Consider the following game. Suppose that players play simultaneously over many periods. In each period, each player best responds to the action played by the opponent the period before.
L M R
U 0,0 4,5 5,4
M 5,4 0,0 4,5
D 4,5 5,4 0,0
Assume that in period 1, players start with the strategy profile (M,L). Describe play in the next 7 periods. Does a pattern emerge?
Period 1 ML strategy, player A will play ML, player B will play UR
Period 2 UM strategy, player A will play DM, Player B will play MR
Period 3 UR strategy, player A will play UR, player B will play ML
Period 4 DL strategy player A will play DM, player B will play UR
Period 5 DM strategy, player A will play ML, Player B will play UR
Period 6 UL strategy, player A will play ML, player B will play DM
Period 7 MM strategy player A will play DM, player B will play ML
A pattern emerges where by each player assumes a strategy that gives maximum payoff
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