18.11 : Multiple Equilibria

Multiple equilibria occur when strategic interactions between players result in several potential stable outcomes, each being a Nash equilibrium. This happens when a player's best response changes depending on the other's choice, leading to various combinations where neither player has an incentive to deviate from their strategy.

Imagine two streaming services, StreamNow and ViewPrime, deciding when to release a new show—spring, winter, or not at all. Both benefit most when they release shows in different seasons, maximizing viewership by avoiding direct competition.

First, consider StreamNow's response: if ViewPrime releases in spring, StreamNow's best option is winter. If ViewPrime chooses winter, StreamNow's best move is spring. If ViewPrime doesn't release anything, StreamNow's optimal choice is spring, facing no competition.

Next, examine ViewPrime's response: if StreamNow releases in spring, ViewPrime's best choice is winter. If StreamNow picks winter, ViewPrime's best response is spring. If StreamNow does not release, ViewPrime's best move is also spring, dominating that period.

In this game, two Nash equilibria exist: one where StreamNow releases in spring and ViewPrime in winter, and another where StreamNow releases in winter and ViewPrime in spring. Both outcomes are stable, as each company maximizes its payoff by avoiding competition. However, which equilibrium will occur cannot be predicted solely from this information, as either configuration is equally beneficial. External factors like coordination or pre-release announcements may influence the final outcome.