1 Applications Here we look at several applications. We will see a classic example of a dilemma that can arise in such games.

2 Pricing Example column player low pricehigh price Row low price0, 050, -10 Player high price-10, 5010, 10 The numbers in the matrix represent profit. The row player has a dominant strategy of a low price and the column player has a dominant strategy of a low price as well. And, low low is a Nash equilibrium. A dilemma that arises here is that both could be better off if they both went with a high price.

3 Prisoner Dilemma Games The game we just saw has the characteristic that has come to be known as the prisoners’ dilemma. When the players act separately (competitively) the outcome is worse than if they cooperated.

4 Don’t be taken advantage of In the pricing example each might be tempted to get together and both charge the high price and both do better than the low price strategy. The problem of the high, high solution is that it is not a Nash equilibrium and thus each would have the incentive to change to the low price strategy. If you were a corporate boss your stockholders would not want you to be taken advantage of by a double crosser. Don’t collude here, for it is not likely to pay off.

5 Advertising Example column player adno ad Row ad4, 420, 1 Player no ad1, 2010, 10 Profits are in the matrix. Each player has a dominant strategy of advertise. This outcome is a Nash equilibrium. A similar dilemma arises here as before. No ads would be better but each does not want to get taken advantage of.

6 Coordination example column player 120 volt90 volt Row 120 volt100, 1000, 0 Player 90 volt0, 0100, 100 In this example say you have consumer appliance manufacturers who have the choice between making the appliances run on 120 or 90 volt plugs. If they both do not use the same plug they will earn less profit because consumers will have to spend on different plugs and thus not be willing to spend as much on the appliances. The game has two Nash equilibria – both doing the same plug. The next question is how do they get the same plug?

7 Coordination Example In this example, the firms need to figure out a way to get on the same page. Agreements to coordinate may be looked at negatively legally, so maybe companies lobby the government to set the standard for a product.

8 Monitoring workers. worker work shirk or play Manager monitor- 1, 11, -1 don’t mon.1, -1-1, 1 Here neither player has a dominant strategy and there is no Nash equilibrium for the game. In this instance each player wants to keep their choice a secret so as to not tip off the other one. The worker would work and the manager would lose out if the worker knew about the manager’s plans. Some games have no dominant strategy and no Nash equilibrium.