Play
One possible version of a centipede game could be played as follows:
Consider two players: Alice and Bob. Alice moves first. At the start of the game, Alice has two piles of coins in front of her: one pile contains 4 coins and the other pile contains 1 coin. Each player has two moves available: either "take" the larger pile of coins and give the smaller pile to the other player or "push" both piles across the table to the other player. Each time the piles of coins pass across the table, the quantity of coins in each pile doubles. For example, assume that Alice chooses to "push" the piles on her first move, handing the piles of 1 and 4 coins over to Bob, doubling them to 2 and 8. Bob could now use his first move to either "take" the pile of 8 coins and give 2 coins to Alice, or he can "push" the two piles back across the table again to Alice, again increasing the size of the piles to 4 and 16 coins. The game continues for a fixed number of rounds or until a player decides to end the game by pocketing a pile of coins.
The addition of coins is taken to be an externality, as it is not contributed by either player.
A second possible version of the centipede game is represented in the diagram above. In this version, passing the coins across the table is represented by a move of R (going across the row of the lattice, sometimes also represented by A for across) and pocketing the coins is a move D (down the lattice). The numbers 1 and 2 along the top of the diagram show the alternating decision-maker between two players denoted here as 1 and 2, and the numbers at the bottom of each branch show the payout for players 1 and 2 respectively.
Read more about this topic: Centipede Game (game Theory)
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