1. Public Policy Analysis MPA 404 Lecture 24

2. Previous Lecture Graphical Analysis of Tariff and Quota Game Theory; The prisoner's Dilemma

3.  Games with one dominant strategy: The above are examples of simple games that have a dominant strategy of each player and a Nash equilibrium. In reality, games are more complex. There are games that have only one dominant strategy and games where there are two Nash equilibriums. Take the example of the prisoner’s dilemma game where trade-offs for both prisoners in equilibrium are equal (1 year of sentence). Suppose in the first box (Confess, Confess), the number of years is changed to 3 months for prisoner B. In that case, it is clear that the pay-offs are not equal. Although the Confess-Confess box would still be an equilibrium, the prisoner A’s decision would just be a reaction to that of prisoner B’s because he doesn’t have a dominant strategy (he’d get more time whether he confesses or doesn’t confess). In other words, prisoner B has an advantage that prisoner A does not enjoy. This situation is a fair reflection of the real world since many a times, one participant has some advantage over his competitor/s.  In the simple Prisoner’s dilemma and games where there is only one dominant strategy, the strategy of one player was formed regardless of what the other did. In games with no dominant strategies, both players’ response depends upon the response of the opponents or the other participant. This kind of game has two Nash equilibria. Consider the following example given below;

4. In the box, grades represent the pay-offs of student A and B. Suppose student A decides to study physics for the exams. Student B’s best strategy has to be study physics, because if he decides to study economics instead, he gets a C grade. Similarly, if student B decides to study economics first, student A has to follow suit because if he does not, he will end up with a C grade. Clearly, the strategy of one player is linked to what the other does. In this game, there are two possible equilibrium’s: either both study econ (lower right box) or both study physics (upper left box).

5.  Repeated games and backward induction: Prisoner’s dilemma represents a game where there is finite time and one outcome as the game ends. However, strategies and games can be repeated over and over, and results may be different each time the game is repeated. For example, Pakistan and India have fought each other many times. Each time the strategy was different, and it will keep changing according to the situation. Similarly, elections or politics do not have a time frame. In a particular election, a strategy may be adopted which may not be used in another election. In these kinds of games, where the outcome can be repeated more than once, it is useful to think ahead and try to reason what the results would be. In other words, a player can gain an advantage by thinking about the result of his strategies, and then start going backward to try to imagine or guess what his opponent would do? This is known as backward induction or backward reasoning, and is used in games where there is more than one outcome.  Sequential games are games that require a sequenced, or step by step response. One player moves first, and the other/s respond. Backward induction can also be used in these games. Sequential moves of players are illustrated through game tree, which is like a tree with branches (representing various decisions).

6.  Its not necessary that games only have two participants. In the real world there are more than two participants and many results of a specific game. One such game, relating to foreign policy, is shown below.

7.  Article: How Australia’s Perth is Battling a Water Crisis @ http://www.bbc.com/news/world-asia-27225396 http://www.bbc.com/news/world-asia-27225396