Nash Equilibrium, Stackelberg & Cournot Models: Oligopoly Competition Explained

(a) Pure strategy Nash equilibrium occurs when each player in a game chooses a strategy that maximizes their own payoff, given the strategies chosen by all other players. In this case, players have a dominant strategy, which means they have a single best response regardless of what the other players choose.

On the other hand, mixed strategy Nash equilibrium occurs when players choose their strategies probabilistically, rather than deterministically. Each player assigns a probability distribution over their available strategies based on their beliefs about the other players' strategies. The players' strategies are chosen in such a way that no player can improve their payoff by unilaterally deviating from their chosen strategy, assuming the other players' strategies remain unchanged.

(b) The Stackelberg and Cournot models both consider markets with oligopolistic competition, where a few firms interact strategically. However, they differ in terms of the order of decision-making and the assumptions made about how firms behave.

In the Cournot model, firms simultaneously choose their quantities of output. Each firm assumes that its competitors' quantities are fixed when deciding its own quantity. This results in a Nash equilibrium where each firm produces a quantity that maximizes its profit given the quantities produced by its competitors. The market equilibrium is achieved when the sum of all firms' quantities equals the market demand.

In the Stackelberg model, one firm acts as a leader and determines its quantity of output first. The other firms, known as followers, observe the leader's quantity and then simultaneously choose their quantities. The market equilibrium is achieved when the sum of the leader's quantity and all the followers' quantities equals the market demand.

The advantage a firm can enjoy in a Stackelberg market is the ability to act as a leader and set its quantity strategically. By setting its quantity before the other firms, the leader can anticipate the followers' reactions and adjust its quantity accordingly to maximize its profit. The leader has a first-mover advantage, as it can effectively influence the market and potentially deter the followers from entering or expanding their market share.

Here's a diagram illustrating the Stackelberg model:

               Leader's Quantity (Ql)
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/——————————————————————— 0 Market Quantity (Q)

In this diagram, the leader chooses its quantity first, denoted by Ql. The followers then choose their quantities simultaneously, resulting in a total market quantity of Q. The leader's advantage lies in its ability to position itself strategically to maximize its profit based on the followers' reactions.