This game, believed to have originated in the Far East, seems to be well known i

Question

This game, believed to have originated in the Far East, seems to be well known in many parts of the world. Two players simultaneously present a hand in one of three positions: open hand (paper) a closed fist (stone), or two open fingers (scissors) the payoff is 1 unit according to the rules:

Paper covers (beats) stone

Stone breaks (beats) scissors

Scissors cute (beats) paper

If both players present the same form, the payoff is zero.

A) Set up the payoff matrix for the game

B) Solve the game using the Simplex method

C) State the optimal row player's strategies, and column player's strategies

D) Determine the value of the game. Is this game fair?

SHOW ALL WORK please. Please show me how you got your answer - if you can upload a pic that would be great =) I will rate you LIFESAVER and first if you can answer and show me =]

Explanation / Answer

Preface Believe it or not, there was life before electronics took over our entertainment needs. Before computers, before television, even before radio, people, especially young people, found creative ways to entertain themselves and each other, and in the process learned very useful social skills. This is a small collection of games that were (could still be) played, with a very minimum of equipment or no equipment at all and required mainly the attentive co-operation of groups or small number of persons. They taught (tacitly, the main idea being fun) the necessity of rule compliance and reciprocity in social interactions, verbal and math skills, self-reliance, co-operation, and self-acceptance based on group acceptance. They fostered ingenuity in the invention of pleasurable activities and games based on personal discovery and interaction with others. They taught young people to function in a world of other real people rather than in some cold, unreal virtual reality. They were sometimes delightful then, and they are still usable, if not used, now, and the preservation of their memory is instructive in our understanding of our cultural roots and current cultural directions. GAMES REQUIRING NO EQUIPMENT ARM WRESTLING Two opponents sit across from each other over a table or some flat surface. Each places his or her right elbow on the table close to the right elbow of the opponent. They clasp right hands and on a given signal they press against the opponent's hand seeking to force him down so that the back of the forearm is flat on the table. The match is over and won when one of the contestants has his or her right wrist pressed to the table surface CHARADES (Lemonade) One person (or team of person) performs movements which suggests words or meanings to a group of observers who try to guess the words which names the meaning being hinted. Points mat be allotted for getting the right message in the least time. In the version called "lemonade" the person performing the hinting motions is addressed by the group (or its spokesperson) as if he or she were a traveler, by this patter: "Hello Stranger, what's your trade?" He or she replies: "Lemonade." The group then says "Show me some signs, if you are not afraid!" Then the body movements suggesting words begin. CLUB FIST A small group (five or six at most) begin with one player extending one clenched fist with the thumb extended upwards. The other players, in turn, grasp the extended thumb of the person preceding them, making a fist of their own hands and letting the next player grasp their raised thumb. When all are engaged they are joined in a stack of fist involving all their hands. When all hands are involved, the first player addresses the person with the tipmost first, saying "What have you got there?" The obligatory reply is "Club Fist!" -- to which the first speaker challenges: "Take it off or I will knock it off!" If the challenge fist owner declines to remove his hand, the challenger (using the bottom hand of the stack) tries to beat it loose. When the hand is removed the ritual is repeated until there is only one fist left. Then one (or all in unison) of the remaining players engage the last fist owner in this patter: "What have you got there?" "Bread and cheese." "Where's my part?" "The rat got it!" "Where is the rat?" "The cat got it!" "Where is the cat?" "The dog killed it!" "Where is the dog?" "The ox gored it!" "Where is the ox?" "The butcher killed it!" "Where is the butcher?" "The rope hung him!" "Where is the rope?" "The rat gnawed it." "Where is the rat?" "The cat got it!" "Where is the cat?" "Behind the door cracking chestnuts." The first one who smiles, laughs, or shows any teeth gets a rousing box (blow with fist) and fifteen pinches. All then endeavor to sit stone faced while causing others to smile. When one person's composure cracks all punch and pinch him or her. COUNTING OUT Counting rhymes, of which there were many and of many variations, were sometimes used by participants in games to determine who played key roles or who was first to start the action. One that is hard to forget is: "Wire Briar Limber Lock, Three geese in a flock One flew east and one flew west And one flew over the Coo Coo's nest." The performance and use of the counting rhymes (other than the pleasure of reciting them) was that the speaker would point at each of the objects or persons being potentially chosen as each word or syllable of the rhyme was pronounced. That person or object being pointed to when the last word or syllable was spoken was the chosen one.

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