Cycles of Learning in the Centipede Game
Traditional game theoretic analysis often proposes the application of backward induction and subgame-perfection as models of rational behaviour in games with perfect information. However, there are many situations in which such application leads to counterinitiative results, casting doubts on the predictive power of theory itself. The Centipede Game, firstly, introduced by Rosenthal (1981), represents one of the critical cases and experimental evidence has been provided to show how people in laboratory behave in a manner which is a significatively different from what the theory expects. In our paper, we construct a dynamic model based on the Centipede Game. Our claim is that the source of these discrepancies between theory and experimental evidence may be explained by appealing to some form of bounded rationality in the players' reasoning. If this is the case, traditional game theoretical analysis could still accurately predict the players' behaviour, provided that they are given time enough to correctly perceive the strategic environment in which they operate. to do so, we provide conditions for convergence to the subgame-perfect equilibrium outcome for a broad class of continuous time evolutionary dynamics, defined as Aggregate Monotonic Selection dynamics(Samuelson and Zhang 1992). Moreover, by introducing a drift term in the dynamics, we show how the outcome of this learning process is intrinsically unstable, and how this instability is positively related with the length of the game.
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