10 - Mixed strategies in baseball, dating and paying your taxes Oct. 8, 2007

from Game Theory (Open Yale Courses)· · 1 listeners

We develop three different interpretations of mixed strategies in various contexts: sport, anti-terrorism strategy, dating, paying taxes and auditing taxpayers. One interpretation is that people literally randomize over their choices. Another is that your mixed strategy represents my belief about what you might do. A third is that the mixed strategy represents the proportions of people playing each pure strategy. Then we discuss some implications of the mixed equilibrium in games; in particular, we look how the equilibrium changes in the tax-compliance/auditor game as we increase the penalty for cheating on your taxes. Mixed strategy equilibria are calculated in simple …



We develop three different interpretations of mixed strategies in various contexts: sport, anti-terrorism strategy, dating, paying taxes and auditing taxpayers. One interpretation is that people literally randomize over their choices. Another is that your mixed strategy represents my belief about what you might do. A third is that the mixed strategy represents the proportions of people playing each pure strategy. Then we discuss some implications of the mixed equilibrium in games; in particular, we look how the equilibrium changes in the tax-compliance/auditor game as we increase the penalty for cheating on your taxes. Mixed strategy equilibria are calculated in simple normal form games. Applications of mixed strategies are discussed in sports such as tennis, baseball and football. Mixed strategies are checked for equilibrium by comparing them with all possible pure strategy deviations. It is shown that this is sufficient for equilibrium. Mixed strategy equilibrium is calculated for the Battle of the Sexes game. A game of tax is developed and its outcomes are compared with tax payment rates in a few countries. Finally, simple comparative statics are discussed in this context.