Credible threats

Definition

Credible threats are actions or statements made by a player in a strategic interaction that are believable and can influence the behavior of others. In sequential games, where players make decisions one after another, the concept of credible threats is crucial for establishing strategic outcomes. If a threat is credible, it can alter the strategies chosen by other players, leading to different equilibria based on the expectations of future actions.

5 Must Know Facts For Your Next Test

1. In sequential games, players anticipate the potential responses of their opponents when making threats or promises.
2. A credible threat often requires that the player making it has the ability and intention to carry it out if necessary.
3. The concept of credible threats is important for maintaining cooperation in repeated games, where the threat of retaliation can deter defection.
4. Not all threats are credible; if a player lacks the means to follow through, it may not influence others’ strategies.
5. The ability to create credible threats can enhance a player's bargaining power and impact negotiation outcomes.

Review Questions

• How do credible threats influence decision-making in sequential games?
  • Credible threats significantly influence decision-making in sequential games by altering the expectations and strategies of other players. When a player makes a threat that they can realistically follow through on, it forces other players to consider this potential action when choosing their own strategies. This can lead to different equilibria as players adjust their actions based on the belief that the threat will be executed if provoked.
• Discuss the relationship between credible threats and subgame perfect equilibrium in sequential games.
  • Credible threats play a critical role in achieving subgame perfect equilibrium because they ensure that strategies are optimal not just at the game's start but also at every possible stage of play. For a strategy profile to qualify as subgame perfect, it must hold up under any possible continuation of the game, meaning players must not only act optimally but also believe that their opponents will carry out credible threats if necessary. Thus, understanding which threats are credible is essential for analyzing the stability of equilibria in dynamic settings.
• Evaluate how the credibility of threats affects cooperation in repeated games and its implications for long-term strategic interactions.
  • In repeated games, the credibility of threats has profound implications for fostering cooperation among players. If players believe that their opponents will follow through with credible threats of punishment for defection, they are more likely to cooperate to avoid negative outcomes. This creates a stable environment where trust can develop over time. Conversely, if threats lack credibility, players may feel incentivized to defect, undermining cooperation and leading to less favorable long-term outcomes. Thus, establishing and maintaining credible threats is key for successful strategic interactions in repeated settings.

Related terms

Subgame perfect equilibrium: A refinement of Nash equilibrium applied to dynamic games, where players' strategies constitute a Nash equilibrium in every subgame of the original game.

Backward induction: A method used to solve sequential games by analyzing the game from the last move backwards to determine optimal strategies at each decision point.

Game theory: The study of mathematical models of strategic interaction among rational decision-makers, focusing on how individuals make choices in competitive situations.