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Do all games have dominant strategies?

This question asked by Anonymous

No, consider Paper, Rock, Scissors. This simple game has no dominant strategy. Paper beats rock (because the paper will cover the rock) and rock beats scissors (because the rock will break the scissors), but scissors beats paper (because the scissors will cut the paper). The preferred choice is strictly a function of what the other player selects. Many situations in life, and business, are more like Paper, Rock, Scissors than the Prisoner’s Dilemma, where a dominant exists to rat on your partner in crime. In many cases, winning at business in the long-run often occurs because you are one step ahead of the competition, not because you deploy a strategy that attempts to take advantage of a short-run opportunity.

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