ࡱ> KMJy hbjbjEE 4B''hNN|55555Y[[[[[[bf[[55pv55YY5;jE0,j.jjD[[jN W: TEST 1 STUDY GUIDE Im going to kick off the guide with an explanation of Nash equilibriums (very important concept for the exam!). Ill follow it with a list of topics that you will want to cover in your studies. NASH EQUILIBRIUMS: One of the most important concepts to grasp is how to find Nash equilibriums in the 2x2 games weve reviewed. Remember the definition: you have a Nash equilibrium when neither player has an incentive to change strategies. One effective way to go about this is to think about the players in terms of rows and columns. On the left of the matrix, we have the Row player, who has two strategies to choose from: Row Player Strat1 Strat2 And at the top we have the column player who also has two strategies to choose from: Column Player Strat1 Strat2  The strategies are what the two players choose. They attempt to choose strategies that maximize their utility (the outcome). In other words, they try to get the highest number they can. But, of course, what number they get is dependent on the choice the other player makes. We find the results of those choices within the cells. A Nash Equilibrium is where neither player has an incentive to switch to the other strategy, given the choice of the other player. An Example: Column Player Strat1 Strat2 10,101,-2-2,1-1,-1Row Player Strat1 Strat2 NOTE: the row players utilities always come IN FRONT of the comma in the cell, while the column players utilities are behind the comma in the cell. So, in the bottom left cell we see -2,1so we know that the row players utility from the BL cell is -2 and the column players utility from the BL cell is 1. In this example, we can see there isnt much of a game. Both players get their maximum utilities by choosing strategy 1. There is no incentive to choose strategy 2. But this should help us see how Nash Equilibriums work. One of the easiest ways to identify Nash Equilibriums is to go from cell to cell and check to see if either player has an incentive to move to the other strategy. If neither player does, then it is a Nash Equilibrium. We start in the TL corner. Does the Row Player have an incentive to switch from strategy 1 to strategy 2? (NOTE: Ive removed all the other utilities below so you can see what were talking about.) Column Player Strat1 Strat2 10,xx,x-2,xx,xRow Player Strat1 Strat2 No. If the Row Player switches to strategy 2, given that the column player is playing strategy 1, then he goes from 10 (in the top left cell) to -2 (in the bottom left cell). A loss of utility. The Row player has no incentive to move. OK, but Nash Equilibriums require that BOTH players have no incentive to move. So we check the column players utility. Column Player Strat1 Strat2 x,10x,-2x,xx,xRow Player Strat1 Strat2 In the TL cell, we see that it is the same as it is for the Row player. If the column player switches from strategy 1 to strategy 2, she too will lose in utility: going from 10 to the -2 in the TR (top right) cell. So, since neither player has an incentive to shift, weve found a Nash equilibrium. The TL cell contains a Nash equilibrium. Of course, our task isnt finished by just checking one cell. There can be more than one Nash equilibrium. So we have to check each cell to see if a player has an incentive to move. Column Player Strat1 Strat2 x,x1,xx,x-1,xRow Player Strat1 Strat2 In the TR cell, we see that the Row player does not have an incentive to move. 1 is greater than -1. OK, but what about the Column player? Ah, the Column player DOES have an incentive to move. Column Player Strat1 Strat2 x,10x,-2x,xx,xRow Player Strat1 Strat2 The utility for strategy 2 that the column player gets when the Row player chooses strategy 1 is LOWER than the utility the column player gets from strategy 1. The column player has an incentive to move. She would shift strategies from strategy 2 to strategy 1. So the TR cell does NOT contain a Nash equilibrium. We would continue this same method for the BR and the BL cells (neither of which contain Nash equilibriums). Once weve done that, we can say how many Nash equilibriums are in the game and in what cell they are located. TOPICS FOR EXAM (remember, these are points of emphasis. The below list is NOT comprehensive!) The Road Building Game. This is covered in the K&J book in the Federalism chapter. Be sure you understand how the road building game works, how transaction and conformity costs relate to federalism decisions, etc. It is very important you understand this. Theories on American Politics. (i.e. pluralism, elite theory, etc.) Virginia Plan v. New Jersey Plan Philosophical foundations of the Constitution (i.e. sources & principles; especially Locke) Liberalism, Representation, Democracy (and historical roots; i.e. Greeks, etc.) Constitutional Supremacy (i.e. in relation to state constitutions, supremacy clause) Principles of Game Theory (transaction costs, public goods, interpreting games, free rider, prisoners dilemma etc.) Articles of Confederation (defects of, Shays Rebellion, reasons for new Constitution, etc.) Sub fields of Political Science Types of Government (federalism, confederalism, etc.) Shared Powers, Separate Institutions Enumerated vs. Implied powers in the Constitution The 10th Amendment (i.e. elastic clause) Federalists 10 & 51 (i.e. Madison, faction, the legislature) Block Grants GOOD LUCK! 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