HMM)
3.7 Discussion
In this paper, we establish a new machine learning method, a hidden markov model, which takes advantage of choice process data (particularly fixations) and can explain the strategic dynamics in games. This model is able to learn the best way to partition an action set into several hidden states. We present an application using the saliency game in chapter one, where the action set contains more than one million options.
The model performed well with only two hidden states and successfully learned that people started with a similar first thought to consider salient choices while turned into different paths afterwards under in three different games, coordination, hiding and seeking.
Our model also contributes to the current level-k literature. We specified a new method to type classify a strategic level for each single choice using fixation data and a trained HMM. The fitting results consolidate previous findings that levels are distributed in Poisson and the average level is often less than three. The new type specification method also solved two problems which previous methods could not achieve: 1) The level identification does not rely on a special game structure and can be generalized. 2) The level is directly defined on the process itself rather than choices. It revolutionized an old concept that strategic levels originate from individual individual differences. Instead, strategic levels come from a combination of performance in a particular game and the average performance of a person.
Last but not least, we build a continuous-time HMM on the top of the discrete one.
The continuous model is able to process fixation time lengths and use them for decision prediction at continuous time domains. In particular, this model success-
fully predicts the game outcome of saliency game, when people are facing a time pressure.
One limitation of our study is that we do not know yet what percentage of people reason without looking. However, such limitation on HMM has less effect on the general interpretation of HMM as they are probabilistic estimations anyway, but it will underestimate the levels because we are not able to identify those higher levels who reason mentally using the gaze method.
An important open question for future research is whether this method can ad- dress the portability issue illustrated in Hargreaves Heap, Rojo-Arjona, and Sug- den (2014). The new definition solves the problem to some extent, but not directly.
Since HMM levels are defined on single trials instead of people, which incorporate the game structure, it naturally relaxes the condition that the same individual should be consistent with their levels. It is still meaningful though to ask this question:
do people have different abilities in strategic games? If so, how should we define it? A possible future research could be to collect large data sets across subjects on different games with their gaze data recorded and to look at individual differences from an HMM perspective.
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