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Table 4: three-player ranking game used in the proof of theorem 2 1. if action a j, 1 can be eliminated by some other action ak, 1 , then a j, 2 could at the same time be eliminated by ak, 2 , if ak, 2 has not been eliminated before. this particularly means that under non-iterated weak dominance, a j, 1 can be eliminated if and only if a j, 2 can be eliminated. 2. every pair of a non-eliminable action a j and another action ak satisfies one of two conditions. either, a j is as least as good as ak at any index i.e., action of the other player ; . or, a j is strictly worse than ak at some index, and strictly better than ak at another index. assume there exists a sequence of eliminations that finally eliminates e in . then, by property 1, an arbitrary element of the sequence where a j eliminates ak , can be mapped to a pair of successive eliminations in where b j, 1 eliminates ak, 1 and a j, 2 eliminates ak, 2 . this results in a sequence of eliminations in ending in the elimination of both e1 and e2 , e's corresponding actions in . conversely, assume that e cannot be eliminated in , and consider a sequence of eliminations in leading to the elimination of e1 and then e2 . we will argue that such a sequence cannot exist. since e is non-eliminable, property 2 holds for j e and any action a1 , restricted to the actions of player 2 that have not been eliminated before e2 . if least as good j as a1 any remaining action ak , then, by construction of 2 the payoff mapping and restricted to the remaining actions of , one of e1 or least as good as any other action of player 1. that means they cannot both be eliminated, a contradiction. k hence, there must be a pair of actions a2 and a such that 2 j k and strictly worse than a j at strictly better than a1 at a2 without loss of generality, we assume that a is the only 2 index where e is strictly worse. then, for both e1 and e2 to be eliminable, one of a, 1 and a, 2 must have been elimi2 2 nated before. observe that this elimination further requires 1 r 2 the other hand, it must not be possible to elimr1 1 , 1 inate both a2 and a, 2 , since otherwise, by property 1, a 2 could be eliminated in , whereafter a1 could eliminate e. we thus get dominance according to property 2, similar to the one for e described above. hence, there again has to be an action e such that exactly one of am, 1 and am, 2 has 1 been eliminated and the other one could not have been eliminated ; . this condition can be traced backwards through the sequence of eliminations that lead to the elimination of e2 . the first elimination in this sequence, however, is in terms of non-iterated dominance, and by property 1 there can be no pair of actions such that exactly one of them can be eliminated. this is a contradiction. we are now ready to state the main result of this section. theorem 2 deciding whether a ranking game with more than two players is solvable by iterated weak dominance is np-complete. when there are only two players, this can be decided in polynomial time. proof: membership in np is immediate. we can simply guess a sequence of eliminations and then verify that this sequence is valid and leaves only one action per player. for hardness, we reduce iwd-pair-eliminable for ranking games with three players, where one of the players has only one action, to iwd-solvable for ranking games with three players. therefore, an instance of the former class is mapped to an instance of the latter as follows: all players' actions from are also part of the new instance , including the two actions e1 and e2 to be eliminated. the payoffs i.e., rankings ; for the corresponding outcomes remain the same. 1 we further add two additional actions a1 and a2 for player 1 and a2 for player 2 and one action for 1, two actions a2 2 player 3, who now has actions a1 and a2 . the rankings 3 for the outcomes induced by these new actions are given in table 4. we claim that, for arbitrary values of ri2 , e1 and e2 can be eliminated in if and only if can be solved by means of iterated weak dominance. assume iwd-pair-eliminable for has a solution. then, the same sequence of eliminations that eliminates both e1 and e2 can also be executed in , because player 1 is i ranked equally in all rows of at a2 , and player 2 is ranked i for i 1, 2, 3. as soon equally in all columns of at a1 and e2 have been eliminated, let a2 be eliminated by 2 a1 , which is strictly preferred at a2 , a1 ; and ranks player 2 1.

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Four children will join mrs. ahearn in her office for a picnic lunch that they will have all planned together. they will finish up their picnic with a fun board game. the top 4 bidders will each win this outing.

To create such images and thereby soften the impact of future shock, we must begin by making speculation about the future respectable. instead of deriding the "crystal-ball gazer, " we need to encourage people, from childhood on, to speculate freely, even fancifully, not merely about what next week holds in store for them but about what the next generation holds in store for the entire human race. we offer our children courses in history; why not also courses in "future, " courses in which the possibilities and probabilities of the future are systematically explored, exactly as we now explore the social system of the romans or the rise of the feudal manor? robert jungk, one of europe's leading futurist-philosophers, has said: "nowadays almost exclusive stress is laid on learning what has happened and has been done. tomorrow . at least one third of all lectures and exercises ought to be concerned with scientific, technical, artistic and philosophical work in progress, anticipated crises and possible future answers to these challenges." we do not have a literature of the future for use in these courses, but we do have literature about the future, consisting not only of the great utopias but also of contemporary science fiction. science fiction is held in low regard as a branch of literature, and perhaps it deserves this critical contempt. but if we view it as a kind of sociology of the future, rather than as literature, science fiction has immense value as a mind-stretching force for the creation of the habit of anticipation. our children should be studying arthur c. clarke, william tenn, robert heinlein, ray bradbury and robert sheckley, not because these writers can tell them about rocket ships and time machines but, more important, because they can lead young minds through an imaginative exploration of the jungle of political, social, psychological, and ethical issues that will confront these children as adults. science fiction should be required reading for future i. but students should not only read. various games have been designed to educate young people and adults about future possibilities and probabilities. future, a game distributed by kaiser aluminum and chemical corporation on the occasion of its twentieth anniversary, introduces players to various technological and social alternatives of the future, and forces them to choose among them. it reveals how technological and social events are linked to one another, encourages the player to think in probabilistic terms, and, with various modifications, can help clarify the role of values in decision-making. at cornell, professor jose villegas of the department of design and environmental analysis, has, with the aid of a group of students, created a number of games having to do with housing and community action in the future. another game developed under his direction is devoted to elucidating the ways in which technology and values will interact in the world of tomorrow. with younger children, other exercises are possible. to sharpen the individual's futurefocused role image, students can be asked to write their own "future autobiographies" in which they picture themselves five, ten or twenty years in the future. by submitting these to class discussion, by comparing different assumptions in them, contradictions in the child's own projections can be identified and examined. at a time when the self is being broken into successive selves, this technique can be used to provide continuity for the individual. if children at fifteen, for example, are given the future autobiographies they themselves wrote at age twelve, they can see how maturation has altered their own images of the future. they can be helped to understand how their values, talents, skills, and knowledge have shaped their own possibilities. students, asked to imagine themselves several years hence, might be reminded that their brothers, parents, and friends will also be older, and asked to imagine the "important others" in their lives as they will be. such exercises, linked with the study of probability and simple methods of prediction that can be used in one's personal life, can delineate and modify each individual's conception.

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I used to watch my friends play and realized that i understood the flow of the game and seemed to ask the right questions. Declaration of emergency department of revenue office of charitable gaming progressive pull-tabs lac 42: i.1775 ; the department of revenue, office of charitable gaming, is exercising the provisions of the administrative procedure act, r.s. 49: 953 b ; , to adopt this emergency rule to implement the provisions of r.s. 4: 725.1 to provide guidance regarding progressive pull-tabs for organizations licensed to hold, operate, or conduct charitable games of chance. act 736 of the 2003 regular session of the louisiana legislature enacted r.s. 4: 725.1 to authorize progressive pull-tabs during sessions licensed by the office of charitable gaming. the act established the jackpot limit and the contribution per deal of pull-tabs for the progressive jackpot. the office is adopting this rule in order to establish guidelines related to progressive pulltabs and to require that certain documentation and information be maintained and submitted to the office. this emergency rule is effective august 15, 2003, and will remain in effect for the maximum period allowed under the administrative procedure act or until adoption of the permanent rule. title 42 louisiana gaming part i. charitable bingo, keno, raffle subpart 1. bingo pull tabs chapter 17. charitable bingo, keno and raffle subchapter e. 1775. progressive pull-tabs a. each progressive pull-tab jackpot must be established only through the play of deals bearing a licensed manufacturer's form number. each jackpot must use the identical form number for each deal contributing to the prize jackpot. pull-tab deals must meet all requirements as set forth in r.s. 4: 725 and 725.1 and in lac 42: i.1715, 1719, 1771, and 1773. b. accountability. organizations participating in a progressive pull-tab jackpot must maintain all required forms as prescribed by the office. 1. for each progressive pull-tab jackpot, the organization must maintain, at a minimum, the following records for a period of three years from the date that the progressive game prize was awarded or the game was considered closed: a. date the progressive jackpot started; b. method or rules of determining a potential jackpot winner; c. method or rules of determining how a player wins the jackpot; d. dollar amount of contribution into the jackpot per deal; e. dollar amount of the jackpot cap; f. accumulated jackpot totals including any backup jackpots; g. serial number and date sold of the pull tab deals contributing to the jackpot; and h. name and identification of the winner with the date and amount won. 2. the organization must maintain a separate non-interest bearing charitable gaming progressive pull-tab checking account. all checks on this account must have preprinted consecutive numbers and have the words "progressive pull-tab account" and the licensee's state charitable gaming license number printed on the face of the checks. all progressive jackpot winners, regardless of the amount, must be paid by check written from this separate progressive pull-tab account. checks made payable to cash are prohibited. 3. the amount of contribution into the jackpot per deal must be deposited into this progressive pull-tab account no later than the next banking day following the sale of a complete deal. 4. the organization must maintain a minimum balance in their progressive pull-tab account that is at least 0 greater than the advertised accumulated jackpot total at the beginning of the.