We report on experiments examining the value of commitment in Stackelberg games where the follower chooses whether to pay some cost to perfectly observe the leader’s action. Várdy [Games Econ. Behav. (2004)] shows that in the unique pure-strategy subgame perfect equilibrium of this game, the value of commitment is lost completely; however, there exists a mixed-strategy subgame perfect equilibri...

Multi-agent systems considered in the paper consist of a finite number of agents, positions of which can be changed by system actions, and of an evaluation function which assigns to each agent a value of its current position (as e.g. the distance from the intended target). The set of all possible values is ordered; the intention of each agent is to reach a position with the minimum value. Any s...

In Science, Truth, and Democracy, Philip Kitcher develops the notion of well-ordered science: scientific inquiry whose research agenda and applications (but not methods) are subject to public control guided by democratic deliberation. Kitcher’s primary departure from his earlier views involves rejecting the idea that there is any single standard of scientific significance. The context-dependenc...

Abstract A previous study by one of the present authors, together with D. Borwein and I. Leonard [8], studied the asymptotic behavior of the p-norm of the sinc function: sinc(x) = (sin x)/x and along the way looked at closed forms for integer values of p. In this study we address these integrals with the tools of experimental mathematics, namely by computing their numerical values to high preci...

The idea that people can entertain propositions without believing them is widespread, intuitive, and most probably false. The main goal of this essay is to argue against the claim that people can entertain a proposition without believing it. Evidence is presented demonstrating that we cannot withhold assent from any proposition we happen to consider. A model of belief fixation is then sketched ...

State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Qlearning. We propose a new notion of action value defined by a Gaussian smoothed version of the expected Q-value. We show that such smoothed Q-values still satisfy a Bellman equation, making them learnable from experience sampled from an environment. ...