## 02 Apr Economics of Game Theory

Game study is the study of strategic interaction where one player’s decision depends on what the other player does. What the opponent does also depends upon what he thinks the first player will do.

#### Examples of Game Theory

- Both players have a dominant strategy.

**A DOMINANT strategy **occurs when there is an optimal choice of strategy for each player no matter what the other does.

- If P2 chooses left P1 will choose UP
- If P2 chooses right P1 will choose UP
- Therefore UP is a dominant strategy for P1

P2 will always choose right no matter what P1 does

The unique equilibrium is (up, left). This is best for both

**One player has a dominant strategy**

PIGLET

Push lever wait for swill

Push lever 8,-2 1,7

PIG

Wait for swill 10,-2 0,0

- piglet will always wait
- Pig will have to push

### Nash Equilibrium

There are many games which don’t have a dominant strategy.

**Definition**: A Nash equilibrium occurs when the payoff to player one is the best given the other’s choice.

In this case If P1 chooses down, P2 will choose right

If P1 choose UP, P2 will choose right. But, if P2 choose right, P1 will want to choose down.

The nash equilibirum will be down right, (5,5) despite UP left being the optimal Pareto outcome.

### Collusion and game theory

The optimal outcome is collusion (high price, high price)

However, there is scope for firms trying to cheat on the agreement and undercut rivals to make more profit. But, if this happens the outcome may revert to non-collusion and low price.

### Repeated Games and Game Theory

If games are repeated then there is the possibility of punishing people for cheating, this will provide an incentive for sticking to the Pareto optimal approach.

However, if they are repeated a finite number of times then there will be an incentive to cheat. If the game is played 10 times then the player will defect on the 10th round so why cooperate. So, therefore, you may as well defect on round 9 and so round 8 as well

If it is played an infinite number of times then it will be different. The best strategy then is to play tit for tat. If a player defects in one round you retaliate in the next round. In other words, you do whatever your opponent does and this is an incentive to enforce the cartel.

### Game Theory: A game of entry deterrence

If a new firm enters the market then the payoff will depend on whether the incumbent fights or accepts. If the incumbent fights they both get 0. If it does not fight then the incumbent gets 1 and the entrant gets 2. Therefore the equilibrium is for the new firm to enter and the incumbent to accept.

However, if the incumbent can give a credible threat that he will fight then he may be able to persuade the entrant to stay out. He could do this by investing in extra capacity, which would give him a bigger payoff in a price war. This would deter entry. So although the monopolist would never use this he would prevent entry.

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