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 Nash bargaining solution is key in cooperative models, while the Rubinstein alternating offers model shines in non-cooperative settings. These frameworks help us understand how factors like patience and communication affect bargaining power and outcomes in various real-world scenarios.

Cooperative vs Non-cooperative Bargaining

Key Differences in Assumptions and Outcomes

• 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 agreement, 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 Pareto efficiency, 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 complete information about each other's preferences and the structure of the game, although extensions to incomplete information 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)