A Dynamic Model of Conflict and Cooperation

A Dynamic Model of Conflict and Cooperation*

Wolfgang Eggert^     Jun-ichi Itaya+     Kazuo Mino§

July 9, 2008

Abstract

We introduce a common-pool contest into a continuous-time, differential game setting
to model the dynamic behavior of agents facing a trade-off between socially productive
activities and appropriation. We are able to identify multiple Markov perfect equilibrium
strategies that are nonlinear in a state space, thus leading the economy to a state where
‘partial cooperation’ occurs. We show that such cooperation can be seen as a response to
conflict. We also discuss the consequences of changes in the effectiveness of appropriation,
the number of contenders, and the rate of time preferences on contest equilibria.

Keywords: Conflict, Cooperation, Differential Game, Markov Perfect Equilibrium, Non-
linear Markov strategy

JEL classifications: D 74, L 11

* Earlier versions of the paper have been presented at the meeting of the Association for Public Economic
Theory in Beijin, the International Conference on Economic Theory in Kyoto, and a CESifo Area Conference
on Applied Microeconomics. We wish to thank Makoto Yano, David , and seminar participants and Herbert
Dawid for useful discussions and are indebted to the ifo Institute for Economic Research in Munich and the
University of Hokkaido for support. The second and third author also acknowledge financial support by Grant-
in-Aid for Scientific Research, Socienty for the Promotions of Science in Japan (#16530117 and #17530232).

^University of Paderborn, Warburgerstr. 100, 33098 Paderborn, Germany and ifo Institute for Economic
Research at the University of Munich. Tel: +49-5251-60-5002; E-mail: Wolfgang.Eggert@uni-paderborn.de

+ Graduate School of Economics and Business Admministration and CESifo, Hokkaido University, Sapporo,
060-0809, Japan. Tel:+81-11-706-2858; Fax:+81-11-706-4947; E-mail: itaya@econ.hokudai.ac.jp

^§Graduate School of Economics, Osaka University, Osaka 657-8501, Japan. Tel/Fax:+81-6-6850-5232; E-
mail: mino@econ.osaka-u.ac.jp

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