SPE Payoffs

Definition

SPE payoffs, or Subgame Perfect Equilibrium payoffs, refer to the outcomes of a game that remain consistent and optimal in every subgame of the original game. This concept emphasizes that players' strategies should not only lead to a Nash Equilibrium but should also be robust at every point of the game, ensuring that each player’s strategy is optimal given the strategies of others, even in future moves. The importance of SPE payoffs lies in their ability to establish credibility and sustainability in strategic interactions.

5 Must Know Facts For Your Next Test

1. SPE payoffs ensure that players' strategies are optimal not just at the game's beginning but also throughout all future possible scenarios.
2. In games with perfect information, the SPE concept can often be demonstrated using backward induction, allowing players to foresee and plan for future moves.
3. The existence of SPE payoffs helps resolve issues related to credibility in commitments, making it easier for players to trust each other's strategies.
4. While Nash Equilibria can exist without being subgame perfect, all SPE payoffs are inherently Nash Equilibria due to their strategic consistency.
5. SPE payoffs are particularly significant in dynamic games where players make decisions over time, as they help predict outcomes based on sequential rationality.

Review Questions

• How do SPE payoffs relate to Nash Equilibrium in game theory?
  • SPE payoffs are a refinement of Nash Equilibrium that ensures not only that players' strategies are optimal at the outset but also throughout every possible subgame. While a Nash Equilibrium may exist in a one-shot game or scenarios where players can make non-credible threats, SPE requires that these strategies remain optimal even when considering future moves and responses by other players. Therefore, every SPE payoff is a Nash Equilibrium, but not all Nash Equilibria are SPE payoffs.
• Discuss how backward induction is utilized in finding SPE payoffs in extensive form games.
  • Backward induction is a crucial technique for determining SPE payoffs in extensive form games with perfect information. This method involves starting from the final moves of the game and analyzing what the optimal choice would be for each player at those stages. By working backwards through each player's potential decisions and identifying best responses at every stage, players can construct a strategy profile that leads to SPE payoffs. This approach ensures that decisions made at earlier stages are consistent with future actions.
• Evaluate the role of SPE payoffs in establishing credibility and trust within repeated games.
  • In repeated games, establishing credibility is essential for fostering cooperation among players over time. SPE payoffs enhance this credibility by ensuring that players' strategies remain optimal at all points in the game, which discourages deviation from cooperative behaviors. When players know that their actions today affect future interactions, they are more likely to stick to agreements that yield favorable long-term outcomes. This dynamic creates an environment where trust can be built as players anticipate each other's rational strategies based on past behavior, solidifying cooperation through sustained credible commitments.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit from changing their strategy while the other players keep theirs unchanged.

Backward Induction: A method used to solve extensive form games by analyzing the last possible moves first and determining optimal strategies backwards to the beginning of the game.

Repeated Games: Games that are played multiple times, allowing players to adjust their strategies based on past actions, often leading to different equilibria than one-shot games.