Infinite horizon games

Definition

Infinite horizon games are strategic interactions that continue indefinitely, where players make decisions over an unbounded number of periods. These games differ from finite horizon games because the lack of a predetermined endpoint allows for the possibility of sustained cooperation and complex strategies that evolve over time, influencing players' decisions based on future payoffs.

5 Must Know Facts For Your Next Test

1. In infinite horizon games, players consider the long-term implications of their actions, making future payoffs just as important as immediate rewards.
2. Cooperation can be more sustainable in infinite horizon games due to the potential for future interactions and repeated play.
3. Strategies such as grim trigger or forgiving strategies can emerge in these games, which are not feasible in finite settings.
4. The concept of discounting future payoffs is crucial, as it reflects how much less players value future gains compared to immediate ones.
5. Infinite horizon games often involve concepts like Folk Theorems, which indicate that a wide range of outcomes can be supported by equilibrium strategies.

Review Questions

• How does the absence of a terminal period in infinite horizon games influence players' strategies compared to finite horizon games?
  • In infinite horizon games, the absence of a terminal period encourages players to consider long-term consequences when making decisions. This leads to the development of strategies that promote cooperation over time, as players recognize that their actions will affect future interactions. In contrast, finite horizon games may lead players to focus on short-term gains, as they know the game will end after a specific number of rounds.
• What role does discounting play in the decision-making process of players in infinite horizon games, and how does it affect their strategies?
  • Discounting plays a significant role in infinite horizon games by allowing players to evaluate future payoffs with a reduced present value. This affects their strategies because players must balance immediate rewards against potential future benefits, leading them to make choices that could prioritize long-term cooperation or short-term gains. The rate at which they discount future payoffs influences their willingness to engage in cooperative behaviors and maintain long-lasting relationships with other players.
• Evaluate how the concept of Folk Theorems applies to infinite horizon games and what implications this has for achieving cooperative outcomes.
  • Folk Theorems suggest that in infinite horizon games, many potential outcomes can be sustained as Nash equilibria, especially cooperative ones. This means that players can achieve cooperation through various equilibrium strategies that promote mutual benefits over time. The implications are significant: if players trust each other to follow through on cooperative strategies due to the ongoing nature of the game, they are more likely to engage in behaviors that lead to socially optimal outcomes. This creates an environment where collaboration is not only possible but can thrive under appropriate conditions.

Related terms

Discounting: The process of reducing the present value of future payoffs, often used in infinite horizon games to account for the time value of money.

Nash Equilibrium: A situation in a game where no player can benefit by changing their strategy while the others keep theirs unchanged; it can be applied to both finite and infinite horizon games.

Trigger Strategy: A strategy where a player cooperates until another player defects, after which they revert to a punishment strategy indefinitely; commonly used in infinite horizon games to maintain cooperation.