9.1 Cooperative and non-cooperative bargaining models
4 min read•july 30, 2024
Bargaining models come in two flavors: cooperative and non-cooperative. Cooperative models assume players can make binding agreements, while non-cooperative ones don't. This difference shapes how negotiations play out and what outcomes we can expect.
The is key in cooperative models, while the shines in non-cooperative settings. These frameworks help us understand how factors like patience and communication affect and outcomes in various real-world scenarios.
Cooperative vs Non-cooperative Bargaining
Key Differences in Assumptions and Outcomes
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- Cooperative bargaining models assume players can make binding agreements and communicate freely, while non-cooperative models do not allow for such commitments or communication
- In cooperative bargaining, players can form coalitions and make side payments to reach mutually beneficial outcomes (labor union negotiations)
- In non-cooperative bargaining, players act independently and cannot make enforceable agreements (salary negotiations)
- Cooperative models focus on the division of the surplus generated by the , while non-cooperative models emphasize the strategic interactions and the process of reaching an agreement
Solution Concepts and Frameworks
- The Nash bargaining solution is a key concept in cooperative bargaining maximizes the product of the players' utility gains relative to their disagreement payoffs
- In non-cooperative bargaining, the Rubinstein alternating offers model is a seminal framework captures the dynamics of bargaining and the impact of patience on the bargaining outcome
- The model predicts the player who is more patient (has a higher discount factor) will receive a larger share of the surplus in the bargaining outcome
Assumptions of Bargaining Models
Cooperative Bargaining Assumptions
- Cooperative bargaining models assume the bargaining set, which represents the possible agreements, is convex and compact, ensuring the existence of a unique bargaining solution
- The Nash bargaining solution satisfies desirable properties such as , symmetry, scale invariance, and independence of irrelevant alternatives
- Pareto efficiency ensures no player can be made better off without making another player worse off
- Symmetry implies if players are identical, they should receive equal shares of the surplus
Non-cooperative Bargaining Assumptions
- Non-cooperative bargaining models often assume players have about each other's preferences and the structure of the game, although extensions to settings exist
- The assumption of common knowledge of rationality is crucial in non-cooperative bargaining models allows players to anticipate each other's strategies and reach subgame perfect equilibria
- Subgame perfect equilibria require strategies to be optimal at every decision point, even if that point is not reached in equilibrium
- This assumption rules out non-credible threats and ensures the stability of the bargaining outcome
Applicability of Bargaining Models
Contexts Suitable for Cooperative Bargaining
- Cooperative bargaining models are more suitable when players have the ability to make binding agreements and engage in open communication
- International trade negotiations often involve cooperative bargaining, as countries can make long-term commitments and engage in multi-issue negotiations
- Labor union bargaining also fits the cooperative framework, as unions and employers can make legally enforceable contracts and negotiate over wages, benefits, and working conditions
Contexts Suitable for Non-cooperative Bargaining
- Non-cooperative bargaining models are more appropriate when players cannot make enforceable commitments, and the bargaining process is characterized by strategic posturing and incomplete information
- Salary negotiations between an employer and an individual employee often resemble non-cooperative bargaining, as the parties cannot make binding agreements and may have private information about their reservation wages
- Political decision-making, such as legislative bargaining, can also be modeled as non-cooperative, as politicians may engage in strategic voting and coalition formation without the ability to make enforceable commitments
Hybrid Models and Empirical Evidence
- In practice, bargaining situations often involve a mix of cooperative and non-cooperative elements, and hybrid models that incorporate both aspects can provide more realistic insights
- Wage negotiations in a unionized firm may involve both cooperative elements (collective bargaining agreement) and non-cooperative elements (individual wage bargaining)
- Empirical studies and experimental evidence can help assess the predictive power and limitations of cooperative and non-cooperative bargaining models in real-world settings
- Ultimatum game experiments have shown that people often deviate from the predictions of non-cooperative bargaining models due to fairness considerations and social norms
Communication and Commitment in Bargaining
Role of Communication
- In cooperative bargaining, unrestricted communication allows players to share information, coordinate strategies, and reach efficient agreements
- Communication helps players identify mutually beneficial outcomes and reduces the risk of misunderstandings or coordination failures
- In non-cooperative bargaining, limited or no communication can lead to inefficiencies and suboptimal outcomes due to the lack of coordination and trust between players
- Without communication, players may engage in strategic posturing or fail to convey important information, leading to delays or breakdowns in negotiations
Importance of Commitment
- The ability to make binding commitments in cooperative bargaining reduces the risk of deviations and facilitates the implementation of agreed-upon outcomes
- Binding contracts ensure that players follow through on their promises and prevent opportunistic behavior
- The absence of commitment devices in non-cooperative bargaining can result in strategic behavior, such as bluffing or delaying tactics, which can prolong the bargaining process and lead to inefficient outcomes
- Without commitment, players may renege on their offers or engage in brinkmanship, reducing the likelihood of reaching a mutually beneficial agreement
Mitigating Inefficiencies in Non-cooperative Bargaining
- Introducing communication channels or commitment mechanisms in non-cooperative bargaining settings can help mitigate inefficiencies and improve the chances of reaching mutually beneficial agreements
- Allowing players to send cheap talk messages or establishing reputational mechanisms can facilitate coordination and trust-building in non-cooperative bargaining (online dispute resolution platforms)
- Contractual clauses, such as penalties for non-compliance or performance bonuses, can serve as commitment devices and encourage cooperative behavior even in non-cooperative settings (procurement contracts)
Key Terms to Review (18)
Agreement: An agreement is a mutual understanding between parties that outlines the terms and conditions they accept in order to reach a resolution or outcome. In the context of bargaining, agreements often emerge from negotiations where parties have to navigate their preferences and strategies to find common ground. These agreements can vary significantly based on whether they arise from cooperative or non-cooperative scenarios, affecting how parties achieve their objectives.
Bargaining Power: Bargaining power refers to the ability of an individual or group to influence the terms and outcomes of a negotiation. It plays a crucial role in determining how resources, benefits, or obligations are shared between parties involved in cooperative and non-cooperative settings. The level of bargaining power can shift based on various factors, including alternatives available to each party, the urgency of reaching an agreement, and the negotiation environment.
Complete information: Complete information refers to a scenario in game theory where all players have full knowledge about the game's structure, including the preferences, payoffs, and strategies available to each player. This concept is crucial because it shapes how players make decisions and negotiate outcomes in both cooperative and non-cooperative settings, ensuring that everyone operates with the same understanding of the situation.
Cooperative games: Cooperative games are a type of game theory where players can negotiate and form binding agreements to achieve better outcomes collectively. In these games, the focus is on the strategies that players can use to collaborate and share resources, leading to joint payoffs rather than individual ones. Understanding cooperative games is essential for analyzing scenarios where collaboration can lead to more favorable outcomes for all parties involved.
Core: The core is a concept in cooperative game theory that refers to a set of outcomes where no group of players would prefer to deviate and form their own coalition because they cannot achieve a better payoff. This idea emphasizes stability among participants since each player's payoff in the core is at least as high as what they could secure by leaving to form a smaller coalition. Understanding the core helps to analyze how resources or benefits can be allocated fairly among individuals or groups, ensuring that cooperation remains beneficial.
Disagreement point: The disagreement point is the outcome that would occur if two parties fail to reach an agreement during a bargaining process. It serves as a baseline or reference point for what each party would receive if negotiations break down, influencing their negotiation strategies and the final agreement achieved. Understanding the disagreement point is crucial in assessing potential payoffs in both cooperative and non-cooperative bargaining scenarios, as well as in strategic models of negotiation.
Extensive Form: Extensive form is a way to represent games in game theory that shows the sequential nature of decisions made by players over time. It illustrates all possible moves, strategies, and outcomes in a branching tree format, allowing for a clear view of how players interact at each stage of the game. This representation is particularly useful for analyzing scenarios where timing and order of actions matter, making it essential in understanding both cooperative and non-cooperative bargaining models.
Grim trigger: A grim trigger is a strategy used in repeated games where a player cooperates until the other player defects, at which point the first player will permanently switch to defection as punishment. This strategy emphasizes a strong commitment to cooperation, but also a severe consequence for betrayal, making it a key element in maintaining long-term cooperation in various scenarios.
Incomplete Information: Incomplete information refers to a situation in game theory where players do not possess full knowledge about certain aspects of the game, such as other players' payoffs, strategies, or types. This uncertainty significantly impacts strategic decision-making and can lead to different outcomes compared to scenarios with complete information, as players must often rely on beliefs or probabilities to make their choices.
Nash bargaining solution: The Nash bargaining solution is a solution concept in cooperative game theory that identifies how two or more parties can reach an agreement through negotiation, while considering their respective utilities. It provides a way to determine the optimal distribution of benefits among parties that engage in bargaining, assuming they will act rationally and seek to maximize their own outcomes. This concept is critical as it bridges cooperative and non-cooperative models by illustrating how players can collaborate while also considering their individual interests.
Non-cooperative games: Non-cooperative games are strategic scenarios where players make decisions independently, often competing against each other to maximize their own payoffs without any collaboration or binding agreements. In these games, each player aims to optimize their strategy based on the expected actions of others, highlighting the tension between competition and individual incentives. This concept is crucial for understanding how individuals navigate strategic interactions, particularly in bargaining situations and econometric analyses of behavior.
Normal form: Normal form is a representation of a game in game theory that summarizes the players, their strategies, and the outcomes or payoffs associated with each combination of strategies. This format is crucial for analyzing both cooperative and non-cooperative bargaining models, as it allows players to visualize their choices and potential results in a structured manner. By presenting the game in this way, it becomes easier to identify optimal strategies and predict outcomes based on players' decisions.
Pareto efficiency: Pareto efficiency refers to a situation in which resources are allocated in such a way that no individual can be made better off without making someone else worse off. It is a key concept in understanding optimal resource allocation and plays a significant role in various strategic interactions, showing how individuals or groups can reach outcomes where any change would harm at least one party involved.
Rubinstein Alternating Offers Model: The Rubinstein Alternating Offers Model is a framework for understanding bargaining situations where two parties take turns making offers to each other until an agreement is reached or one party walks away. This model highlights the strategic decision-making process involved in negotiations, illustrating how the timing and content of offers can influence outcomes and the importance of discounting future payoffs in reaching a deal.
Shapley Value: The Shapley Value is a concept from cooperative game theory that provides a fair distribution of payoffs to players based on their individual contributions to the overall success of a coalition. It takes into account the value each player brings to the group and ensures that they receive compensation that reflects their marginal contributions, promoting equitable outcomes in various scenarios.
Subgame Perfection: Subgame perfection is a refinement of Nash equilibrium used in game theory that ensures players' strategies constitute a Nash equilibrium in every subgame of the original game. This concept is crucial in analyzing dynamic games where players make decisions at different points, allowing us to focus on strategies that are credible and rational throughout the entire game, not just in the initial stages. Subgame perfection helps identify outcomes that are stable and can be sustained through the players' choices in subsequent moves.
Tit-for-tat: Tit-for-tat is a strategic decision-making approach in game theory where a player responds to another's action with the same action, particularly in cooperative interactions. This strategy fosters cooperation by starting with a cooperative move and then mirroring the opponent's previous action, creating a pattern of reciprocity that can lead to mutually beneficial outcomes. It has real-world implications in various scenarios, from economics to social interactions, where establishing trust and cooperation is essential.
Utility Function: A utility function is a mathematical representation that assigns a real number to each possible outcome or choice, reflecting the level of satisfaction or preference that an individual derives from that outcome. This concept is crucial in understanding decision-making processes and is linked to how players evaluate their options in strategic interactions, providing insights into their preferences, strategies, and behaviors.