How do you tell cooperative and non-cooperative games apart?

1 What are cooperative and non-cooperative games?

A cooperative game is one where the players can communicate, negotiate, and form binding agreements or coalitions to achieve a common goal or maximize their joint payoff. A non-cooperative game is one where the players cannot or do not coordinate their actions or make enforceable contracts. Instead, they act independently and rationally, taking into account the expected responses of other players. Cooperative and non-cooperative games differ in their assumptions, models, and solutions.

2 How to model cooperative and non-cooperative games?

The most common way to model a cooperative game is by using a characteristic function, which assigns a value to each possible coalition of players. The value represents the maximum payoff that the coalition can obtain by cooperating among themselves. The solution of a cooperative game is a way of distributing the value among the coalition members, such as the core, the Shapley value, or the Nash bargaining solution. The most common way to model a non-cooperative game is by using a normal form or a strategic form, which specifies the set of players, the set of strategies available to each player, and the payoff function that maps each combination of strategies to a payoff for each player. The solution of a non-cooperative game is a strategy profile that satisfies some equilibrium concept, such as the Nash equilibrium, the subgame perfect equilibrium, or the Bayesian equilibrium.

3 How to compare cooperative and non-cooperative games?

One way to compare cooperative and non-cooperative games is by looking at their outcomes and efficiency. The outcome of a cooperative game is determined by the coalition structure and the value distribution, while the outcome of a non-cooperative game is determined by the equilibrium strategy profile. In general, cooperative games tend to have more Pareto efficient outcomes than non-cooperative games, meaning that there is no other outcome that makes some players better off without making others worse off. However, cooperative games may also face problems of stability, fairness, and incentive compatibility, depending on the solution concept and the game structure.

4 How to choose between cooperative and non-cooperative games?

When deciding between cooperative and non-cooperative games, one must consider the nature and context of the strategic interaction. Factors that may influence the decision include the availability and credibility of communication and commitment mechanisms among the players, the degree of repetition, uncertainty, and asymmetry in the game, the number and diversity of players and their preferences, as well as any social norms or institutions that govern the game. In certain cases, it may be beneficial to combine or switch between cooperative and non-cooperative approaches, like in repeated games, bargaining games, or coalitional games with externalities.

5 How to apply cooperative and non-cooperative games?

Cooperative and non-cooperative games have many applications in various fields of economics and beyond, such as industrial organization, public economics, international economics, political economy, social choice, and behavioral economics. These applications can be used to analyze market structure, competition, collusion, regulation, public goods, externalities, collective action, trade agreements, tariffs, sanctions, voting, lobbying, coalition formation, social welfare, fairness and justice, bounded rationality, social preferences and psychological biases.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?