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Game Theory

- Tool used for analyzing multiagent economic situations involving strategic interdependence

How Do We Describe a Game?

- A game is described by:
- number of players/agents
- the “strategies” available to each player
- each player’s preferences over outcomes of the game
- For any game, a strategy choice by each one of the players results in a unique outcome of the game

What is a Strategy?

- A strategy is an action plan for a player. It specifies:
- what action the player takes
- when the player takes the action
- the way that the action choice depends on the information the player has when taking the action
- Two action plans that specify different actions represent two different strategies

Predicting Behavior in Games

- If games are to help us understand observables, we need a way of predicting how agents behave in game settings; i.e., we need a notion of equilibrium for games
- The standard notion of equilibrium is the Nash equilibrium
- Roughly speaking a Nash equilibrium has the feature that each player’s strategy choice is best for that player given other players’ strategies

Determinants of Pricing Decision

- Economic analysis of pricing in imperfectly competitive markets identifies the following elements of the market environment as important to pricing decision:
- number of competitors/ease of entry
- similarity of competitors’ products
- capacity limitations
- on-going interactions
- Information on past pricing decisions

Bertrand

- Simultaneous price setting
- Identical products
- No capacity constraints
- One time interaction

Price competition results in price equal marginal cost for all firms and zero profits

Bertrand

- Bertrand paradox (p=mc even though few firms in market) can be resolved by relaxing certain assumptions:
- No Capacity Constraints
- Undifferentiated Products
- One-shot competition

Capacity Constraints

- Suppose each firm has max capacity of Ki
- If firm j sets a higher price than firm i, j may get the left-over demand that firm i can’t satisfy if demand exceeds i’s capacity
- So setting price above MC may be worthwhile

Cournot

- Same analysis can be applied to situations where firms decide first on how much to produce and then on what price to set
- If total quantity produced is low relative to market demand, then it is as if constrained
- Firms will set prices such that total demand just clears total output

Cournot

- Capacity (or output) constraint limits the usefulness of price competition
- Can get p>mc and firms can earn economic profits

Cournot vs. Bertrand

- Cournot:

-when demand is large relative to capacity

-when capacity is more difficult to adjust than price

- Bertrand:

-when demand is small relative to capacity

-when capacity is easier to adjust than price

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