Prospect_Theory

1. Structure

The decision rule is broken down into two phases: editing and evaluation.

1) Editing Phase

1. Coding + code gains and losses in terms of a reference point + further discussion for references are needed
2. Combination + (200, 0.25 ; 200, 0.25) = (200, 0.5)
3. Segregation + break into uncertain part and certain part
4. Cancellation + same outcomes are canceled out in comparison
5. Simplification + rounding, discarding extremely unlikely outcomes
6. Detection of Dominance + dominated propects are not evaluated

2) Evaluation Phase

1. Comparing total value, V
2. Pick the one with the highest V
3. V is determined by decision weight, \(\pi(.)\) and value function, \(v(.)\)

[\[\begin{align} &\text{(1) regular cases}\\ &V(x, \ p \ ; \ y, \ q ) = \pi(p)v(x) + \pi(q)v(y)\\ \\ &\text{(2) strict cases (negative or positive)}\\ &V(x, \ p \ ; \ y, \ q ) = v(y) + \pi(p)[v(x)-v(y)] \\ \\ &\text{by subcertainty rule, (2) cannot be reduced to (1)} \end{align}\]]

2. Value function: \(v(.)\)

1. two arguments: \(w\) and \(x\) → initial reference point and changes
2. \(w\) is largely negligible: good approximation obtained using just one argument, \(x\)
3. In general, Concave when \(x>0\), Convex when \(x<0\) → kinked curve

• for some circumstances, concavity in negative \(x\) and convexity in positive \(x\) is observed

4. steeper when \(x\) is negative: \(v'(x) < v'(-x)\)
5. greater absolute value when \(x\) is negative: \(v(x) < -v(-x)\)

3. Decision weights: \(\pi(.)\)

1. subadditivity(for small p)

• \(\pi(rp) > r\pi(p)\)

2. overweighting(for small p)

• \(\pi(p) > p\)

3. subcertainty

• \(\pi(p) + \pi(1-p) < 1\)

4. subproportionality

• \(\frac{\pi(pq)}{\pi(p)} < \frac{\pi(pqr)}{\pi(pr)}\)

4. Application

(omitted)