2
$\begingroup$

Two players, A and B, are each given 10000 dollars. They'll play a 10 round game. In each round both have to gamble some of this money (can be zero); in the 10th round, they both must use all their remaining money. The winner of each round is the one who gambles less. He gets both sums gambled in that round; these winnings are put away and not added to the money available for gambling. The winner of the game is the one who won more money.

What is the best strategy to win this kind of game?

Example for a 3 round-game: round 1, A gambles 5000, B gambles 4000 --> B gets 9000. Round 2, A 5000, B 4000 --> B gets 9000. Round 3, A 0, B 2000 --> A gets 2000, B wins getting 18000.

This seems like a zero-sum game theory, but there's something different, any help will be appreciated.

  • 0
    Here's the example: http://en.wikipedia.org/wiki/Example_of_a_game_without_a_value. Apparently the seminal paper about this is [The Existence of Equilibrium in Discontinuous Economic Games](http://web.mit.edu/~nstein/Public/Game%20Theory%20Papers/Dasgupta%20+%20Maskin%20-%20The%20Existence%20of%20Eqilibrium%20in%20Discontinuous%20Economic%20Games,%20I:%20Theory.pdf) by Partha Dasgupta and Eric Maskin.2011-12-14

1 Answers 1

2

You don't say what happens in case of a tie: I'll suppose they both keep their money.

If they both must gamble all their money in the 10th round, the winner will be the one with the least money after the 9th round. So in the 9th round, the players are trying to lose all their money: obviously they will gamble all their money. The winner is the one with the most money after the 8th round. In the 8th round, the players want to get as much money as possible, so the optimal strategy is to gamble 0 and win whatever your opponent is foolish enough to gamble. Similarly in each of rounds 1 to 7, the optimal strategy is to gamble 0.

  • 0
    To the downvoter: This is a correct solution to the game one might easily have taken the initial question to describe.2011-12-14