Eye Movements in Strategic Choice

In risky and other multiattribute choices, the process of choosing is well described by random walk or drift diffusion models in which evidence is accumulated over time to threshold. In strategic choices, level‐k and cognitive hierarchy models have been offered as accounts of the choice process, in which people simulate the choice processes of their opponents or partners. We recorded the eye movements in 2 × 2 symmetric games including dominance‐solvable games like prisoner's dilemma and asymmetric coordination games like stag hunt and hawk–dove. The evidence was most consistent with the accumulation of payoff differences over time: we found longer duration choices with more fixations when payoffs differences were more finely balanced, an emerging bias to gaze more at the payoffs for the action ultimately chosen, and that a simple count of transitions between payoffs—whether or not the comparison is strategically informative—was strongly associated with the final choice. The accumulator models do account for these strategic choice process measures, but the level‐k and cognitive hierarchy models do not. © 2015 The Authors. Journal of Behavioral Decision Making published by John Wiley & Sons Ltd.     

A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

Modelling the History of Ideas

We propose a new method for the history of ideas that has none of the shortcomings so often ascribed to this approach. We call this method the model approach to the history of ideas. We argue that any adequately developed and implementable method to trace (dis)continuities in the history of human thought, or concept drift, will require that historians use explicit interpretive conceptual frameworks. We call these frameworks models. We argue that models enhance the comprehensibility of historical texts, and provide historians of ideas with a method that, unlike existing approaches, is susceptible neither to common holistic criticisms nor to Skinner's objections that the history of ideas yields arbitrary and biased reconstructions. To illustrate our proposal, we discuss the so-called Classical Model of Science and draw upon work in computer science and cognitive psychology.     

The counterintuitive impact of responses and response times on parameter estimates in the drift diffusion model

Given a drift diffusion model with unknown drift and boundary parameters, we analyse the behaviour of maximum likelihood estimates with respect to changes of responses and response times. It is shown analytically that a single fast response time can dominate the estimation in that no matter how many correct answers a test taker provides, the estimate of the drift (ability) parameter decreases to zero. In addition, it is shown that although higher drift rates imply shorter response times, the reverse implication does not hold for the estimates: shorter response times can decrease the drift rate estimate. In the light of these analytical results, we illustrate the actual impact of the findings in a small simulation for a mental rotation test. The method of analysis outlined is applicable to a broader range of models, and we emphasize the need to further check currently used reaction time models within this framework.