APPLIED MACROECONOMICS

AdaTeachesAPPLIED MACROECONOMICS

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Game theory is_____the study of strategic decision making. the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.the analysis of competitive situations (or situations of conflict) using mathematical modelsGAME THEORY

economicspolitical sciencepsychologylogic biology

uSES

Players participants, each may be an individual, a group or organisation, a machine, and so on. Moves where a move is an action carried out during the game, including chance moves (when nature plays a hand) as in the toss of a coin.Enter a bid in an auction?Decide whether to end a strike?When to sell a stock?Decide how to vote?

ELEMENTS

3. Outcomes where an outcome is the result of the completion of one or more moves [e.g. game of chess may end in checkmate or a draw]4. Payoff an amount received for a given outcome. Do they care about some profit?Do they care about other players?Do they want to minimize cost?5. Rules-which specify the conditions for the players, moves, outcomes and payoffs.

In game theory, the strategic form (or normal form) is a way of describing a game using a matrix. The game is defined by exhibiting on each side of the matrix the different players (here players 1 and 2), each strategy or choice they can make (here strategies A and B) and sets of payoffs they will each receive for a given strategy (p1A,p2A ; p1A,p2B ; p1B,p2A ; p1B,p2B).Strategic Form

Columns are the decisions (called strategies) taken by player 1, rows are the strategies chosen by vendor 2. Each possible result of the game (called outcome) is situated in one cell of the matrix (identified by a unique strategy combination or profile).Outcomes are written as payoff-tuples (P1x, P2x) in units of expected utility. The first entry P1x of the outcome tuple is player 1s payoff, the second P2x is player 2s payoff.Conventions

The strategic form is usually the right description for simultaneous games, where both players choose simultaneously, as opposed to sequential games for which is better to describe the game using the extensive form (or tree form). Its worth mentioning that simultaneous games imply there is complete and imperfect information, and the rules of the game as well as each players payoffs are common knowledge.strategic form

Simultaneous games are those where decisions are simultaneous: both we and the other player choose at the same time. The simplest example of this is probably rock, paper, scissors. Complete information means that we know what we stand to win or lose: we know that rock beats scissors and that this will give us some form of utility (we might get to pick the plan for that evening or simply feel a warm glow of superiority). We also know that our opponent has this same information, this is, the rules of the game and each players payoffs are common knowledge. Simultaneous games

What this all means is that we only have one chance to get it right, but that we can play smart by knowing what our opponent will do and acting accordingly. An equilibrium is reached when both players will rationally make a decision that they have no reason to change: whatever else they do, they will only be worse off. Our situation can only be improved if our opponent chooses to do something else. These equilibria are known as Nash equilibria after John Nash, an economist from the early/mid 20th century. The most famous example of this is the prisoners dilemma.equilibria

Two suspects are arrested and charged with a crime. The police lack sufficient evidence to convict the suspects, unless at least one confesses. The police hold the suspects in separate cells and explain the consequences that will follow from the actions they could take. If neither confesses then both will be convicted of a minor offense and sentenced to one month in jail. If both confess then both will be sentenced to jail for six months. Finally, if one confesses but the other does not, then the confessor will be released immediately but the other will be sentenced to nine months in jailsix for the crime and a further three for obstructing justice.prisoners dilemma.

PRISONERS DILENMA

In this game, each player has two strategies available: confess and lie. The payoffs to the two players when a particular pair of strategies is chosen are given in the appropriate cell of the bi-matrix. By convention, the payoff to the so-called row player (here, Prisoner 1) is the first payoff given, followed by the payoff to the column player (here. Prisoner 2). Thus, if Prisoner 1 chooses Confess and Prisoner 2 chooses Lie, for example, then Prisoner 1 receives the payoff 0 (representing immediate release and Prisoner 2 receives the payoff -9 (representing nine months in jail) . STRATEGIES

Although we stated that in a stragetic-form game the players choose their strategies simultaneously, this does not imply that the parties necessarily act simultaneously: it suffices that each choose his or her action without knowledge of the others' choices, as would be the case here if the prisoners reached decisions at arbitrary times while in their separate cells.

BUNKS INTERROGATION TECHNIQUES

The normal-form representation of a game specifies: the players in the gamethe strategies available to each player, the payoff received by each player for each combination of strategies that could be chosen by the players. STRATEGIC-form representation

Players---We will often discuss an n-player game in which the players are numbered from 1 to n and an arbitrary player is called player i. Strategies----Let Si denote the set of strategies available to player i (called is strategy space), and let si, denote an arbitrary member of this set .Strategy si, is a member of the set of strategies Si.) Let (si , ... ,sn) denote a combination of strategies, one for each player, andPayoff---- let ui denote player i's payoff function: ui(si,...,sn) is the payoff to player i if the players choose the strategies (si,... ,sn)STRATEGIC-form representation

Players : N= {1,..n}Strategies for player i Sis=(s1,.,sn) S= S1 AnPayoff function of player i : ui : S Ru=(u1,.,un)

The normal-form representation of an n-player game specifies the players' strategy spaces S1,..., Sn and their payoff functions u1. Un. We denote this game by G = {S1,..., Sn; u1. Un}A GAME IN STRATEGIC FORM

Players: N= {1,,10000000}

Strategy set for player i Ai ={Revolt, Not }

Utility function for player iui(a)=1 if #{j: aj=Revolt}2000000} ui(a)=-1 if #{j: aj=Revolt}d a>d, bc, b