hybrid form of power encompassing human decision-makers in a hierarchical chain of command, and all of the technical and computerized functions necessary to maintain command and control at every moment of the sovereign's existence: this sovereign power cannot sleep. This article analyzes how the form of rationality that informs this hybrid exercise of power historically developed to be computable. By definition, computable rationality must be able to function without any intelligible grasp of the context or the comprehensive significance of decision-making outcomes. Thus, maintaining nuclearized sovereignty necessarily must be able to execute momentous life and death decisions without the type of sentience we usually associate with ethical individual and collective decisions

    Reputation in Long-Run Relationships

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    We model a long-run relationship as an infinitely repeated game played by two equally patient agents. In each period, the agents play an extensive-form game of perfect information. There is incomplete information about the type of player 1 while player 2’s type is commonly known. We show that a sufficiently patient player 1 can leverage player 2’s uncertainty about his type to secure his highest payoff in any perfect Bayesian equilibrium of the repeated game.Repeated Games, Reputation, Equal Discount Factor, Long-run Players. JEL Classification Numbers: C73, D83

    Do Quasi-Hyperbolic Preferences Explain Academic Procrastination? An Empirical Evaluation

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    Traditional neoclassical thought fails to explain questions such as problems of self-control. Behavioural economics have explained these matters on the basis of the intertemporal preferences of individuals and, specifically, the so-called (β, δ) model which emphasises present bias. This opens the way to the analysis of new situations in which people can adopt incorrect indecisions that make it necessary for the government to intervene. The literature which has developed the (β, δ) model and its implications has generated a categorisation of people that is widely used but which lacks a systematic empirical evaluation. It is important to value the need for this public action. In this article, we develop a method which makes it possible to verify the main implications that this model has to explain the procrastination of university students. Using an experimental time discount task with real monetary incentives, we estimate the students’ β and δ parameters and we analyse their correlation with their answers to a series of questions concerning how they plan to study for an exam. The results are ambiguous given that they back some of the model’s conclusions but reject others, including a number of the most basic ones, such as the relation between present biases and some of the categories of people, these being essential to predict their behaviour
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