18.20: Commitment

In game theory, a credible commitment in sequential games is a strategy where a player influences another's decision by making a believable and enforceable promise or threat. Sequential games differ from simultaneous games as players act after observing the decision of another player, allowing the first player to shape the expectations and actions of the second. For such a commitment to be credible, it must be realistic and enforceable, ensuring both sides see cooperation as the most beneficial option.

Consider two supermarket chains, FreshMart and Greengrocer, operating in the same region. FreshMart aims to deter GreenGrocer from launching a discount campaign, which could trigger a price war and reduce profits for both. To prevent this, FreshMart proposes a partnership with shared suppliers and joint advertising. This partnership reduces costs by allowing savings from bulk purchases from suppliers and joint marketing efforts. Such a partnership would boost profitability for both firms. This offer is a credible commitment as it aligns incentives and shows that cooperation is beneficial.

If Greengrocer declines and continues with discounts, FreshMart commits to aggressive promotions and expanding its store locations and committing long-term leases on new retail spaces, increasing the costs for both firms and reducing overall profits. This setup ensures that cooperation, where both avoid aggressive competition, becomes the more attractive option. Given the other's strategy, this creates a Nash equilibrium, a stable outcome where neither supermarket has an incentive to deviate.

Similar strategies are used in industries like airlines and automakers, where alliances allow companies to share routes or technology, reducing competition and costs while maximizing stability. These examples illustrate how credible commitments create conditions where cooperation is mutually beneficial, ensuring long-term profitability and minimizing competition risks.

In a sequential game, credible commitment means players make promises or threats they are likely to keep because they have no incentive to deviate from the commitment.

Consider two competing pharmaceutical companies: Nova and Erks.

Nova plans a credible commitment strategy that encourages Erks to collude rather than engage in a price war.

One possible commitment strategy for Nova could involve changing the payoffs to make collusion more attractive for Erks.

By doing this, Nova alters the future payoffs in the game, making collusion more appealing to Erks.

If Erks chooses a price war despite Nova's offer to collude, the payoff will drop from 600 dollars to 200 dollars due to the increased costs.

However, if Erks colludes, both companies receive 500 dollars. Since the gains from a price war are much lower, collusion becomes a more appealing option for Erks.

This shift in payoffs makes collusion Erks' most rational choice.

Knowing this, Nova will also choose to collude, leading both companies to a payoff of 500 dollars.

The commitment strategy ensures that collusion becomes both players' most attractive and sustainable option due to credible commitment, making it the Nash equilibrium.