Équilibre de Nash dans les jeux à une période

A Nash equilibrium is a stable outcome where no player can improve their payoff by changing their decision, assuming the other player's choice remains unchanged. In one-period games, players make simultaneous decisions without knowing each other's choices. Once both players reach this equilibrium point, neither has an incentive to switch strategies, as doing so would reduce their profits.

In simultaneous-move games, players choose strategies without knowing their opponent's decision, making equilibrium prediction crucial. Each player must anticipate the other's best response and select their own strategy accordingly. This independence of choice creates a stable equilibrium when both players' decisions are optimal given their expectations, resulting in predictable market outcomes.

A dominant strategy is one that yields the best payoff regardless of the opponent's choice. When a player has a dominant strategy, they will always select it, simplifying equilibrium identification. In the mobile catering example, T-Truck's dominant strategy of choosing Downtown guarantees it the best outcome, which directly determines the Nash equilibrium outcome with B-Van's best response.

At Nash equilibrium, each player's location choice maximizes their profit given the other's decision. Switching would reduce their earnings because they would either face direct competition or lose their monopoly advantage. In the catering example, T-Truck downtown and B-Van in the industrial area both earn optimal profits, so neither benefits from changing locations alone.

Reputation creates asymmetric payoffs between competitors. When players share a location, the player with stronger reputation captures a larger customer share. This advantage influences each player's best response strategy. In the catering case, T-Truck's superior reputation makes Downtown more attractive, while B-Van rationally chooses the industrial area to avoid direct competition and capture that market alone.

Yes, Nash equilibrium commonly occurs in non-cooperative games where players act independently without coordination or binding agreements. Players make decisions based solely on maximizing their own payoffs given others' choices. The mobile catering example demonstrates this: T-Truck and B-Van independently choose locations without cooperating, yet reach a stable equilibrium that neither wants to abandon.

Payoff matrices display each player's earnings for every possible strategy combination, enabling systematic analysis of best responses. By examining each player's payoffs under all opponent choices, you identify which strategies maximize individual profit. The matrix reveals dominant strategies and mutual best responses, making the Nash equilibrium point where both players' choices are optimal clearly visible.