Dominant Strategy Examples to Know for Game Theory

Dominant strategies in game theory show how players make choices that can lead to better or worse outcomes. These examples reveal the balance between individual interests and collective benefits, impacting business decisions and economic behavior in real-world scenarios.

1. Prisoner's Dilemma

   • Two players must decide whether to cooperate or betray each other.
   • The dominant strategy for both players is to betray, leading to a worse outcome for both.
   • Highlights the conflict between individual rationality and collective benefit.

2. Chicken Game

   • Two players drive towards each other; the first to swerve loses, but if neither swerves, both face a disastrous outcome.
   • Demonstrates the tension between risk-taking and cooperation.
   • The dominant strategy can vary based on the players' perceptions of each other's willingness to yield.

3. Matching Pennies

   • Two players choose heads or tails; one wins if they match, the other wins if they do not.
   • No dominant strategy exists; players must randomize their choices.
   • Illustrates the concept of mixed strategies in game theory.

4. Battle of the Sexes

   • Two players want to coordinate on an activity but have different preferences.
   • Each player has a dominant strategy to choose their preferred option, but cooperation leads to a better outcome.
   • Highlights the importance of communication and negotiation in achieving mutual benefits.

5. Stag Hunt

   • Two players can either hunt a stag together (high reward) or hunt a hare individually (low reward).
   • Cooperation is the dominant strategy for the best outcome, but individual risk leads to a lower reward.
   • Emphasizes trust and the value of collaboration in achieving optimal results.

6. Traveler's Dilemma

   • Two players independently choose a number; the lower number wins, but both receive a penalty if they choose differently.
   • The dominant strategy is to choose the lowest possible number, leading to a suboptimal outcome for both.
   • Illustrates how competition can lead to worse outcomes than cooperation.

7. Hawk-Dove Game

   • Players can choose to be aggressive (hawk) or passive (dove) in a conflict over resources.
   • The dominant strategy depends on the proportion of hawks and doves in the population.
   • Highlights the balance between aggression and cooperation in resource allocation.

8. Ultimatum Game

   • One player proposes a division of a sum of money; the second player can accept or reject the offer.
   • The proposer has a dominant strategy to offer the smallest amount, but rejection leads to no gain for either.
   • Demonstrates fairness and negotiation dynamics in economic behavior.

9. Dictator Game

   • One player decides how to split a sum of money with another player who has no say.
   • The dominant strategy for the dictator is to keep all the money, but many choose to share.
   • Highlights altruism and social preferences in decision-making.

10. Public Goods Game

    • Players decide how much to contribute to a public good that benefits all, regardless of individual contributions.
    • The dominant strategy is to free-ride, but collective contributions lead to the best outcome for the group.
    • Illustrates the challenges of cooperation in providing public goods and the tragedy of the commons.