Dominated Strategy
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Dominated Strategy
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A dominated strategy is a strategy which doesn’t result in the optimal outcome in any case. A strategy is dominated if there always exist a course of action which results in higher payoff no matter what the opponent does.
Identifying strategic dominance in a game is important in identifying its Nash equilibrium, an outcome which no player would want to change. In a two-strategy game, if one strategy is dominant, the other must be a dominated strategy. Since not all games have a dominant strategy, it is not necessary for all games to have dominated strategies. But if there are more than two strategies available, it is possible for a game to have a dominated strategy even if there is no dominant strategy (as illustrated in example 2).
In the example on dominant strategy, we identified that hiring a lawyer is a dominant strategy for both firms. Hence, we can conclude that not hiring a lawyer is the dominated strategy for both firms.
Now, let’s see what happens in a game in which there are more than two strategies available to each player. Assume that Firm A and Firm B are firms who must decide about whether to decrease their advertising budget, not change it or increase it. The following payoff matrix shows different scenarios:
In this game there is no dominant strategy for Firm A. It is because when Firm B cuts advertising, Firm A’s maximum payoff occurs when it increases its budget (see Row 3 and Column 1). Similarly, when Firm B doesn’t change its advertising budget, maximum payoff for Firm A occurs when it increases its budget (see Row 3 and Column 2). But if Firm B also increases its advertising, maximum payoff for Firm A exists when it doesn’t change its budget (see Row 2 and Column 3). Since the maximum payoff changes with change in strategy of the opponent, there is no dominant strategy.
But the game has a dominated strategy, a strategy which is no good no matter what the opponent do. In order to identify the dominated strategy, we need to find if a row exists which corresponds to the lowest Firm A payoffs in all columns.
by Obaidullah Jan, ACA, CFA and last modified on Mar 11, 2019 Studying for CFA ® Program? Access notes and question bank for CFA ® Level 1 authored by me at AlphaBetaPrep.com
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