Course Notes| Game Theory 3

1. Iterative Elimination of Dominated Strategies

The Medium Voter Theorem

Suppose: Voters are evenly distributed

Findings: Candidates crowed in the center in political science

From American election history, the medium voter theorem have being doing well. Some of elected president all presented a relatively medium political views.

Some violations:

(2) Different parties have different quota in election

(3) voters are not always voting based on political standpoints, but also other aspects

(4) This model is not suitable in solving games concerning more than 2 candidates

(5) Candidates may not be true in explaining their positions, and the voters might not believe in candidates commitment that they are conservative or centralist.

Models are always abstract, the reason why we have models is to try and capture and test our intuitions (crowed in the center might earn more votings). What we should to is not to give up modeling, but to enrich models and to add more into the model.

2. Mixed strategies

1. If player 1 suppose player 2s probability to choose left and right is (0.5, 0.5).

Expected payoffs:

EU(T) = 0.5* 5 + 0.5* 0 = 2.5

EU (M) = 1 *0.5 + 4*0.5 = 2.5

EU (B) = 4*0.5 + 2* 0.5 = 3.0

2. If player 2 is expected to choose left and right at the probability of ...