Game theory is a widely studied field that deals with the analysis of strategic decision-making. It is used to model various scenarios in which individuals or organizations interact with each other to achieve their objectives. One of the most fundamental problems in game theory is the problem of commitment.
What is the Problem of Commitment?
The problem of commitment arises when one party in a game has an incentive to break an agreement that has been made with another party. This can occur when there is no way for the other party to enforce the agreement or when it is too costly or risky to do so. In such cases, the first party may decide to renege on the agreement and pursue a different strategy.
For example, consider a situation where two firms are deciding whether to enter a new market. If both firms enter, they will compete and both will earn lower profits than if only one firm enters.
Suppose that Firm A enters first, and then Firm B must decide whether to follow suit or stay out. If both firms enter, they will earn lower profits than if only Firm A enters and Firm B stays out.
In this scenario, Firm A has an incentive to commit to entering the market first because it knows that if both firms enter, its profits will be lower. However, Firm B knows that if it enters after Firm A, it will earn higher profits than if it stays out altogether. Thus, there is a conflict between what each firm wants individually and what they would collectively prefer.
Why Does the Problem of Commitment Arise?
The problem of commitment arises in game theory because players are often not able to make credible commitments. A credible commitment is one that other players believe will be upheld even if it goes against the self-interest of the player who made it.
There are several reasons why credible commitments may be difficult or impossible to make:
- Opportunity Costs: A player may have a better option that becomes available after the agreement has been made. For example, in the scenario above, Firm B may discover a more profitable opportunity after Firm A has entered the market, and decide to pursue it instead.
- No Enforcement Mechanism: If there is no way to enforce the agreement, a player may be tempted to break it.
For example, in a situation where two countries agree to reduce their nuclear weapons stockpiles, there is no way to verify that each country has followed through on its promise.
- Risk of Retaliation: A player may fear retaliation if it upholds the agreement. For example, if one firm agrees not to lower its prices below a certain level, but then sees its competitor doing so, it may be tempted to do the same in order to avoid losing market share.
How Can the Problem of Commitment be Addressed?
There are several strategies that can be used to address the problem of commitment:
- Third-Party Enforcement: If there is a third party that can enforce the agreement, such as a government or international organization, players may be more likely to make credible commitments. This is because they know that if they break the agreement, they will face sanctions from the third party.
- Social Norms: Social norms can play a powerful role in encouraging players to make credible commitments.
For example, if there is an expectation that players will uphold their agreements even if it goes against their self-interest, they may be more likely to do so.
- Mutually Beneficial Outcomes: If players can find outcomes that are mutually beneficial, they may be more likely to make credible commitments. In the scenario above, for example, if both firms agree to enter the market simultaneously and share the profits, they will both be better off than if only one firm enters.
In conclusion, the problem of commitment is a fundamental issue in game theory that arises when players have an incentive to break an agreement. This can occur due to various reasons such as opportunity costs, lack of enforcement mechanisms, or fear of retaliation.
However, there are strategies that can be used to address this problem such as third-party enforcement, social norms, and mutually beneficial outcomes. By understanding the problem of commitment and its causes, players can make more informed decisions and achieve better outcomes in strategic situations.