Here is another famous proposition in game theory proposed by Duncan Black (1948). The idea is related to the positioning of ideology in the political spectrum but fits equally well in other areas, such as product launches.
Imagine two candidates who want to choose their positions on the political landscape in an election. In a simple realisation, suppose there are 10 positions ranging from extreme left (1) to extreme right (10). If candidate 2 knows that candidate 1 is to make a stand in position 1, what is the best place for the former position herself? Let’s look at the payoff. Candidate 1 will get all the votes of people who hold the idealogy of (in this case) the extreme left. Candidate 2 will get everybody else (from 2 to 10). And if the voters are split equally among the whole spectrum, that becomes 10% and 90% for 1 and 2, respectively. Note that choosing 9 vs 10 also yields the same outcome.
Knowing that candidate 2 will position at 2, the other can now stand at 3 and get all votes from 3 onwards (80%). Continuing this further, you end up at positions 5 and 6. Or the candidates are close to the middle to maximise their chance of winning.
References
Iterative deletion and the median-voter theorem: YaleCourses
Median voter theorem: Wiki
