Lecture

one strict deadline for the first batch

• do we understand it?
• does it do what it's supposed to do?

if $c=0$, it's a zero-sum game ($u_1=-u_2$)

• strategy $\pi_i$
• strategy profile $\pi=(\pi_1,\dots,\pi_N)$
• $\pi_{-i}$ … strategies of all players in $\pi$ except $\pi_i$
• support of strategy $\pi_i$ … set of all actions with non-zero probability

set of strategies that maximize utility for given $\pi_{-i}$

• for any best response strategy $\pi_i$, all actions in its support have the same expected utility
• (otherwise, we could move all the mass to the “best” one)

any convex combination of BRs is also BR

iterated removal of dominated strategies

1. strategy profile evaluation (what is the expected utility?)
2. best response calculation
3. iterated removal of dominated strategies

• maximin strategy
  • we maximize our expected utility assuming the worst-case scenario
• Nash equilibrium
  • none of the players can benefit from unilaterally deviating from their policy
  • support enumeration