The three gardeners, Emily, Nina, and Talia, play a equential version of the street-garden game in which there are four distinguishable outcomes. For each player, the four outcomes are:
(i) player does not contribute, both of the others do (pleasant garden. saves cost of own contribution)
(ii) player contributes, and one or both of the others do (pleasant garden. incurs cost of contribution)
(iii) player does not contribute, only one or neither of the others does (sparse garden, saves cost of own contribution)
(iv) player contributes, but neither of the others does (sparse garden, incurs cost of own contribution) Of them, outcome i is the best (payoff 4) and outcome iv is the worst (payoff 1). If each player regards a pleasa n t garden more highly tha n her own contribution, then outcome ii gets payoff 3 and outcome iii gets payoff 2.
(a) Suppose that the gardeners play this game simultaneously, decid ing whether to contribute to the street garden without knowing wh at choices the others will make. Draw the three-player game table for this version of the game.
(b) Find all of the Nash equilibria in this game.
(c) How might this simultaneous version of the street-garden game be played out in reality?