Reduced Game After Two Rounds of IDSDS
3,2
5,1
1,3Player 1
Player 2
a
c
d
0,4
1,4
4,2
w z
FIGURE 3.26 Reduced Game After Three Rounds of IDSDS
5,1
1,3 Player 1
Player 2
c
d 1,4
4,2
w z
Summary This chapter outlines methods for solving a game when players are rational, players know that players are rational, players know that players know that players are rational, and so on, and so on. We emphasize the implication that a rational player will not use a strictly dominated strategy. A strategy is strictly dominated when another strategy yields a higher payoff, regardless of what the other players do. Thus, no matter what beliefs a player holds con- cerning the other players’ strategies, it is never optimal for him to use a strictly dominated strategy. A dominant strategy is surely the unique compelling way to play a game, as it strictly dominates every other strategy.
It is also prudent to avoid playing a weakly dominated strategy. A strategy is weakly dominated when the use of another strategy is better some of the time (i.e., for some strategies of the other players) and is at least as good all of the time. You may end up regretting using a weakly dominated strategy, and you’ll never regret having avoided it. In some games—such as the second-price
For the game in Figure 3.16, find the strategies that survive the IDSDS.