The war of attrition involves two players making simultaneous moves. The play moves from period to period. Each player at each period has an option to fight or quit. The game ends when at least one player quits. The player that did not quit gets the prize, V. Each period in which both fights incur a cost of C for each player. If both leave at once, then they get 0.
After the first period,
| Action A | Fight | Fight | Quit | Quit |
| Action B | Fight | Quit | Fight | Quit |
| Payoff A | -C | V | 0 | 0 |
| Payoff B | -C | 0 | V | 0 |
If both fight, then the game continues to the second period. Let’s check what can happen in the second period.
| Action A | Fight | Fight | Quit | Quit |
| Action B | Fight | Quit | Fight | Quit |
| Payoff A | -2C | V-C | -C | -C |
| Payoff B | -2C | -C | V-C | -C |
The game can go on taking, adding more costs to the players. At some stage, you realise the war of attrition is no longer about the prize – you might lose more than you can win – it’s about winning. An example is two firms fighting for a market that can hold one company. The game occurs when they compete with each other, losing money but hoping the rival will eventually withdraw.
A well-known example is the competition between British Satellite Broadcasting (BSB) and Sky Television in the 1980s over the satellite television market. By the time they ended the fight and merged into one first, they had accumulated over £1 billion in losses.
