## Abstract

We study a dynamic game in which players can steal parts of a homogeneous and perfectly divisible pie from each other. The effectiveness of a player’s theft is a random function which is stochastically increasing in the share of the pie the agent currently owns. We show how the incentives to preempt or to follow the rivals change with the number of players involved in the game and investigate the conditions that lead to the occurrence of symmetric or asymmetric equilibria.

## Keywords

Stealing Stochastic games Optimal timing Pie allocation## Notes

### Acknowledgments

I thank an anonymous referee for very helpful comments that substantially improved the paper. I am also grateful to Pascal Courty, Dino Gerardi, Edoardo Grillo, Dorothea Kubler, Vilen Lipatov, Marco Mariotti, Ignacio Monzon, and Karl Schlag for useful suggestions and discussions. All remaining errors are my own.

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