# A duopoly preemption game with two alternative stochastic investment choices

## TL;DR

This paper models a duopoly investment game with stochastic choices, analyzing how firms decide when to invest to maximize benefits under uncertainty, revealing asymmetric equilibria and preemptive behaviors.

## Contribution

It introduces a novel stochastic control game framework for duopoly investments with two irreversible options and characterizes asymmetric equilibria under uncertainty.

## Key findings

- No pure symmetric subgame perfect Nash equilibrium exists.
- Asymmetric equilibrium involves preemptive investment in certain demand intervals.
- Firms are reluctant to be the first mover outside preemption zones.

## Abstract

This paper studies a duopoly investment model with uncertainty. There are two alternative irreversible investments. The first firm to invest gets a monopoly benefit for a specified period of time. The second firm to invest gets information based on what happens with the first investor, as well as cost reduction benefits. We describe the payoff functions for both the leader and follower firm. Then, we present a stochastic control game where the firms can choose when to invest, and hence influence whether they become the leader or the follower. In order to solve this problem, we combine techniques from optimal stopping and game theory. For a specific choice of parametres, we show that no pure symmetric subgame perfect Nash equilibrium exists. However, an asymmetric equilibrium is characterized. In this equilibrium, two disjoint intervals of market demand level give rise to preemptive investment behavior of the firms, while the firms otherwise are more reluctant to be the first mover.