Abstract
The proposal-making model is applied to the class of three-player/three-cake problems. The set of subgame perfect equilibria (SPEs) and the limit set of SPE payoffs as the risk of breakdown vanishes is characterized. The necessary and sufficient condition for uniqueness is derived. The results for the alternating offer model play an important role. The model always admits one stationary SPE and this equilibrium is related to a multilateral Nash solution. The stationary SPE is the coalition-proof SPE and the limit result differs from the result known for the model without risk of breakdown.
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