## What should be a good playing strategy in this 2-player simultaneous game?

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This is a bot making problem from here. I am detailing the problem.

The picture above shows the initial configuration of the game. P1 represents player1 and P2 represents player2. A scotch bottle is kept(initially) at the position #5 on the number line. Both players start with 100 dollars in hand. Note that players don't move, only the bottle moves.

Rules of the game:

1. The first player makes a secret bid followed by a secret bid by the second player.
2. The bottle moves one position closer to the winning bidder.
3. In case of drawn bid, the winner is the player, who has the draw advantage.
4. Draw advantage alternates between the two player, that is, the first draw is won by the first player, the second draw if it occurs is won by the second player and so on.
5. The winning bid is deducted from the player's hand, the loser keeps his bid.
6. The bottle moves one position closer to the winning bidder.
7. Each bid must be greater than 0 dollar. In the case when there's no money left, the player has no choice but to bid 0 dollar. Only integral bids are allowed.

The player who gets the bottle wins. If no one gets it, the game ends in a draw.

Both the players,thus,have complete knowledge of the history of biddings of each other, and the location of bottle at the current time.

So far, i know this is an instance of poorman bidding games. I have used some strategies like I am intentionally losing some bids and let the opponent use his money, in a hope that difference of money increases to the point of allowing for the emergence of a winning strategy. Also, i pull stronger the bottle as it goes further. This isn't performing well with other bots.

What should be the strategy of a bot playing this game?

1I wonder how different the game would be if it were simplified by removing rules 3 and 4, which seem to be an unnecessary complication. – Ray Butterworth – 2020-04-25T13:38:36.227

Yes, that is a thing. But ,I guess, that is one way to eliminate the possibility of an infinite game. Another way would have been to deduct the drawn amount from both of them and let the bottle unmoved. – Arpit Gupta – 2020-04-25T15:25:32.090

did you mean integer bids? – carlo – 2020-06-01T17:56:36.293