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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

We submitted three models to the competition which were based on the I-SAW model. The models introduced four new assumptions. In the first model an adjustment process was introduced through which the tendency for exploration was higher at the beginning and decreased over time in the exploration stage. Another new assumption was that surprise as a factor influencing the weight of a trial in the sampling procedure was added. In the second model we added the possibility of an exclusion of unreliable experiences gained in the early trials of a game and the possibility of a revision of a reasonable alternative which was responsible for a very bad outcome in the previous trial. Three of the four added assumptions were combined in the third model. Because each of our models contains at least two new assumptions, we estimated the relative effect of each assumption on the estimation and prediction scores and carried out a test of robustness. In this way, we were able to clarify the usefulness of each added assumption.

We submitted three models to the market entry prediction competition 2010. All three models are based on the inertia, sampling and weighting (I-SAW) model which will be explained in Section 2. In Section 3 we describe the four additional assumptions we examined throughout the three models, which we present in Section 4. In Section 5 we discuss the relative effect of each added assumption. Lastly, in Section 6 we summarize the analysis results and the theoretical conclusions.

Both the estimation experiment and the competition experiment are modeled as a series of _{m}_{m}_{i}_{i}_{i}_{i}_{i}_{i,t} ∊ A

The decision process of each agent ^{enter}

If an agent does not explore, then she enters the second stage. Inertia implies to repeat the last action _{i,t}_{i,t}_{−1} with probability

All agents that have neither entered the exploration stage nor have decided in the inertia stage to repeat their last action, make their decision in the exploitation stage. In this stage each agent chooses the action _{i,t} ∊ A

Given the set of payoffs for all past cases _{i,past case}_{i}_{,1}), …, _{i,t}_{−1})} and the number of sample experiences or sample cases _{i}_{i,t}_{i}^{1}, … ^{μi}_{i}^{l}_{i}^{l}

In the I-SAW model, the probability to explore
_{i} if t > 1. The variable ε_{i} differs between people, but is constant within a person throughout all trials of a game. However, it seems reasonable to assume that when faced with an unfamiliar environment, subjects will display higher explorative behavior at the beginning than after gaining some experience. As indicated by machine learning models, the change of exploration can be linear [

Thus, the individual tendency to explore
_{i}

In the I-SAW model, when sampling (past) experiences, the most recent trial has a higher probability to be included in the sample due to the recency effect. All other past trials have the same probability to be sampled. However, studies concerning the von-Restorff-Effect [^{t}^{−1} exceeds a threshold of 0.85 (according to fitted data), the probability to sample this trial for the calculation of the ESV is increased. To take the underweighting of rare events in decisions from experience [_{i}_{i}

As previously noted, besides the most recent trial the sampling procedure of the I-SAW model assigns the same probability to be recalled to all other past trials. However, in the first trials of a new game, strategic uncertainty and uncertainty about the payoff rule is likely to be higher. Thus, early choices are more prone to randomness. This led us to the assumption, that later in the game, the participants should be more likely to question the reliability of the information gained through the very early trials of the game. In order to include this “doubt about experiences in very early trials” we introduced the following modification: Early experiences or cases are revised and can be excluded from the sample even if they are drawn at first during the sampling process. Revision implies that the agent repeats the sampling procedure for a given sample experience or sample case ^{l}^{l}^{l}^{l}^{l}

Imagine action a_{i,t} = not enter has the higher

Revision implies to choose a_{i,t} = enter with probability λ_{i}∼U[0,0.5] (a trait) and otherwise the action with the higher ESV a_{i,t} = not enter. Note that the revision process is analogous if action a_{i}_{,}_{t}

The model of Teodorescu, Hariskos and Leder (2010) introduces two changes in the I-SAW model: First, the tendency for exploration is higher at the beginning and decreases over time in the exploration stage (3.1). Second, the last surprising trial is included with higher probability in the sampling of past cases in the exploitation stage (3.2). One of the main advantages of these suggested changes to the I-SAW model is that although it takes into account the changes of exploration over time and the effect of surprise on memory processes, it does not add any other traits than the ones estimated by the original I-SAW model.

The model of Hariskos, Leder and Teodorescu (2010) introduces two changes to the exploitation stage of the I-SAW model: First, very early trials are excluded with higher probability from the sample of experiences (3.3). Second, the affective reaction caused by negative experiences was addressed (3.4).

After simulating the first two models, we created a third model in which we integrated the decreasing tendency to explore with increasing numbers of trials (additional assumption 3.1), the doubt about the reliability of experiences in very early trials (additional assumption 3.2), and the revision of a reasonable alternative given an associated very bad experience in the previous trial (additional assumption 3.4). We kept all parameters other than a slight change in the function determining the tendency to explore as depicted below:

All three models yield a better fit for the data from the estimation set than the I-SAW model. The fit of the first model (3.1) was slightly better than the I-SAW model, and the fit of the other two models (3.2 and 3.3) were by far better. However, only the first model predicted the competition data set better than the I-SAW model. In the following section we will focus on this issue.

Because we added more than one assumption to the I-SAW model in each of our models, we cannot state the relative effect of each assumption individually. For this reason, we calculated the MSD scores after the competition by adding only one assumption to the I-SAW model (10,000 simulations) and summarized the relative effect of each assumption. The relative effect for the estimation and competition score is depicted in

As depicted, each of our additional assumptions improved the estimation score. The first three assumptions (3.1, 3.2, and 3.3) also improved the competition score. Whereas the fourth assumption (3.4), while leading to the largest improvement for the estimation set, impaired the competition score, this clearly indicates over-fitting. Thus, we can conclude that the additional fourth assumption is responsible for the poor predictive performance of our second and third models.

In order to examine whether the very small improvement that resulted from adding the first assumption (3.1) was not obtained by chance, we conducted an additional analysis. One simple prediction of the decreasing exploration assumption is that in problems in which the best reply is relatively stable across trials, best reply behaviors are expected to become more common as time advances. On the other hand, constant exploration rate, as assumed by the original I-SAW model, predicts that in these cases, the frequency of best reply behaviors will remain constant over all trials. Problems 3 and 8 satisfy the relatively stable best reply requirement, since in these problems about 95% of the experiences yielded better payoffs for entering than staying out (obtained greater than forgone payoffs for entering and

In this paper, we examined four additional assumptions to the I-SAW model [

The performance of our models relative to the baseline model.

I-SAW Model (2) | 1.38 | 1.1749 | ||

Teodorescu |
1.3507 | −2.12% | 1.16 | −1.27% |

Hariskos |
1.1546 | −16.33% | 1.2197 | 3.81% |

Leder |
1.1546 | −16.07% | 1.1932 | 1.56% |

The relative effect of each assumption on the estimation and competition score.

I-SAW Model (2) | 1.38 | 1.1749 | ||

Exploration Over Time (3.1) | 1.3485 | −2.28% | 1.1738 | −0.09% |

Surprising Experiences (3.2) | 1.3496 | −2.20% | 1.1617 | −1.12% |

Very Early Trials (3.3) | 1.2791 | −7.31% | 1.1375 | −3.18% |

Bad Experience in the Previous Trial (3.4) | 1.2312 | −10.78% | 1.2486 | 6.27% |

Percentage of best reply behavior to previous trials for trial 1–12.

2 | 75.0% |

4 | 73.3% |

6 | 86.7% |

8 | 86.7% |

10 | 91.7% |

12 | 90.0% |