# Human Capital Accumulation and the Evolution of Overconfidence

## Abstract

**:**

## 1. Introduction

## 2. Related Literature

## 3. Empirical Evidence

## 4. The Model

#### 4.1. Solving the Model

**Lemma**

**1.**

#### 4.2. Skill Comparisons

^{+}.

## 5. Results

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proposition**

**4.**

## 6. Applications

#### 6.1. Overconfidence, Experience, and Trading Activity

#### 6.2. Overconfidence of Poker and Chess Players

## 7. Discussion

#### 7.1. Main Assumptions

#### 7.2. Alternative Explanations

## 8. Conclusions

## Funding

## Conflicts of Interest

## Appendix A

**Derivation of Equation (2)**The Hamiltonian for the human capital accumulation problem is given by

**Derivation of Equation (3)**Equation (2) is a Bernoulli differential equation with constant coefficients and can be solved by performing a change of variable. If we let ${W}_{i}\left(t\right)={\left({I}_{i}\left(t\right)\right)}^{1-b}$ we have that

**Derivation of Equation (6)**Rearranging (5) we have that

**Proof**

**of**

**Lemma**

**1.**

**Proof**

**of**

**Proposition**

**1.**

**Proof**

**of**

**Proposition**

**2.**

**Proof**

**of**

**Proposition**

**3.**

**Proof**

**of**

**Proposition**

**4.**

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Santos-Pinto, L. Human Capital Accumulation and the Evolution of Overconfidence. *Games* **2020**, *11*, 46.
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Santos-Pinto L. Human Capital Accumulation and the Evolution of Overconfidence. *Games*. 2020; 11(4):46.
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Santos-Pinto, Luis. 2020. "Human Capital Accumulation and the Evolution of Overconfidence" *Games* 11, no. 4: 46.
https://doi.org/10.3390/g11040046