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---
title: "Sampling Strategies in DfE - Pilot study"
author: "Linus Hof"
date: "2021"
output: html_document
---

# Study Description

In this pilot study, choice data will be generated by applying the *comprehensive* and *piecewise sampling strategy* and hybrids thereof to a series of two-prospect gambles. 

The simulated data will be explored for characteristic patterns of (or differences between) sampling strategies under varying structures of the environment, i.e., the features of a gamble's prospects, and other aspects of the sampling and decision behavior (model parameters).

# Dataset

## Agents

Under each condition (sampling strategy x all possible parameter settings), all gambles are played by N = 150 synthetic agents. 

## Gambles 

Two different types of two-prospect gambles will be tested: (a) Gambles, in which one of the prospects contains a safe outcome only and the other two risky outcomes (safe/risky gambles). (b) Gambles, in which both prospects contain of two risky outcomes (risky/risky gambles). 

All outcomes are in the gain range $\omega_i \geq 0$.

```{r}
n_agents <- 150
```

# Model parameters 

**Switching probability:** $s$ is the positive (negative) probability increment added to (subtracted from) the unbiased attendance probability $p = .5$ with which agents draw the succesive single sample from the prospect they did not get their most recent single sample from. We vary $s$ between 0 to .4 in increments of .1.    

**Boundary type**: Can either be the minimum value *any* prospect's sum of random variable realizations must reach (absolute boundary) or the minimum value for the difference of these sums (relative boundary).

**Boundary value:** 

**Noise parameter:**

```{r}

```