Pigs in a Box:
To observe how this works consider a game played by two pigs, one weak and the other strong. The pigs’ strategies are simple: either Push a lever that distributes 100 calories of feed down a shoot about 20 feet away or Wait at the end of the feed shoot. Waiting burns no calories, but rushing from the lever to the shoot burns 10 calories. If both pigs wait, the lever is not pushed, so neither gets any feed. If the strong pig pushes the lever, he gets some of the feed by chasing the weak pig away; however, the weak pig cannot push the strong one aside, so the weak pig would get nothing by pushing the lever. Consequently, the caloric payoffs are given in the following game matrix:
Begin with the strong pig’s best response: if the weak pig waits, the strong pig does better by pushing the lever; but if the weak pig pushes the lever, the strong pig’s best response is to wait.
So neither of the strong pig’s strategies dominates the other. However, for the weak pig, waiting dominates pushing: 75 > - 10 and 0 > - 10. So we eliminate the weak pig’s push strategy: it’s dominated. Since only one strategy remains for the weak pig, that strategy is its dominant strategy. A strategy is dominant if it’s the best response no matter what the other players’ strategies are – that is, for every value of si .
The resolution to this game is dominant strategy equilibrium. It is determined by eradicate all the dominated strategies. If what’s left is unique, we have the equilibrium. Here behind you is the weak pig’s dominant strategy. Specified that the weak pig waits the strong pig’s best response is to push. Hence the equilibrium is the pair of strategies (Wait, Push) with associated payoffs (75, 15); that is, it’s lower-left element of the game matrix. Merely the weak survive!
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