A first experimental test of multilevel game theory: the PD case

Abstract

The prisoner's dilemma (PD) is played by two players in each of two groups. The two groups compete for an external prize whose allocation is determined by the degree of within-group coordination. The experimental evidence supports the predictions of multilevel game theory well.

Acknowledgements

We thank Ivan Otenko for expert programming of the experiment and help in running the experimental sessions, and Werner Gueth, Peter Katuscak and participants at the GEW Conference on Experimental Game Theory, October 14–16, 2004, in Prague, Czech Republic, for useful comments.

Notes

¹ Bornstein and Rapoport (1988) have also performed experimental research, accounting for social psychological phenomena such as preplay communication, and showing that intergroup competition may enhance cooperation.

² See Hausken (2005) and Hausken and Cressman (2004), and the references therein.

³ An MNE must be, for each player, a best reply against itself with respect to alternative strategies that may have other players deviate as well, in contrast to the Nash equilibrium (NE) for conventional games where simultaneous deviations by more than one player are not considered. Although every pure or mixed MNE must give the same outcome as an NE of the extensive form representation, an NE is not necessarily an MNE. An MNE need not exist in pure or mixed strategies and, if it does, it may not be unique. In the former case, the multilevel structure is considered unmaintainable.

⁴ Two cooperators in one group share the entire prize when there is one cooperator in the other group. With allocation proportional to the number of cooperators in each group, indifference between cooperation and defection occurs when P = 12 (Hausken, 1995, p. 476).

⁵ According to the official conversion rate 100 koruns are about $4. In terms of real purchasing power it is about twice as much. E.g. a large glass of beer is <$1 in a neighbourhood pub. Thus, our subjects faced an interactive choice task with relevant pecuniary consequences.