A Primer in Game Theory 8.9分

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In the normal-form game ($G=\{S_1,\dots,S_n;u_1,\dots,u_n\}$), let ($s_i'$) and ($s_i''$) be feasible strategy for player ($i$). Strategy ($s_i'$) is strictly dominated by strategy ($s_i''$) if for each feasible combination of other players' strategies, ($i$)'s payoff from playing ($s_i'$)  is strictly less than playing ($s_i''$):
$$u_i(s_1,\dots,s_{i-1},s_i',s_{i+1},\dots,s_n) < u_i(s_1,\dots,s_{i-1},s_i'',s_{i+1},\dots,s_n)$$
\noindent for each ($(s_1,\ldots,s_{i-1},s_{i+1},\ldots,s_n)$) that can be constructed from the other players' strategy spaces ($S_1,\dots,S_{i-1},S_{i+1},\ldots,S_n$).

Rational players do not play strictly dominated strategy, because there is no belief that a player could hold (about other players will choose) such that it would be optimal to play such a strategy.
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