Iterative Deletion and Median Voter Theorem

Sometimes, iterative deletion of dominated strategies lead to converging——only one final option.

Application of politics, theme.

• 2 candidates choosing political spectrum from 10 positions, ranging from left to right.
• Assume each position has 10% of vote, and vote to the candidate closest to the position.
• Assume payoff: number of vote.

Analysis. Position 1 and position 10 are strictly dominated by 2 and 9 respectively.

Currently, 2 is not dominated by 3. However, deleting the dominated strategies(1 and 10), 2 is strictly dominated by 3.

Do iterative deleting, and at the end, only position 5 and 6 remain.——The Median Voter Theorem.

Flaws:

• Voter not evenly distributed throughout spectrum
• Voters not voting
• Politics problem as being multi-dimensional
• Announcing to have some political stance does not necessarily entail commitment to a position

Football Match and Best Response in Business

Theme. Goalie and shooter choose position to dive/shoot.

Lesson: Do not choose strategy that is not best response under any belief.