Two players independently and simultaneously decide how much to donate to a charity. Each has a budget of Rs 200. Whenever the charity receives at least Rs 100 in aggregate, each player enjoys a payoff equivalent to Rs 60 (they are somewhat altruistic). Additional aggregate donation above Rs 100 brings no extra payoff. If the first player donates Rs and the second donates Rs , the first player's payoff is if , and if . Which of the following is true?
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Two players independently and simultaneously decide how much to donate to a charity. Each has a budget of Rs 200. Whenever the charity receives at least Rs 100 in aggregate, each player enjoys a payoff equivalent to Rs 60 (they are somewhat altruistic). Additional aggregate donation above Rs 100 brings no extra payoff. If the first player donates Rs x and the second donates Rs y, the first player's payoff is [(200 - x) + 60] if (x + y) ≥ 100, and (200 - x) if (x + y) < 100. Which of the following is true? (A) This game has no Nash equilibrium in pure strategies (B) This game has only one Nash equilibrium in pure strategies (C) This game has many Nash equilibria in pure strategies, where the aggregate donation is less than 100 (D) This game has many Nash equilibria in pure strategies, where the aggregate donation is Rs 100
Also written as: Two players independently and simultaneously decide how much to donate to a charity. Each has a budget of Rs 200. Whenever the charity receives at least Rs 100 in aggregate, each player enjoys a payoff equivalent to Rs 60 (they are somewhat altruistic). Additional aggregate donation above Rs 100 brings no extra payoff. If the first player donates Rs x and the second donates Rs y, the first player's payoff is [(200 - x) + 60] if (x + y) >= 100, and (200 - x) if (x + y) < 100. Which of the following is true?
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This question is on Applied games: public goods, voting and location, part of Game theory and strategic behaviour in Game Theory.
Strategic models of provision, voting, bargaining and where to locate.
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Question from the DSE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.