(Extensions of BoS with vNM preferences) Construct a table of payoffs for a strategic game with…

(Extensions of BoS with vNM preferences) Construct a table of payoffs for a strategic game with vNM preferences in which the players’ preferences over deterministic outcomes are the same as they are in BoS and their preferences over lotteries satisfy the following condition: each player is indifferent between going to her less preferred concert in the company of the other player and the lottery in which with probability 1 2 she and the other player go to different concerts and with probability 1 2 they both go to her more preferred concert. Do the same in the case that each player is indifferent between going to her less preferred concert in the company of the other player and the lottery in which with probability 3 4 she and the other player go to different concerts and with probability 1 4 they both go to her more preferred concert. (In each case set each player’s payoff to the outcome that she least prefers equal to 0 and her payoff to the outcome that she most prefers equal to 2.) Despite the importance of saying how the numbers in a payoff table should be interpreted, users of game theory sometimes fail to make the interpretation clear. When interpreting discussions of Nash equilibrium in the literature, a reasonably safe assumption is that if the players are not allowed to choose their actions randomly then the numbers in payoff tables are payoffs that represent the players’ ordinal preferences, whereas if the players are allowed to randomize then the numbers are payoffs whose expected values represent the players’ preferences regarding lotteries over outcomes.