# Conflicts with Momentum

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## Abstract

**:**

## 1. Introduction

## 2. A Model of Conflicts with Momentum

#### 2.1. Model Setup

#### 2.2. Participation, Parameter Restrictions, and Pyrrhic Victories

**Participation Constraint (i)**(PC (i)): ${\alpha}^{{r}_{2}}\ge ({r}_{2}-1)$.

**Participation Constraint (ii)**(PC (ii)): $2\ge {r}_{1}$.

**Pyrrhic Victory**(PV): ${\alpha}^{{r}_{2}}(1+{\alpha}^{{r}_{2}})-{r}_{2}{\alpha}^{{r}_{2}}<\frac{{r}_{1}}{4}(1-{\alpha}^{2{r}_{2}}).$

#### 2.3. Rent Dissipation

## 3. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Equilibrium Payoff to the First−Stage Winner with $\alpha =0.75$, $V=1$, as ${r}_{1}$ and ${r}_{2}$ Vary.

**Figure 2.**Equilibrium Payoff to the First−Stage Winner with $\alpha =0.5$, $V=1$, as ${r}_{1}$ and ${r}_{2}$ Vary.

**Figure 3.**Equilibrium Payoff to the First−Stage Winner with $\alpha =0.25$, $V=1$, as ${r}_{1}$ and ${r}_{2}$ Vary.

**Figure 4.**Equilibrium Payoff to the First−Stage Loser with $\alpha =0.75$, $V=1$, as ${r}_{1}$ and ${r}_{2}$ Vary.

**Figure 5.**Equilibrium Payoff to the First−Stage Loser with $\alpha =0.5$, $V=1$, as ${r}_{1}$ and ${r}_{2}$ Vary.

**Figure 6.**Equilibrium Payoff to the First−Stage Loser with $\alpha =0.25$, $V=1$, as ${r}_{1}$ and ${r}_{2}$ Vary.

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## Share and Cite

**MDPI and ACS Style**

Boudreau, J.W.; Mathews, T.; Sanders, S.D.; Bagchi, A. Conflicts with Momentum. *Games* **2022**, *13*, 12.
https://doi.org/10.3390/g13010012

**AMA Style**

Boudreau JW, Mathews T, Sanders SD, Bagchi A. Conflicts with Momentum. *Games*. 2022; 13(1):12.
https://doi.org/10.3390/g13010012

**Chicago/Turabian Style**

Boudreau, James W., Timothy Mathews, Shane D. Sanders, and Aniruddha Bagchi. 2022. "Conflicts with Momentum" *Games* 13, no. 1: 12.
https://doi.org/10.3390/g13010012