# Unbeatable Imitation

## Peter Dürsch

University of Heidelberg - Faculty of Economics and Social Studies

## Joerg Oechssler

University of Heidelberg - Alfred Weber Institute for Economics

## Burkhard C. Schipper

University of California, Davis - Department of Economics

November 10, 2011

Abstract:
We show that for many classes of symmetric two-player games, the simple decision rule "imitate if-better'' can hardly be beaten by any strategy. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that there is no strategy that can exploit imitation as a money pump. In particular, imitation is subject to a money pump if and only if the relative payoff function of the game is of the rock-scissors-paper variety. We also show that a sufficient condition for imitation not being subject to a money pump is that the relative payoff game is a generalized ordinal potential game or a quasiconcave game. Our results apply to many interesting examples of symmetric games including $2 \times 2$ games, Cournot duopoly, price competition, public goods games, common pool resource games, and minimum effort coordination games.

Number of Pages in PDF File: 18

Keywords: Imitate-the-best, learning, symmetric games, relative payoffs, zero-sum games, rock-paper-scissors, finite population ESS, generalized ordinal potential games, quasiconcave games

JEL Classification: C72, C73, D43

working papers series

#### Suggested Citation

Dürsch, Peter, Oechssler, Joerg and Schipper, Burkhard C., Unbeatable Imitation (November 10, 2011). Available at SSRN: http://ssrn.com/abstract=1556730 or http://dx.doi.org/10.2139/ssrn.1556730

#### Contact Information

##### Peter Dürsch
University of Heidelberg - Faculty of Economics and Social Studies ( email )
Grabengasse 14
Heidelberg, D-69117
Germany
##### Joerg Oechssler
University of Heidelberg - Alfred Weber Institute for Economics ( email )
Grabengasse 14
Heidelberg, D-69117
Germany
+49 6221 54 3548 (Phone)
+49 6221 54 3630 (Fax)
##### Burkhard C. Schipper (Contact Author)
University of California, Davis - Department of Economics ( email )
One Shields Drive
Davis, CA 95616-8578
United States
530-752-6142 (Phone)
530-752-9382 (Fax)