Minmax payoff

Definition

The minmax payoff is the smallest maximum loss that a player can guarantee themselves in a strategic game, even in the worst-case scenario. This concept helps players identify a strategy that minimizes their potential losses while taking into account the strategies of their opponents. In the context of equilibrium payoffs and folk theorems, minmax payoffs serve as a benchmark for evaluating strategies and outcomes in competitive situations.

5 Must Know Facts For Your Next Test

1. The minmax payoff is crucial in zero-sum games, where one player's losses are equivalent to another's gains.
2. Players often use the minmax strategy to minimize their maximum possible losses, especially when faced with uncertain opponent behavior.
3. In repeated games, folk theorems suggest that players can achieve cooperative outcomes that exceed their minmax payoffs through effective communication and trust.
4. The minmax payoff can be used to analyze mixed strategies, as it provides insights into how players might randomize their choices to avoid predictability.
5. Understanding minmax payoffs aids in designing strategies that lead to more favorable equilibrium outcomes.

Review Questions

• How does the concept of minmax payoff influence player decision-making in competitive games?
  • The minmax payoff influences player decision-making by providing a safety net against worst-case scenarios. Players aim to adopt strategies that ensure their maximum possible loss is minimized, thereby increasing their chances of achieving better outcomes in competitive settings. This approach encourages players to think strategically about their own moves and anticipate those of their opponents, ultimately guiding them towards more robust strategies.
• Discuss the relationship between minmax payoffs and Nash Equilibrium in game theory.
  • Minmax payoffs are closely related to Nash Equilibrium because both concepts involve strategic interactions among players. While a Nash Equilibrium represents a stable state where no player has an incentive to deviate from their chosen strategy, the minmax payoff helps identify the least favorable outcome that a player can secure. In many cases, players may reach an equilibrium point that is at or above their minmax payoffs, ensuring they do not fall into worse outcomes as they interact strategically with others.
• Evaluate how folk theorems provide insights into achieving payoffs above the minmax threshold in repeated games.
  • Folk theorems suggest that in repeated games, players have the potential to achieve payoffs that surpass their minmax thresholds through cooperation and credible commitments. By fostering communication and building trust over time, players can coordinate their strategies to create more favorable outcomes than those dictated by their individual minmax payoffs. This dynamic illustrates how sustained interaction among players allows for strategic collaboration that can lead to mutually beneficial results, thereby enhancing overall game value beyond mere minimization of loss.

Related terms

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

Dominated Strategy: A strategy that results in worse outcomes for a player than another strategy, regardless of what the other players do.

Zero-Sum Game: A type of game where one player's gain is exactly balanced by the losses of other players, leading to a total payoff of zero.