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 \noindent   
 September 30, 2009\\
 Eric Rasmusen, erasmuse@indiana.edu

 
\begin{center} {\bf   The Centipede Game   }
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Consider the perfect-information game in the figure below, adapted from Rosenthal (1981, JET). Players A and B are seated at a table, and Player A has two plates in front of him,  a big plate with one gold  coins and a littler plate with no gold coins. He can take the big plate and get the coin on it, leaving the little plate for Player B,  or he can push both plates across the table, in  which case the referee will  add one coin to each plate. In round 2, Player B can take the big plate  and its 2 coins, or push both plates across the table, the referee again adding one coin to each pile. This continues until  the 100th round, when if player B does not take the big plate and get 101 coins, leaving 99 for Player A, the referee splits the coins equally, each player getting 100 of them.

 In the unique subgame perfect equilibrium, each player follows the strategy of always $Take$. The equilibrium outcome is for Player A to $Take$ in round 1,  for payoffs of (2,0). Yet in experiments people do $Push$ for a while, to their benefit.     Palacios-Huerta  \& Volij (2009, AER) survey the theoretical and empirical  literature well. They found in their  6-round version of the Centipede Game  that chess players do tend to $Take$ early playing against each other, and Grandmasters {\it always}  choose $Take$ in the first round. Playing against non-chess-players, though, even chess players choose  $Push$ more. 

The lesson is that when games are iterated like this, common knowledge of the ability to do complicated inductive reasoning becomes very important to the result.  

 

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Palacios-Huerta, I. \& Volij, O. (2009)  ``Field Centipedes," American Economic Review 99(4):  1619--1635.


Rosenthal, R. (1981)  ``Games of Perfect Information, Predatory Pricing, and the Chain Store," Journal of Economic Theory 25:92--100.


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