On Markovian Cake Sharing Problems
AbstractPure strategy Markov perfect equilibria (MPE) in dynamic cake sharing problems are analyzed. Each player chooses under perfect information how much to eat from the current cake and how much to leave to the next period. The left over cake grows according to a given growth function. With linear utilities and strictly concave increasing growth function the only symmetric equilibrium with continuous strategies is the trivial equilibrium in which a player eats the whole cake whenever it is his turn to move. This is quite different than in the corresponding single person decision problem (or at a social optimum) where the cake grows from small initial values towards the steady state. A non-trivial equilibrium with a positive steady state exist in the game. In such an equilibrium strategies cannot be continuous. When utilities are concave and the growth function is linear, a nontrivial MPE with a positive steady state may not exist.
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Bibliographic InfoPaper provided by Aboa Centre for Economics in its series Discussion Papers with number 72.
Date of creation: Mar 2012
Date of revision:
common pool resources; dynamic cake sharing; Markov perfect equilibrium;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D92 - Microeconomics - - Intertemporal Choice - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-05-02 (All new papers)
- NEP-GTH-2012-05-02 (Game Theory)
- NEP-HPE-2012-05-02 (History & Philosophy of Economics)
- NEP-MIC-2012-05-02 (Microeconomics)
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- Marco Battaglini & Salvatore Nunnari & Thomas Palfrey, 2012. "The Free Rider Problem: a Dynamic Analysis," NBER Working Papers 17926, National Bureau of Economic Research, Inc.
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