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• Print publication year: 2012
• Online publication date: November 2012

# 9 - Strategy

## Summary

Strategic Equilibrium

Key ideas: simultaneous move game, normal form, pure and mixed strategies, dominant strategy equilibrium, Nash equilibrium, common knowledge, correlated strategies

In all the previous chapters, the primary focus was on resource allocation via a Walrasian equilibrium (WE). In a WE allocation all players are price takers so there are no strategic issues. However, the price-taking assumption only makes sense if there are a sufficiently large number of competing players. As we have seen, if a production set exhibits increasing returns to scale, one firm can produce at a lower cost than two or more firms so there is a natural monopoly. When a commodity is sold by one firm there is a strategic issue. Instead of being a price taker, the firm is a price setter, choosing a pricing strategy to maximize the firm's payoff. But suppose that production sets in an industry exhibit increasing returns to scale at low outputs and decreasing returns at outputs that are a significant fraction (but less than 50%) of market demand. Then average cost is minimized, with a few firms producing near the average cost-minimizing output. Now strategic issues become much more subtle because a change in the production plan of one firm affects the sales of that firm's competitors. This typically causes a reaction by each competitor. Making a good choice then requires all players to forecast the actions of their competitors. Using the language of social competition (sports, card games, etc.) any such strategic competition is called a game and the participants in the game are called players.

To begin, consider the following simple economic game. There are two players. Player i, i = 1, 2 is the manager of firm i. Each player submits the price of the firm's product for the next week to be posted on the web. To keep things simple, each player sets a high price pH or a low price pL. Let Ai be the set of possible actions; then Ai = {pH, pL}.

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