Équilibres Multiples

Multiple equilibria occur when a game has several stable outcomes, each representing a Nash equilibrium where neither player benefits from changing their strategy unilaterally. This happens when a player's best response varies depending on the other player's choice, creating multiple strategy combinations where both players maximize their payoffs simultaneously.

To identify Nash equilibria, examine each cell in the payoff matrix and mark it with a tick if it represents each player's best response to the other's choice. A cell with two tick marks—one for each player—indicates a Nash equilibrium, showing the outcome where both players are simultaneously playing their best responses.

When multiple equilibria exist, each outcome is equally stable and beneficial for both players, making it impossible to predict which will occur based solely on payoff analysis. External factors such as coordination mechanisms, pre-announcements, or communication between players may influence which equilibrium ultimately emerges.

A best response is the strategy that maximizes a player's payoff given the other player's chosen strategy. In the burger launch example, if one chain chooses summer, the competitor's best response is fall, as launching in different seasons avoids market splitting and maximizes each company's profit.

When firms launch products in different seasons, they avoid direct competition and market splitting, allowing each to capture distinct customer segments and maximize viewership or sales. This differentiation strategy benefits both players more than simultaneous launches, which would divide the available market between them.

Yes, coordination mechanisms like pre-release announcements or formal agreements can help firms select a specific equilibrium from multiple options. However, without such cooperative arrangements, firms operating in non-cooperative games cannot guarantee which equilibrium will be chosen, leaving the outcome uncertain.

An outcome is stable when it represents a Nash equilibrium—a state where each player's strategy is the best response to the other's choice, and neither player has incentive to deviate. In multiple equilibria games, several such stable outcomes coexist, each self-reinforcing once established.