Infinite horizon

Definition

Infinite horizon refers to a modeling framework in which decision-making extends indefinitely into the future. In this context, agents consider not only immediate payoffs but also the long-term consequences of their actions across an unbounded time frame, leading to strategic interactions that can significantly impact bargaining outcomes and stability.

5 Must Know Facts For Your Next Test

1. In an infinite horizon model, players make decisions based on the expected utility of their actions over an unlimited time period, considering future consequences.
2. The concept is essential in bargaining scenarios where ongoing negotiations may lead to different outcomes depending on how future interactions are perceived.
3. Players often use strategies that involve cooperation or punishment in response to the behavior of others over time, influencing their bargaining positions.
4. The existence of an infinite horizon can lead to different equilibrium outcomes compared to finite horizon models due to the importance placed on future payoffs.
5. In the Rubinstein bargaining model, the infinite horizon allows for the possibility of a unique equilibrium outcome that depends heavily on players' patience levels as represented by their discount factors.

Review Questions

• How does the concept of infinite horizon influence strategic decision-making in bargaining models?
  • The concept of infinite horizon affects strategic decision-making by encouraging players to consider not only immediate outcomes but also the long-term effects of their choices. In bargaining models, this means that players might adopt more cooperative strategies if they anticipate ongoing interactions, leading them to prioritize long-term gains over short-term advantages. Consequently, this perspective can shift negotiation dynamics significantly, as players weigh future implications against present actions.
• Discuss how discount factors relate to the idea of infinite horizon in the context of player strategy and negotiation outcomes.
  • Discount factors play a crucial role in infinite horizon models as they quantify how much future payoffs are valued compared to immediate gains. A higher discount factor indicates greater patience from players, allowing them to invest more in long-term strategies during negotiations. As a result, players with higher discount factors are more likely to reach mutually beneficial agreements since they value ongoing relationships and future cooperation more than those with lower discount factors who may favor immediate results.
• Evaluate the implications of infinite horizon scenarios for achieving subgame perfect equilibria in bargaining situations.
  • Infinite horizon scenarios have significant implications for achieving subgame perfect equilibria in bargaining situations because they require players to consider the consequences of their actions across all possible future states. In such settings, strategies must be robust enough to ensure that players will continue to follow through on their commitments and cooperate in subsequent rounds. This complexity often leads to more intricate strategy profiles that take into account potential deviations and responses from other players, ultimately shaping how equilibria are formed and sustained over time.

Related terms

discount factor: A value used in models to represent the present value of future payoffs, reflecting how future rewards are perceived less valuable than immediate ones.

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

cooperative game theory: A branch of game theory that studies how groups of players can form coalitions and make collective decisions to achieve better outcomes than they could individually.