Each player in a game faces a choice among two or more possiblestrategies. A strategy is a predetermined ‘programme ofplay’ that tells her what actions to take in response toevery possible strategy other players might use. Thesignificance of the italicized phrase here will become clear when wetake up some sample games below.
A crucial aspect of the specification of a game involves theinformation that players have when they choose strategies. Thesimplest games (from the perspective of logical structure) are thosein which agents have perfect information, meaning that atevery point where each agent's strategy tells her to take an action,she knows everything that has happened in the game up to that point. Aboard-game of sequential moves in which both players watchall the action (and know the rules in common), such as chess, is aninstance of such a game. By contrast, the example of thebridge-crossing game from Section 1 above illustrates a game ofimperfect information, since the fugitive must choose abridge to cross without knowing the bridge at which the pursuer haschosen to wait, and the pursuer similarly makes her decision inignorance of the choices of her quarry. Since game theory is abouteconomically rational action given the strategically significant actions of others,it should not surprise you to be told that what agents in games believe,or fail to believe, about each others' actions makes a considerabledifference to the logic of our analyses, as we will see.
Conventions on standards of evidence and scientific rationality, thetopics from philosophy of science that set up the context for Lewis'sanalysis, are likely to be of the Pareto-rankable character. Whilevarious arrangements might be NE in the social game of science, asfollowers of Thomas Kuhn like to remind us, it is highly improbablethat all of these lie on a single Pareto-indifference curve. Thesethemes, strongly represented in contemporary epistemology, philosophyof science and philosophy of language, are all at least implicitapplications of game theory. (The reader can find a broad sample ofapplications, and references to the large literature, in .)
present the followingexample of a real-life coordination game in which the NE are notPareto-indifferent, but the Pareto-inferior NE is more frequentlyobserved. In a city, drivers must coordinate on one of two NE withrespect to their behaviour at traffic lights. Either all must followthe strategy of rushing to try to race through lights that turn yellow(or amber) and pausing before proceeding when red lights shift togreen, or all must follow the strategy of slowing down on yellows andjumping immediately off on shifts to green. Both patterns are NE, inthat once a community has coordinated on one of them then noindividual has an incentive to deviate: those who slow down on yellowswhile others are rushing them will get rear-ended, while those whorush yellows in the other equilibrium will risk collision with thosewho jump off straightaway on greens. Therefore, once a city's trafficpattern settles on one of these equilibria it will tend to staythere. And, indeed, these are the two patterns that are observed inthe world's cities. However, the two equilibria are notPareto-indifferent, since the second NE allows more cars to turn lefton each cycle in a left-hand-drive jurisdiction, and right on eachcycle in a right-hand jurisdiction, which reduces the main cause ofbottlenecks in urban road networks and allows all drivers to expectgreater efficiency in getting about. Unfortunately, for reasons aboutwhich we can only speculate pending further empirical work andanalysis, far more cities are locked onto the Pareto-inferior NE thanon the Pareto-superior one.
Real, complex, social and political dramas are seldomstraightforward instantiations of simple games such as PDs. offers an analysis of two tragically real political cases, theYugoslavian civil war of 1991–95, and the 1994 Rwandan genocide, asPDs that were nested inside coordination games.
This paper will seek to answer if a balanced plant works, the explanation of the changes in inventory, what is a constraint and did it change in the game, how in the game can the constraint be relieved, what adjustments were made in the game, how did those adjustments affect inventory and throughput and if the adjustments were successful....
These quick definitions may not mean very much to you until you followthem being put to use in our analyses of trees below. It will probablybe best if you scroll back and forth between them and the examples aswe work through them. By the time you understand each example, you'llfind the concepts and their definitions natural and intuitive.
There are also ongoing innovations in game theoretic applications in political science that look very promising. One such innovation is to incorporate insights from psychological research in specifications of utilities for players and their ways of processing information. Another innovation is to allow players in a model to make various errors. Often referred to as bounded rationality models, these models are often made to allow better reflection of reality in a model.
This research paper provides a gentle introduction to game theory. As a tool for researchers to deduce logically consistent hypotheses, game theory has been widely used in many different social science contexts. Basic terms and elements of game theory and the most important solution concepts are introduced with some sample applications. Then three representative examples in political science are provided in the latter part of the research paper. One can see that game theoretic models can be used to study many interesting political phenomena, including legislative bargaining in American politics, decisions to go to war in international relations, and formation of coalition governments in comparative politics. For its relatively short history in political science, the influence of game theory on the ways in which researchers approach research questions has been substantial.
Look first at each of the terminal nodes (those along the bottom).These represent possible outcomes. Each is identified with anassignment of payoffs, just as in the strategic-form game, with Player I'spayoff appearing first in each set and Player II's appearing second. Each ofthe structures descending from the nodes 1, 2 and 3 respectively is asubgame. We begin our backward-induction analysis—using atechnique called Zermelo's algorithm—with the sub-gamesthat arise last in the sequence of play. If the subgame descendingfrom node 3 is played, then Player II will face a choice between apayoff of 4 and a payoff of 3. (Consult the second number,representing her payoff, in each set at a terminal node descendingfrom node 3.) II earns her higher payoff by playing D. We maytherefore replace the entire subgame with an assignment of the payoff(0,4) directly to node 3, since this is the outcome that will berealized if the game reaches that node. Now consider the subgamedescending from node 2. Here, II faces a choice between a payoff of 2and one of 0. She obtains her higher payoff, 2, by playing D. We maytherefore assign the payoff (2,2) directly to node 2. Now we move tothe subgame descending from node 1. (This subgame is, of course,identical to the whole game; all games are subgames of themselves.)Player I now faces a choice between outcomes (2,2) and(0,4). Consulting the first numbers in each of these sets, he seesthat he gets his higher payoff—2—by playing D. D is, ofcourse, the option of confessing. So Player I confesses, and then Player IIalso confesses, yielding the same outcome as in thestrategic-form representation.
We have thus seen that in the case of the Prisoner's Dilemma, thesimultaneous and sequential versions yield the same outcome. This willoften not be true of other games, however. Furthermore, only finite extensive-form(sequential) games of perfect information can be solved usingZermelo's algorithm.
Solving the game is complicated but logically straightforward since one needs only to follow the backward induction methods presented previously. In the equilibrium, it will always be the case that the majority party, if one exists, forms a government by itself, and if the party with the highest number of seats does not enjoy a majority, then the parties with the highest and the lowest number of seats form the governing coalition. This is because the party with the highest number of seats finds it cheaper to offer a coalition to the party with the lowest number of seats.