Question 1

What is a Nash equilibrium in one-period games?

Accepted Answer

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.

Question 2

How do simultaneous moves affect Nash equilibrium outcomes?

Accepted Answer

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.

Question 3

What role does a dominant strategy play in finding Nash equilibrium?

Accepted Answer

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.

Question 4

Why don't players switch locations after reaching Nash equilibrium?

Accepted Answer

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.

Question 5

How does reputation affect Nash equilibrium in competitive markets?

Accepted Answer

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.

Question 6

Can Nash equilibrium occur in non-cooperative games?

Accepted Answer

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.

Question 7

How do payoff matrices help identify Nash equilibrium?

Accepted Answer

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.

Nash Equilibrium in One-Period Games

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