“A game player would never prefer an outcome in which every player gets a little profit to an outcome in which he gets all the available profit.” Is this statement true or false? Explain why in one or...

“A game player would never prefer an outcome in which every player gets a little profit to an outcome in which he gets all the available profit.” Is this statement true or false? Explain why in one or two sentences.

You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations?

(a) There is a 50% chance that the game ends in a tie, but only a 10% chance that you win. (There is thus a 40% chance that you lose.)

(b) There is a 50–50 chance that you win or lose. There are no ties.

(c) There is an 80% chance that you lose, a 10% chance that you win, and a 10% chance that you tie.