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(Y,Y). That is, if the players are jointly playing either of those
combinations of strategies, neither has an incentive to deviate.
Their response is a best response to the other players'
actions.
When this game is played in the laboratory, about 3/4 of the row
players (player A) choose X while about 3/4 of the column players
(player B) choose Y.
This outcome is striking. The players mis-coordinate: there is a
high chance that they both get nothing. Furthermore, each player
tries to coordinate on the strategy that the other player would be
better off coordinating on. That is, Player A receives 6 from
successful coordination choosing X, which is less than the 6.1
Player A would get from coordinating on Y.
Suppose players in this game think according to the level-k
model. Assume a Level-0 agent randomises between options with equal
probability.
a) What would player A and player B do if they were level-1
players? [1 mark]
b) What would player A and player B do if they were level-2
players? [1 mark]
c) What would player A and player B do if they were level-3
players? [1 mark]
d) Given your answers to a) through c), how might a mix of
level-k players explain the mis-coordination described above? [2
marks]
For all four questions, remember the idea behind level-k
thinking: given their own cognitive level, a player forms an
expectation of what others will do and tries to be "one step ahead
of them".
B х TY Y х D 6, 6.1 0,0 0,0 6.1,6 Y